WEBVTT 00:00:00.000 --> 00:00:02.435 align:middle line:90% [SQUEAKING] 00:00:02.435 --> 00:00:04.870 align:middle line:90% [RUSTLING] 00:00:04.870 --> 00:00:07.305 align:middle line:90% [CLICKING] 00:00:07.305 --> 00:00:11.210 align:middle line:90% 00:00:11.210 --> 00:00:15.150 align:middle line:84% ANA BELL: All right, so let's begin today's lecture. 00:00:15.150 --> 00:00:19.490 align:middle line:84% We have only two lectures left, this one and next Monday. 00:00:19.490 --> 00:00:21.560 align:middle line:84% I realized that there are no more 00:00:21.560 --> 00:00:23.340 align:middle line:90% deliverables for this class. 00:00:23.340 --> 00:00:26.390 align:middle line:84% No more quizzes after tonight, no more P sets. 00:00:26.390 --> 00:00:28.670 align:middle line:84% So I do appreciate you coming to these lectures. 00:00:28.670 --> 00:00:32.360 align:middle line:84% They're intended to be a little bit more fun. 00:00:32.360 --> 00:00:33.410 align:middle line:90% No need to take notes. 00:00:33.410 --> 00:00:35.690 align:middle line:84% Just kind of sit back and enjoy the content. 00:00:35.690 --> 00:00:40.310 align:middle line:84% Today, we're going to be talking about a library in Python that 00:00:40.310 --> 00:00:41.540 align:middle line:90% can help you do plotting. 00:00:41.540 --> 00:00:43.945 align:middle line:84% And the reason why we talk about this plotting library as 00:00:43.945 --> 00:00:46.070 align:middle line:84% opposed to something else that's maybe more machine 00:00:46.070 --> 00:00:48.680 align:middle line:84% learning or something else like that is because 00:00:48.680 --> 00:00:50.420 align:middle line:84% at one point or another, if you decide 00:00:50.420 --> 00:00:54.470 align:middle line:84% to take any other course that kind of builds upon this intro 00:00:54.470 --> 00:00:57.680 align:middle line:84% course, you'll probably want to create some graphs 00:00:57.680 --> 00:00:59.570 align:middle line:90% or visualize something. 00:00:59.570 --> 00:01:01.400 align:middle line:84% Even if you do a UROP, you'll probably 00:01:01.400 --> 00:01:03.540 align:middle line:84% have to visualize some sort of data. 00:01:03.540 --> 00:01:07.490 align:middle line:84% And it's a really nice next step to show you 00:01:07.490 --> 00:01:09.660 align:middle line:84% how to use a library that already exists. 00:01:09.660 --> 00:01:11.400 align:middle line:84% So somebody already put in the work 00:01:11.400 --> 00:01:14.440 align:middle line:84% in creating this library that can plot things for us. 00:01:14.440 --> 00:01:17.050 align:middle line:90% So let's just try to use it. 00:01:17.050 --> 00:01:19.710 align:middle line:84% And so it's just a really, really nice way for us 00:01:19.710 --> 00:01:25.930 align:middle line:84% to wrap up the course by showing you this visualization library. 00:01:25.930 --> 00:01:28.230 align:middle line:84% So we're going to-- the library we're 00:01:28.230 --> 00:01:31.320 align:middle line:84% going to do to use is called matplotlib. 00:01:31.320 --> 00:01:34.980 align:middle line:84% And it's the most basic plotting visualization library 00:01:34.980 --> 00:01:36.240 align:middle line:90% that we can have. 00:01:36.240 --> 00:01:38.730 align:middle line:84% And the way that we bring it into our code, 00:01:38.730 --> 00:01:40.590 align:middle line:84% just like we have in the past few lectures, 00:01:40.590 --> 00:01:43.080 align:middle line:90% is with this import statement. 00:01:43.080 --> 00:01:47.580 align:middle line:84% And the actual file that comes into our-- 00:01:47.580 --> 00:01:49.080 align:middle line:84% that we would bring into our program 00:01:49.080 --> 00:01:51.570 align:middle line:90% is called matplotlib.pyplot. 00:01:51.570 --> 00:01:53.430 align:middle line:90% Now, that's kind of a mouthful. 00:01:53.430 --> 00:01:56.460 align:middle line:84% And a lot of times when we want to use this-- 00:01:56.460 --> 00:01:58.530 align:middle line:84% or when we want to use this library, 00:01:58.530 --> 00:02:02.610 align:middle line:84% you'd have to basically say matplotlib.pyplot dot function 00:02:02.610 --> 00:02:04.030 align:middle line:90% name from that file. 00:02:04.030 --> 00:02:07.240 align:middle line:84% And so that's a lot of writing and a lot of typing. 00:02:07.240 --> 00:02:09.030 align:middle line:90% So when we bring it into our-- 00:02:09.030 --> 00:02:11.580 align:middle line:84% when we bring in this library into our own file, 00:02:11.580 --> 00:02:13.590 align:middle line:90% we can actually rename it. 00:02:13.590 --> 00:02:17.430 align:middle line:84% So "as plt" tells Python that now I 00:02:17.430 --> 00:02:21.750 align:middle line:84% would like to refer to this file and this library as the name 00:02:21.750 --> 00:02:27.480 align:middle line:84% plt. So if we ever want to call functions or maybe objects 00:02:27.480 --> 00:02:29.010 align:middle line:84% and things like that from this file, 00:02:29.010 --> 00:02:33.300 align:middle line:84% we would do it using plt dot and then the name of whatever we 00:02:33.300 --> 00:02:34.090 align:middle line:90% want to use. 00:02:34.090 --> 00:02:38.250 align:middle line:84% So it's just a much nicer way to grab the contents of the file 00:02:38.250 --> 00:02:41.100 align:middle line:84% instead of always writing matplotlib.pyplot dot 00:02:41.100 --> 00:02:41.730 align:middle line:90% something else. 00:02:41.730 --> 00:02:42.390 align:middle line:90% Yeah, question. 00:02:42.390 --> 00:02:44.040 align:middle line:84% AUDIENCE: Is plt a variable name? 00:02:44.040 --> 00:02:46.260 align:middle line:84% ANA BELL: You can think of it as a variable name. 00:02:46.260 --> 00:02:48.180 align:middle line:90% It's anything you want it to be. 00:02:48.180 --> 00:02:51.360 align:middle line:84% So you can import it matplotlib.pyplot as ana. 00:02:51.360 --> 00:02:52.980 align:middle line:84% And then from there on, you can say 00:02:52.980 --> 00:02:56.890 align:middle line:84% ana dot process name, or plot, or whatever it is. 00:02:56.890 --> 00:02:59.040 align:middle line:84% So it's just whatever name you want to give it. 00:02:59.040 --> 00:03:02.040 align:middle line:90% 00:03:02.040 --> 00:03:06.090 align:middle line:84% OK, so there are other visualization libraries 00:03:06.090 --> 00:03:09.350 align:middle line:90% that exist out there. 00:03:09.350 --> 00:03:12.530 align:middle line:84% A lot of them-- or all of them build upon this one. 00:03:12.530 --> 00:03:15.650 align:middle line:84% So this is the most basic library that you can get. 00:03:15.650 --> 00:03:18.560 align:middle line:84% And the other ones that exist build upon it 00:03:18.560 --> 00:03:21.710 align:middle line:84% by doing some things behind the scenes 00:03:21.710 --> 00:03:25.460 align:middle line:84% to maybe make your lives easier or to do 00:03:25.460 --> 00:03:27.680 align:middle line:84% some really cool visualizations or maybe 00:03:27.680 --> 00:03:31.550 align:middle line:84% things where you can hover the mouse over a coordinate 00:03:31.550 --> 00:03:32.480 align:middle line:90% and things like that. 00:03:32.480 --> 00:03:35.180 align:middle line:84% But we don't need to do any of that at this time. 00:03:35.180 --> 00:03:38.390 align:middle line:84% It's just nice to take a look at this really basic visualization 00:03:38.390 --> 00:03:40.560 align:middle line:90% library. 00:03:40.560 --> 00:03:42.780 align:middle line:84% So throughout the lecture, we're going 00:03:42.780 --> 00:03:44.250 align:middle line:84% to look a little bit at some code. 00:03:44.250 --> 00:03:46.320 align:middle line:84% We're going to run it on the Python-- 00:03:46.320 --> 00:03:47.830 align:middle line:90% just from the Python file. 00:03:47.830 --> 00:03:50.240 align:middle line:84% Then we'll just talk about it on the slides. 00:03:50.240 --> 00:03:52.490 align:middle line:84% So whenever we're plotting things, 00:03:52.490 --> 00:03:58.550 align:middle line:84% we need to tell Python a set of x values and a set of y values. 00:03:58.550 --> 00:03:59.660 align:middle line:90% That's pretty common. 00:03:59.660 --> 00:04:01.790 align:middle line:84% If you've used Matlab, you'll know 00:04:01.790 --> 00:04:05.030 align:middle line:84% that that's kind of the way it's done-- same in Python. 00:04:05.030 --> 00:04:07.790 align:middle line:84% So when we're creating the coordinates 00:04:07.790 --> 00:04:10.490 align:middle line:84% that we'd like to plot in a 2D plane, 00:04:10.490 --> 00:04:15.230 align:middle line:84% we're essentially just creating two lists, where index by index 00:04:15.230 --> 00:04:17.420 align:middle line:84% we're going to have a list containing 00:04:17.420 --> 00:04:21.680 align:middle line:84% all the values that we want for the x coordinate and a list-- 00:04:21.680 --> 00:04:24.620 align:middle line:84% and in a separate list all the values that we'd 00:04:24.620 --> 00:04:25.860 align:middle line:90% like for the y coordinate. 00:04:25.860 --> 00:04:28.400 align:middle line:84% So at index 0 in each of these lists, 00:04:28.400 --> 00:04:31.880 align:middle line:84% you're basically creating x values at index 0, 00:04:31.880 --> 00:04:35.150 align:middle line:84% y values at index 0 becomes the coordinate-- one 00:04:35.150 --> 00:04:36.630 align:middle line:90% coordinate point. 00:04:36.630 --> 00:04:39.590 align:middle line:84% So one of the very simplest things that we can do 00:04:39.590 --> 00:04:42.620 align:middle line:84% is we can create a nice list of values 00:04:42.620 --> 00:04:45.090 align:middle line:90% that will be our x values. 00:04:45.090 --> 00:04:50.190 align:middle line:84% So our x-axis will basically be the numbers 0 through 29. 00:04:50.190 --> 00:04:53.820 align:middle line:84% And then down here we can create four different lists 00:04:53.820 --> 00:04:58.450 align:middle line:84% containing four different y value coordinates. 00:04:58.450 --> 00:04:59.910 align:middle line:84% So when we're plotting, we're going 00:04:59.910 --> 00:05:03.780 align:middle line:84% to plot this x value list against all 00:05:03.780 --> 00:05:06.810 align:middle line:84% these linear points, this x value list against all 00:05:06.810 --> 00:05:08.550 align:middle line:84% these quadratic points, and this x value 00:05:08.550 --> 00:05:10.780 align:middle line:84% list against the cubic points, and so on. 00:05:10.780 --> 00:05:12.990 align:middle line:84% So the way we're creating these lists 00:05:12.990 --> 00:05:16.800 align:middle line:84% are a pretty familiar Python syntax. 00:05:16.800 --> 00:05:19.500 align:middle line:90% Our n is going through 0 to 29. 00:05:19.500 --> 00:05:21.660 align:middle line:84% And then we're appending to the end 00:05:21.660 --> 00:05:24.060 align:middle line:84% of each one of these lists, linear, quadratic, cubic, 00:05:24.060 --> 00:05:27.000 align:middle line:84% and exponential, some function of that n. 00:05:27.000 --> 00:05:31.060 align:middle line:84% So the linear list will just have all the values again. 00:05:31.060 --> 00:05:33.810 align:middle line:84% So we're plotting 0, 0, 1, 1, 2, 2, so on. 00:05:33.810 --> 00:05:38.640 align:middle line:84% The quadratic list, we'll be plotting 0, 0, 1, 1, 2, 4, 3, 00:05:38.640 --> 00:05:40.000 align:middle line:90% 9, and so on. 00:05:40.000 --> 00:05:43.200 align:middle line:84% Same with the cubic and then this exponential. 00:05:43.200 --> 00:05:46.180 align:middle line:84% I just chose randomly 1.5 to the power of n 00:05:46.180 --> 00:05:48.180 align:middle line:84% just because it kind of looked nice in the plot, 00:05:48.180 --> 00:05:50.160 align:middle line:84% but you can imagine different number 00:05:50.160 --> 00:05:53.210 align:middle line:90% for the exponential in there. 00:05:53.210 --> 00:05:59.410 align:middle line:84% So the way we plot some values is by, not surprisingly, 00:05:59.410 --> 00:06:00.460 align:middle line:90% the plot command. 00:06:00.460 --> 00:06:03.790 align:middle line:84% So plt was how we decided to import 00:06:03.790 --> 00:06:06.280 align:middle line:84% that library as, the name that we gave it, 00:06:06.280 --> 00:06:09.310 align:middle line:84% dot plot tells Python we'd like to plot 00:06:09.310 --> 00:06:11.990 align:middle line:90% some list of x and y values. 00:06:11.990 --> 00:06:14.140 align:middle line:84% So the parameters to the plot command 00:06:14.140 --> 00:06:17.270 align:middle line:84% are going to be two sequences of values. 00:06:17.270 --> 00:06:20.620 align:middle line:84% They can be lists typically, but they could also be tuples. 00:06:20.620 --> 00:06:23.110 align:middle line:84% They could also be the keys you get 00:06:23.110 --> 00:06:26.450 align:middle line:84% from a dictionary that was also an iterable, things like that. 00:06:26.450 --> 00:06:30.140 align:middle line:84% So we have to pass in a list of numerical things. 00:06:30.140 --> 00:06:33.075 align:middle line:84% So this will be typically the stuff on your x-axis. 00:06:33.075 --> 00:06:34.450 align:middle line:84% And the second parameter is going 00:06:34.450 --> 00:06:37.850 align:middle line:84% to be the function of those values of the x-axis. 00:06:37.850 --> 00:06:40.580 align:middle line:84% The lists have to be the same length, obviously, 00:06:40.580 --> 00:06:43.520 align:middle line:84% so Python knows which coordinates we're plotting. 00:06:43.520 --> 00:06:46.370 align:middle line:84% If they're not the same length by accident, 00:06:46.370 --> 00:06:49.700 align:middle line:84% then Python will throw an error and then you don't-- 00:06:49.700 --> 00:06:52.890 align:middle line:90% it just won't plot anything. 00:06:52.890 --> 00:06:58.400 align:middle line:84% So when we run the code, Python will generally plot the values 00:06:58.400 --> 00:07:02.330 align:middle line:84% in either a new window or directly 00:07:02.330 --> 00:07:05.820 align:middle line:84% in line in the console, so right over here. 00:07:05.820 --> 00:07:08.840 align:middle line:84% So right in here, it could put the plot 00:07:08.840 --> 00:07:11.480 align:middle line:84% directly sort of in line with a bunch of stuff 00:07:11.480 --> 00:07:13.010 align:middle line:90% that you might print out. 00:07:13.010 --> 00:07:15.430 align:middle line:84% To toggle between that, just out of curiosity, 00:07:15.430 --> 00:07:19.070 align:middle line:84% you go to Tools, Preferences, iPython console, Graphics. 00:07:19.070 --> 00:07:21.590 align:middle line:84% And then here you can choose either automatic, 00:07:21.590 --> 00:07:23.528 align:middle line:84% which will make a new window for us that's 00:07:23.528 --> 00:07:25.070 align:middle line:84% interactive, you can zoom in and out, 00:07:25.070 --> 00:07:28.130 align:middle line:84% things like that, or inline, which will just 00:07:28.130 --> 00:07:32.030 align:middle line:84% put the plot that you tell Python to generate directly 00:07:32.030 --> 00:07:33.930 align:middle line:90% in the console here. 00:07:33.930 --> 00:07:37.070 align:middle line:84% So I prefer the new window because it's easier for me 00:07:37.070 --> 00:07:37.920 align:middle line:90% to interact with it. 00:07:37.920 --> 00:07:39.810 align:middle line:90% So we'll do that. 00:07:39.810 --> 00:07:42.710 align:middle line:84% So let's actually run one of the plot commands. 00:07:42.710 --> 00:07:47.810 align:middle line:84% So plt.plot, we're plotting here the x-axis as just 00:07:47.810 --> 00:07:49.340 align:middle line:90% the numbers 0 through 29. 00:07:49.340 --> 00:07:52.700 align:middle line:84% And the y-axis is just going to also be the value 0 through 29. 00:07:52.700 --> 00:07:54.710 align:middle line:84% So we've made a nice little linear plot. 00:07:54.710 --> 00:07:58.160 align:middle line:84% And you notice it popped up a little window down here for me. 00:07:58.160 --> 00:08:00.650 align:middle line:84% And this is the plot that it generated. 00:08:00.650 --> 00:08:02.040 align:middle line:90% Yay, not surprising. 00:08:02.040 --> 00:08:06.520 align:middle line:84% This is exactly what we expected out of it. 00:08:06.520 --> 00:08:11.320 align:middle line:84% OK, so what do we notice about that plot? 00:08:11.320 --> 00:08:16.510 align:middle line:84% We notice how Python nicely fit the line within this frame. 00:08:16.510 --> 00:08:19.000 align:middle line:84% So it added a little bit of wiggle room to the left 00:08:19.000 --> 00:08:22.540 align:middle line:84% and to the right of my line and to the below and above my line 00:08:22.540 --> 00:08:26.050 align:middle line:84% just so it fits nicely within the frame. 00:08:26.050 --> 00:08:29.920 align:middle line:84% It didn't zoom out to some standard 0 to 100 value. 00:08:29.920 --> 00:08:33.940 align:middle line:84% It zoomed in to this 0 to 30-ish range, 0 to 30-ish 00:08:33.940 --> 00:08:34.990 align:middle line:90% on the y-axis range. 00:08:34.990 --> 00:08:40.929 align:middle line:84% So really, really nice that it did all that for us. 00:08:40.929 --> 00:08:44.000 align:middle line:84% The order of the points does matter in the list. 00:08:44.000 --> 00:08:46.930 align:middle line:84% So you'll notice one of the other things in this plot 00:08:46.930 --> 00:08:50.680 align:middle line:84% here is we gave it actual points that it needed to plot. 00:08:50.680 --> 00:08:54.940 align:middle line:84% But the plot command doesn't plot the points by default. 00:08:54.940 --> 00:08:57.650 align:middle line:84% Instead, it just connects all the points by line. 00:08:57.650 --> 00:09:01.750 align:middle line:84% So it connects consecutive indices of points by a line. 00:09:01.750 --> 00:09:06.140 align:middle line:84% So connected the 0, 0, 1, 1, 2, 2, and so on. 00:09:06.140 --> 00:09:08.830 align:middle line:84% So the order of the points does actually matter. 00:09:08.830 --> 00:09:13.190 align:middle line:84% If we have a function, for example, in this case, 00:09:13.190 --> 00:09:14.600 align:middle line:90% n and n squared-- 00:09:14.600 --> 00:09:18.274 align:middle line:84% so n being 0 through 29 and n squared being 0, 1, 2, 4-- 00:09:18.274 --> 00:09:22.050 align:middle line:90% 0, 1, 4, 9, and so on-- 00:09:22.050 --> 00:09:24.860 align:middle line:84% but they're in-- but they're out of order, 00:09:24.860 --> 00:09:27.440 align:middle line:84% Python will just take consecutive pairs 00:09:27.440 --> 00:09:31.020 align:middle line:84% from those lists and connect them with a line. 00:09:31.020 --> 00:09:32.700 align:middle line:90% So here's an example. 00:09:32.700 --> 00:09:37.310 align:middle line:84% I've got my x values list is this testSamples. 00:09:37.310 --> 00:09:40.280 align:middle line:84% It's all the numbers 0 through 29 but out of order. 00:09:40.280 --> 00:09:44.150 align:middle line:84% And the test values associated with each one of those, again, 00:09:44.150 --> 00:09:46.110 align:middle line:90% they are correct. 00:09:46.110 --> 00:09:47.180 align:middle line:90% This is 0 squared. 00:09:47.180 --> 00:09:48.590 align:middle line:90% This 25 is 5 squared. 00:09:48.590 --> 00:09:49.820 align:middle line:90% This 9 is 3 squared. 00:09:49.820 --> 00:09:51.810 align:middle line:90% But they're out of order. 00:09:51.810 --> 00:09:58.150 align:middle line:84% So if we run that just with a pure plot command, 00:09:58.150 --> 00:10:03.055 align:middle line:84% we're going to get some garbage plot. 00:10:03.055 --> 00:10:07.420 align:middle line:84% It doesn't look very nice, and we already 00:10:07.420 --> 00:10:08.500 align:middle line:90% know what's wrong, right? 00:10:08.500 --> 00:10:15.520 align:middle line:84% Python just connected 0, 0, 5, 25, and then 3, 9 by a line-- 00:10:15.520 --> 00:10:18.700 align:middle line:90% not really very nice. 00:10:18.700 --> 00:10:23.290 align:middle line:84% Instead, what we'd like to do is to just tell 00:10:23.290 --> 00:10:25.040 align:middle line:90% Python to plot the points. 00:10:25.040 --> 00:10:27.440 align:middle line:84% So I don't care about connecting them with a line. 00:10:27.440 --> 00:10:29.320 align:middle line:84% In this case, I would tell Python, 00:10:29.320 --> 00:10:32.680 align:middle line:84% instead of just plotting it, to create a scatter plot for me. 00:10:32.680 --> 00:10:37.540 align:middle line:84% So plt.scatter with the same list of x and y values 00:10:37.540 --> 00:10:41.950 align:middle line:84% is going to just create for me this nice plot where 00:10:41.950 --> 00:10:43.908 align:middle line:90% it plots the coordinates. 00:10:43.908 --> 00:10:46.450 align:middle line:84% It doesn't matter that they're out of order because they just 00:10:46.450 --> 00:10:49.206 align:middle line:84% get plotted without anything connecting them. 00:10:49.206 --> 00:10:52.520 align:middle line:90% So pretty nice. 00:10:52.520 --> 00:10:55.220 align:middle line:84% So that's this example that we just did here. 00:10:55.220 --> 00:10:58.640 align:middle line:84% And then this is us doing a scatter plot giving us 00:10:58.640 --> 00:11:00.840 align:middle line:90% this nice plot. 00:11:00.840 --> 00:11:03.570 align:middle line:84% OK, one of the other things that you might want to do 00:11:03.570 --> 00:11:06.480 align:middle line:84% is to have a whole bunch of lines 00:11:06.480 --> 00:11:09.600 align:middle line:90% being plotted on one window. 00:11:09.600 --> 00:11:13.230 align:middle line:84% So to do that, all you have to tell Python 00:11:13.230 --> 00:11:15.882 align:middle line:84% is just a sequence of all the commands, all 00:11:15.882 --> 00:11:17.340 align:middle line:84% the plotting commands or everything 00:11:17.340 --> 00:11:19.920 align:middle line:84% that you'd like to plot on the one figure. 00:11:19.920 --> 00:11:22.110 align:middle line:84% So without telling Python you'd like 00:11:22.110 --> 00:11:26.120 align:middle line:84% to create a new figure, anytime it sees a plot command, 00:11:26.120 --> 00:11:29.660 align:middle line:84% it will just keep adding whatever points get generated 00:11:29.660 --> 00:11:32.890 align:middle line:84% or whatever lines get generated to the current figure that's 00:11:32.890 --> 00:11:33.390 align:middle line:90% open. 00:11:33.390 --> 00:11:36.290 align:middle line:84% So we just have one thing that's open right now. 00:11:36.290 --> 00:11:39.860 align:middle line:84% So it'll just keep adding stuff to our figure. 00:11:39.860 --> 00:11:42.550 align:middle line:84% So here I've got four plotting commands in a row. 00:11:42.550 --> 00:11:46.120 align:middle line:84% I never explicitly told Python to create a new figure for me. 00:11:46.120 --> 00:11:49.570 align:middle line:84% So it's just going to add all four of these lines 00:11:49.570 --> 00:11:51.070 align:middle line:90% to the same plot. 00:11:51.070 --> 00:11:53.050 align:middle line:84% So it just doesn't create a new figure. 00:11:53.050 --> 00:11:55.120 align:middle line:84% It just keeps adding stuff to my plot. 00:11:55.120 --> 00:11:57.730 align:middle line:84% So you can imagine if I added a scatter plot as well, 00:11:57.730 --> 00:12:00.760 align:middle line:84% it would just add the individual dots to this plot. 00:12:00.760 --> 00:12:05.490 align:middle line:90% 00:12:05.490 --> 00:12:08.620 align:middle line:90% OK, so again, what do we notice? 00:12:08.620 --> 00:12:13.610 align:middle line:84% Well, Python nicely framed everything for me 00:12:13.610 --> 00:12:16.850 align:middle line:84% to make sure that every line that I have fits 00:12:16.850 --> 00:12:18.930 align:middle line:90% within this graph. 00:12:18.930 --> 00:12:21.980 align:middle line:84% So my x-axis is comfortably between 0 and 30. 00:12:21.980 --> 00:12:23.900 align:middle line:84% And my y-axis is also comfortably 00:12:23.900 --> 00:12:26.540 align:middle line:90% between 0 and 120,000. 00:12:26.540 --> 00:12:28.850 align:middle line:84% So there's a little bit of gap up at that top 00:12:28.850 --> 00:12:31.670 align:middle line:90% of that exponential line. 00:12:31.670 --> 00:12:35.330 align:middle line:84% But this leads us, if we were presented this graph, 00:12:35.330 --> 00:12:39.380 align:middle line:84% to kind of mistakenly not know what's going on 00:12:39.380 --> 00:12:40.940 align:middle line:90% with these bottom lines here. 00:12:40.940 --> 00:12:43.040 align:middle line:84% So this is our linear, the blue line. 00:12:43.040 --> 00:12:46.070 align:middle line:84% And the orange one is the quadratic. 00:12:46.070 --> 00:12:48.350 align:middle line:84% We're not really sure what's going on down there 00:12:48.350 --> 00:12:51.530 align:middle line:90% because the scales are just-- 00:12:51.530 --> 00:12:54.500 align:middle line:90% the y scale is just too high. 00:12:54.500 --> 00:12:57.700 align:middle line:84% So in this particular case, it would be better 00:12:57.700 --> 00:13:01.720 align:middle line:84% to visualize the data in separate, different windows. 00:13:01.720 --> 00:13:07.930 align:middle line:84% So instead of having everything be plotted in one window, 00:13:07.930 --> 00:13:11.950 align:middle line:84% we're going to tell Python to create a new window 00:13:11.950 --> 00:13:14.120 align:middle line:90% and plot some stuff in it. 00:13:14.120 --> 00:13:17.560 align:middle line:84% So the way we tell Python to create a new window for us 00:13:17.560 --> 00:13:21.190 align:middle line:90% is with the command plt.figure. 00:13:21.190 --> 00:13:24.790 align:middle line:84% So as soon as Python sees plt.figure, 00:13:24.790 --> 00:13:27.610 align:middle line:84% it will create a new window, bring it to the foreground. 00:13:27.610 --> 00:13:29.650 align:middle line:84% And any further plotting commands 00:13:29.650 --> 00:13:31.880 align:middle line:84% will be added to this new figure. 00:13:31.880 --> 00:13:34.940 align:middle line:84% So there's a parameter that this figure can take. 00:13:34.940 --> 00:13:37.610 align:middle line:84% And that's going to be the name of the figure. 00:13:37.610 --> 00:13:40.780 align:middle line:84% So you know like when you have a window at the top, 00:13:40.780 --> 00:13:42.670 align:middle line:84% it has a name for the name of the program 00:13:42.670 --> 00:13:43.690 align:middle line:90% or whatever is running? 00:13:43.690 --> 00:13:45.580 align:middle line:84% Well, the string that you put in there 00:13:45.580 --> 00:13:49.250 align:middle line:84% is going to be the name that you give to that figure. 00:13:49.250 --> 00:13:53.110 align:middle line:84% If Python doesn't have a figure with that name already there, 00:13:53.110 --> 00:13:55.540 align:middle line:84% it creates a new figure, brings it to the foreground. 00:13:55.540 --> 00:13:58.990 align:middle line:84% But if there's a figure with that name already there 00:13:58.990 --> 00:14:02.290 align:middle line:84% and you just happen to call plt.figure with that same name, 00:14:02.290 --> 00:14:06.850 align:middle line:84% it'll just rebring that window up to the foreground 00:14:06.850 --> 00:14:10.820 align:middle line:90% again to readd more stuff to it. 00:14:10.820 --> 00:14:14.280 align:middle line:84% So we're going to look at this example here. 00:14:14.280 --> 00:14:16.880 align:middle line:84% We've got a whole bunch of stuff being plotted. 00:14:16.880 --> 00:14:19.640 align:middle line:84% So the first two lines of code here, 00:14:19.640 --> 00:14:23.100 align:middle line:84% first we've got a new figure being created. 00:14:23.100 --> 00:14:24.620 align:middle line:90% And we called it expo. 00:14:24.620 --> 00:14:28.580 align:middle line:84% And then this plot command here coming up right 00:14:28.580 --> 00:14:31.340 align:middle line:84% after the figure will add this exponential 00:14:31.340 --> 00:14:34.360 align:middle line:84% that we created to that expo figure. 00:14:34.360 --> 00:14:37.600 align:middle line:84% Then we've got a plt.figure right after that. 00:14:37.600 --> 00:14:40.840 align:middle line:84% So Python will bring this new figure to the foreground. 00:14:40.840 --> 00:14:42.880 align:middle line:84% And the plot command that comes right 00:14:42.880 --> 00:14:46.600 align:middle line:84% after that will add the linear, this line, 00:14:46.600 --> 00:14:49.570 align:middle line:84% to this new figure-- one that we called lin. 00:14:49.570 --> 00:14:51.670 align:middle line:84% A couple more times we're going to create and do 00:14:51.670 --> 00:14:54.040 align:middle line:84% the same thing to create this quad and this cube. 00:14:54.040 --> 00:14:57.570 align:middle line:84% And those will each get one line added to them. 00:14:57.570 --> 00:15:01.220 align:middle line:84% And then down here, we're going to say, well, let me just 00:15:01.220 --> 00:15:03.110 align:middle line:84% go back to that exponential figure 00:15:03.110 --> 00:15:05.700 align:middle line:84% and add another different exponential curve to it. 00:15:05.700 --> 00:15:08.940 align:middle line:84% So we're going to create the exponential curve, 00:15:08.940 --> 00:15:12.080 align:middle line:84% this time 1.6 to the power of i instead of 1.5 00:15:12.080 --> 00:15:13.850 align:middle line:90% to the power of i. 00:15:13.850 --> 00:15:17.570 align:middle line:84% Then we're going to tell Python to bring the figure called expo 00:15:17.570 --> 00:15:18.770 align:middle line:90% back up to the foreground. 00:15:18.770 --> 00:15:20.900 align:middle line:84% So remember, we created it up here. 00:15:20.900 --> 00:15:22.730 align:middle line:84% So it doesn't create a new figure. 00:15:22.730 --> 00:15:24.260 align:middle line:84% It'll just bring that one back up. 00:15:24.260 --> 00:15:26.210 align:middle line:84% And it already has a curve in it. 00:15:26.210 --> 00:15:28.010 align:middle line:84% And then we're going to tell Python 00:15:28.010 --> 00:15:31.900 align:middle line:90% to plot a second curve to it. 00:15:31.900 --> 00:15:33.690 align:middle line:90% So let's see that. 00:15:33.690 --> 00:15:37.210 align:middle line:90% 00:15:37.210 --> 00:15:39.140 align:middle line:90% That's all this code right here. 00:15:39.140 --> 00:15:41.900 align:middle line:90% Run it. 00:15:41.900 --> 00:15:45.710 align:middle line:90% OK, so not just one figure-- 00:15:45.710 --> 00:15:47.660 align:middle line:84% one window got created, but four. 00:15:47.660 --> 00:15:48.980 align:middle line:90% So this is my cube. 00:15:48.980 --> 00:15:51.600 align:middle line:84% And you can see up in the top here, a little hard to see, 00:15:51.600 --> 00:15:53.690 align:middle line:84% but that's the name that we gave it. 00:15:53.690 --> 00:15:55.610 align:middle line:90% This is my quad. 00:15:55.610 --> 00:15:58.580 align:middle line:90% This is my lin, my linear. 00:15:58.580 --> 00:16:00.800 align:middle line:90% And this is my exponential. 00:16:00.800 --> 00:16:05.090 align:middle line:84% So we see the exponential one has two lines in it 00:16:05.090 --> 00:16:07.270 align:middle line:84% because we added one way at the beginning 00:16:07.270 --> 00:16:09.200 align:middle line:84% and then we brought it back for processing 00:16:09.200 --> 00:16:11.000 align:middle line:90% to add another line to it. 00:16:11.000 --> 00:16:14.700 align:middle line:90% 00:16:14.700 --> 00:16:20.580 align:middle line:84% So again, so these graphs are actually on the slide. 00:16:20.580 --> 00:16:21.570 align:middle line:90% This is the quad one. 00:16:21.570 --> 00:16:22.560 align:middle line:90% This is the cube one. 00:16:22.560 --> 00:16:23.760 align:middle line:90% This is the linear one. 00:16:23.760 --> 00:16:25.710 align:middle line:90% And this is the exponential one. 00:16:25.710 --> 00:16:29.430 align:middle line:84% The blue line was our original curve, 1.5 to the power of x. 00:16:29.430 --> 00:16:32.100 align:middle line:84% And the orange one is 1.6 to the power of x. 00:16:32.100 --> 00:16:35.090 align:middle line:84% So they both got added to the same plot. 00:16:35.090 --> 00:16:35.780 align:middle line:90% Cool. 00:16:35.780 --> 00:16:38.300 align:middle line:84% So again, just something to note, 00:16:38.300 --> 00:16:42.140 align:middle line:84% you'll see how Python nicely framed our lines so that it's 00:16:42.140 --> 00:16:44.840 align:middle line:84% able to fit everything that it needs 00:16:44.840 --> 00:16:46.790 align:middle line:90% to plot within this graph. 00:16:46.790 --> 00:16:50.150 align:middle line:90% 00:16:50.150 --> 00:16:52.230 align:middle line:90% So what we're going to do next-- 00:16:52.230 --> 00:16:54.470 align:middle line:84% I know, that was a little bit tedious. 00:16:54.470 --> 00:16:56.630 align:middle line:84% What we're going to do next is we're 00:16:56.630 --> 00:16:59.700 align:middle line:84% start looking at some real examples, some real-world data. 00:16:59.700 --> 00:17:02.480 align:middle line:84% So first we're going to do some toy real-world data. 00:17:02.480 --> 00:17:05.180 align:middle line:84% And then soon we're going to start 00:17:05.180 --> 00:17:08.510 align:middle line:84% dealing with some actual data sets that we're 00:17:08.510 --> 00:17:11.569 align:middle line:84% going to read in, we're going to plot, 00:17:11.569 --> 00:17:13.280 align:middle line:84% we're going to investigate, try to answer 00:17:13.280 --> 00:17:15.690 align:middle line:84% some questions about them, and things like that. 00:17:15.690 --> 00:17:20.030 align:middle line:84% So first, let's look at this real-life example 00:17:20.030 --> 00:17:23.359 align:middle line:84% where we've got months and temperatures 00:17:23.359 --> 00:17:24.690 align:middle line:90% for each of those months. 00:17:24.690 --> 00:17:30.320 align:middle line:84% So notice the months here is actually the value 00:17:30.320 --> 00:17:32.900 align:middle line:84% that this range returns, which is like an iterable, 00:17:32.900 --> 00:17:34.050 align:middle line:90% like a tuple. 00:17:34.050 --> 00:17:36.090 align:middle line:84% So it's still a sequence of values. 00:17:36.090 --> 00:17:39.080 align:middle line:84% It's not a list but totally fine to be passed 00:17:39.080 --> 00:17:43.060 align:middle line:90% in as an argument to the plot. 00:17:43.060 --> 00:17:45.070 align:middle line:84% And temps, of course, are going to be 00:17:45.070 --> 00:17:49.600 align:middle line:84% temperatures corresponding to each of those months as a list. 00:17:49.600 --> 00:17:52.900 align:middle line:84% So the plot looks something like this 00:17:52.900 --> 00:17:56.400 align:middle line:90% if we actually run that code. 00:17:56.400 --> 00:17:57.340 align:middle line:90% What do we notice? 00:17:57.340 --> 00:18:01.350 align:middle line:84% Well, just like before, matplotlib nicely framed 00:18:01.350 --> 00:18:02.467 align:middle line:90% our data. 00:18:02.467 --> 00:18:04.800 align:middle line:84% It's got a little bit of wiggle room left and right, top 00:18:04.800 --> 00:18:05.640 align:middle line:90% and bottom. 00:18:05.640 --> 00:18:09.570 align:middle line:84% And it automatically selected the scales, how low to go, 00:18:09.570 --> 00:18:13.860 align:middle line:84% how high to go, and the tick marks for this. 00:18:13.860 --> 00:18:19.500 align:middle line:84% But let's say that you're the advisor to a student 00:18:19.500 --> 00:18:23.280 align:middle line:84% and they came to you with a plot that looked like this. 00:18:23.280 --> 00:18:27.690 align:middle line:84% Would you be able to tell anything about this plot 00:18:27.690 --> 00:18:30.910 align:middle line:84% without knowing exactly what the code that generated this plot 00:18:30.910 --> 00:18:31.410 align:middle line:90% is? 00:18:31.410 --> 00:18:33.360 align:middle line:90% Not really, right? 00:18:33.360 --> 00:18:35.190 align:middle line:90% It just looks like a bump. 00:18:35.190 --> 00:18:36.970 align:middle line:90% It could be any sort of data. 00:18:36.970 --> 00:18:40.530 align:middle line:84% So what we'd like to do before actually-- for your apps 00:18:40.530 --> 00:18:42.120 align:middle line:84% and things like that in the future, 00:18:42.120 --> 00:18:45.060 align:middle line:84% before presenting a plot to somebody else, 00:18:45.060 --> 00:18:50.700 align:middle line:84% you'll want to add a title, and you'll want to label your axes. 00:18:50.700 --> 00:18:55.620 align:middle line:84% So what we want to do, in addition to actually plotting 00:18:55.620 --> 00:18:59.850 align:middle line:84% the data, is to tell Python to add for us a title 00:18:59.850 --> 00:19:02.200 align:middle line:90% and labels for our axes. 00:19:02.200 --> 00:19:06.040 align:middle line:84% So we do this using these three lines of code here. 00:19:06.040 --> 00:19:09.180 align:middle line:84% So since we haven't told Python to create a new figure 00:19:09.180 --> 00:19:11.340 align:middle line:84% or anything like that, any commands 00:19:11.340 --> 00:19:13.110 align:middle line:84% that we do with regards to plotting 00:19:13.110 --> 00:19:15.410 align:middle line:84% will just get added on to this figure. 00:19:15.410 --> 00:19:20.080 align:middle line:84% So here I've got Python adding this title, these two 00:19:20.080 --> 00:19:21.910 align:middle line:90% labels to our axis-- 00:19:21.910 --> 00:19:24.500 align:middle line:90% to our axes. 00:19:24.500 --> 00:19:29.030 align:middle line:84% So here I've got this and this plot. 00:19:29.030 --> 00:19:33.280 align:middle line:84% So I run it, and ta-da, we have something 00:19:33.280 --> 00:19:34.930 align:middle line:90% that looks much nicer. 00:19:34.930 --> 00:19:37.030 align:middle line:84% So now we can hand this plot to somebody, 00:19:37.030 --> 00:19:38.935 align:middle line:84% and they'll know what it's about. 00:19:38.935 --> 00:19:41.840 align:middle line:90% 00:19:41.840 --> 00:19:47.090 align:middle line:84% Now, that's fine, but since it's temperatures what I'd really 00:19:47.090 --> 00:19:50.390 align:middle line:84% like to do is to say, well, the temperature-- the lowest 00:19:50.390 --> 00:19:53.720 align:middle line:84% temperature I have should really start at the y-axis here, 00:19:53.720 --> 00:19:55.370 align:middle line:90% this intersect with the y-axis. 00:19:55.370 --> 00:19:57.380 align:middle line:84% And the highest temperature I've got, 00:19:57.380 --> 00:19:59.060 align:middle line:84% I don't really want that wiggle room 00:19:59.060 --> 00:20:02.150 align:middle line:84% because this is my last temperature value. 00:20:02.150 --> 00:20:05.580 align:middle line:84% Let's just have the frame just end there. 00:20:05.580 --> 00:20:09.200 align:middle line:84% So we can do that little change by setting limits 00:20:09.200 --> 00:20:10.980 align:middle line:90% on our x-axis. 00:20:10.980 --> 00:20:15.110 align:middle line:84% So here I'm going to limit the x-axis to say that it starts 00:20:15.110 --> 00:20:18.780 align:middle line:90% from 1, and it ends at 12. 00:20:18.780 --> 00:20:21.530 align:middle line:84% So if I do that, again, that's just a little command 00:20:21.530 --> 00:20:24.920 align:middle line:84% we put in, a continuation with the rest of the commands. 00:20:24.920 --> 00:20:27.390 align:middle line:84% And it gets applied to this plot. 00:20:27.390 --> 00:20:29.510 align:middle line:84% So as soon as I do that, Python now 00:20:29.510 --> 00:20:34.130 align:middle line:84% creates for me the same plot, except that the x-axis starts 00:20:34.130 --> 00:20:37.730 align:middle line:84% at 1 and ends at 12 nicely framed within here, so no more 00:20:37.730 --> 00:20:38.360 align:middle line:90% wiggle room. 00:20:38.360 --> 00:20:41.110 align:middle line:90% 00:20:41.110 --> 00:20:46.210 align:middle line:84% Still some improvements to be made to this plot as in here 00:20:46.210 --> 00:20:47.530 align:middle line:90% the months skip. 00:20:47.530 --> 00:20:53.575 align:middle line:84% So Python decided that it's best to just show 2, 4, 6, 8, 10, 00:20:53.575 --> 00:20:56.500 align:middle line:90% 12 as the ticks on the x-axis. 00:20:56.500 --> 00:21:00.340 align:middle line:84% But I decide that I would-- since I'm 00:21:00.340 --> 00:21:03.230 align:middle line:84% showing all the months of the year and their temperatures, 00:21:03.230 --> 00:21:07.300 align:middle line:84% I would really like to have ticks for every single month. 00:21:07.300 --> 00:21:11.290 align:middle line:84% So again, a little command will do that for us. 00:21:11.290 --> 00:21:17.200 align:middle line:84% So plt.xticks takes in a tuple of all of the places 00:21:17.200 --> 00:21:20.770 align:middle line:84% where you'd like one of those little ticks to be created. 00:21:20.770 --> 00:21:22.630 align:middle line:90% So if we do that-- 00:21:22.630 --> 00:21:26.680 align:middle line:84% again, just another little command in series here-- 00:21:26.680 --> 00:21:30.040 align:middle line:84% if we do that, Python now fills in the ticks 00:21:30.040 --> 00:21:33.430 align:middle line:84% for every single spot that we told it to fill in. 00:21:33.430 --> 00:21:36.130 align:middle line:84% So it's looking way better already. 00:21:36.130 --> 00:21:38.820 align:middle line:90% 00:21:38.820 --> 00:21:40.380 align:middle line:90% What's still not quite right-- 00:21:40.380 --> 00:21:44.040 align:middle line:84% I promise, this will be the last improvement we make. 00:21:44.040 --> 00:21:48.420 align:middle line:84% I personally find it hard to map numbers to the months. 00:21:48.420 --> 00:21:50.430 align:middle line:90% I still count my fingers. 00:21:50.430 --> 00:21:55.840 align:middle line:84% So what would be nice is to say, well, 00:21:55.840 --> 00:21:58.810 align:middle line:84% instead of having numbers on my x-axis, 00:21:58.810 --> 00:22:03.660 align:middle line:84% I would like to have the actual names of my months, Jan, Feb, 00:22:03.660 --> 00:22:05.140 align:middle line:90% Mar, and so on. 00:22:05.140 --> 00:22:07.680 align:middle line:84% So to do that, we're going to make one small change 00:22:07.680 --> 00:22:10.890 align:middle line:90% to our xticks command here. 00:22:10.890 --> 00:22:13.530 align:middle line:84% We're going to give it a second parameter. 00:22:13.530 --> 00:22:17.910 align:middle line:84% So first one is, of course, what we had before, saying these 00:22:17.910 --> 00:22:20.080 align:middle line:84% are all the ticks that I would like to have. 00:22:20.080 --> 00:22:23.010 align:middle line:84% And the second parameter is the labels 00:22:23.010 --> 00:22:24.300 align:middle line:90% for each one of those ticks. 00:22:24.300 --> 00:22:26.770 align:middle line:84% So one by one, they'll be mapped. 00:22:26.770 --> 00:22:29.250 align:middle line:84% So 1 will be mapped to Jan, 2 will be mapped to February, 00:22:29.250 --> 00:22:30.010 align:middle line:90% and so on. 00:22:30.010 --> 00:22:32.430 align:middle line:84% So instead of using the numerical values, 00:22:32.430 --> 00:22:38.480 align:middle line:84% Python will create for us the string 00:22:38.480 --> 00:22:40.530 align:middle line:90% values that I've told it to do. 00:22:40.530 --> 00:22:41.360 align:middle line:90% So here it is. 00:22:41.360 --> 00:22:44.970 align:middle line:84% Run creates for me this very nice-looking plot. 00:22:44.970 --> 00:22:48.230 align:middle line:84% So this I would be happy to receive as an advisor 00:22:48.230 --> 00:22:50.450 align:middle line:84% compared to that very first one that we had. 00:22:50.450 --> 00:22:53.400 align:middle line:90% 00:22:53.400 --> 00:22:56.680 align:middle line:90% All right, questions so far? 00:22:56.680 --> 00:22:58.000 align:middle line:90% We seem all right? 00:22:58.000 --> 00:23:00.720 align:middle line:90% OK. 00:23:00.720 --> 00:23:04.080 align:middle line:84% The other thing that you can do is potentially add grid lines 00:23:04.080 --> 00:23:05.700 align:middle line:90% if you wanted to. 00:23:05.700 --> 00:23:08.620 align:middle line:84% So plt.grid will either toggle the grid lines on and off. 00:23:08.620 --> 00:23:10.540 align:middle line:84% So if there's already grid lines, 00:23:10.540 --> 00:23:12.540 align:middle line:84% it'll toggle them off when it sees that command. 00:23:12.540 --> 00:23:14.880 align:middle line:84% If there are no grid lines, it'll toggle them on. 00:23:14.880 --> 00:23:18.120 align:middle line:84% So you could potentially have a bunch of plt.grid commands 00:23:18.120 --> 00:23:22.420 align:middle line:84% that keep toggling things on and off and so on. 00:23:22.420 --> 00:23:28.870 align:middle line:84% OK, so that was us plotting one city's temperature 00:23:28.870 --> 00:23:31.780 align:middle line:84% values for a year, let's say, an average. 00:23:31.780 --> 00:23:36.130 align:middle line:84% Let's say that we wanted to plot two different cities. 00:23:36.130 --> 00:23:38.720 align:middle line:84% The code to do that is as follows. 00:23:38.720 --> 00:23:42.100 align:middle line:84% So again, we've got months being this range, 1 through 12, 00:23:42.100 --> 00:23:42.970 align:middle line:90% inclusive. 00:23:42.970 --> 00:23:45.520 align:middle line:84% I've got a list of all the Boston temperatures here, 00:23:45.520 --> 00:23:48.160 align:middle line:84% I plot that, a list of all the Phoenix temperatures here, 00:23:48.160 --> 00:23:49.030 align:middle line:90% and I plot that. 00:23:49.030 --> 00:23:54.390 align:middle line:84% And of course I'm going to add some labels to my graph. 00:23:54.390 --> 00:23:59.380 align:middle line:90% So like that. 00:23:59.380 --> 00:24:06.030 align:middle line:84% So if I run that, we get something that looks like this. 00:24:06.030 --> 00:24:10.730 align:middle line:84% Now, of course, I could remove those little wiggle rooms 00:24:10.730 --> 00:24:14.140 align:middle line:84% on the left and right, but for now it's fine. 00:24:14.140 --> 00:24:16.300 align:middle line:90% What's missing from this plot? 00:24:16.300 --> 00:24:18.220 align:middle line:84% Let's say you didn't see the code 00:24:18.220 --> 00:24:20.354 align:middle line:84% and you were just given this plot. 00:24:20.354 --> 00:24:22.354 align:middle line:84% AUDIENCE: You wouldn't know which city is which. 00:24:22.354 --> 00:24:23.870 align:middle line:90% ANA BELL: Yeah, exactly. 00:24:23.870 --> 00:24:25.130 align:middle line:90% I don't know what-- 00:24:25.130 --> 00:24:26.720 align:middle line:84% yes, these are different temperatures 00:24:26.720 --> 00:24:30.380 align:middle line:84% from the title and the labels, but you don't know 00:24:30.380 --> 00:24:32.360 align:middle line:90% which city is which, exactly. 00:24:32.360 --> 00:24:36.230 align:middle line:84% So what we'd like to do is tell Python 00:24:36.230 --> 00:24:40.060 align:middle line:90% how to label these two lines. 00:24:40.060 --> 00:24:43.750 align:middle line:84% So to do that, it's just an extra parameter 00:24:43.750 --> 00:24:45.200 align:middle line:90% here in the plot command. 00:24:45.200 --> 00:24:48.220 align:middle line:84% So when you tell it which data to plot, 00:24:48.220 --> 00:24:51.520 align:middle line:84% you can also tell it what label that data should get. 00:24:51.520 --> 00:24:54.880 align:middle line:84% So here I've got Boston label for the first one, Phoenix 00:24:54.880 --> 00:24:56.320 align:middle line:90% label for the second one. 00:24:56.320 --> 00:25:01.190 align:middle line:84% And then you tell Python to add a legend to your plot. 00:25:01.190 --> 00:25:04.090 align:middle line:84% So here the parameter is the location for the legend. 00:25:04.090 --> 00:25:05.680 align:middle line:84% And best just means Python should 00:25:05.680 --> 00:25:09.130 align:middle line:84% decide where to put the legend, top left, top right, middle, 00:25:09.130 --> 00:25:12.610 align:middle line:84% wherever, so it doesn't really interfere much with the data. 00:25:12.610 --> 00:25:16.420 align:middle line:84% Or you can just tell it where to put that legend. 00:25:16.420 --> 00:25:21.350 align:middle line:84% So you can force the legend to be in a particular spot. 00:25:21.350 --> 00:25:23.560 align:middle line:84% So here I've got already labeled data. 00:25:23.560 --> 00:25:25.240 align:middle line:90% And then we add the legend. 00:25:25.240 --> 00:25:27.560 align:middle line:84% And now you can see in this particular case, 00:25:27.560 --> 00:25:29.170 align:middle line:84% it decided to put it in the top right. 00:25:29.170 --> 00:25:31.630 align:middle line:84% But again, you can force it to go somewhere else. 00:25:31.630 --> 00:25:34.150 align:middle line:84% Bottom middle seemed like a fine choice as well. 00:25:34.150 --> 00:25:37.860 align:middle line:90% 00:25:37.860 --> 00:25:39.450 align:middle line:90% OK, very nice. 00:25:39.450 --> 00:25:44.610 align:middle line:90% So now we've got Python-- 00:25:44.610 --> 00:25:48.150 align:middle line:84% it automatically did the x and y-axes for us, 00:25:48.150 --> 00:25:50.580 align:middle line:84% as we told it to do, but the colors that it picked 00:25:50.580 --> 00:25:51.210 align:middle line:90% were random. 00:25:51.210 --> 00:25:57.100 align:middle line:84% Now, we can specify a bunch of different details for the plot. 00:25:57.100 --> 00:26:01.240 align:middle line:84% So we're going to do that next just to show you that you can. 00:26:01.240 --> 00:26:03.330 align:middle line:84% So we're going to choose different colors 00:26:03.330 --> 00:26:05.100 align:middle line:84% and different styles for our plots. 00:26:05.100 --> 00:26:09.130 align:middle line:84% We're going to choose different widths for our lines. 00:26:09.130 --> 00:26:12.840 align:middle line:84% And then maybe we can-- and then we'll also add some markers, 00:26:12.840 --> 00:26:15.120 align:middle line:84% so where exactly-- each data point we have, 00:26:15.120 --> 00:26:16.260 align:middle line:90% we're going to mark. 00:26:16.260 --> 00:26:18.942 align:middle line:84% And then I'll show you how you can create subplots. 00:26:18.942 --> 00:26:20.400 align:middle line:84% So instead of creating new windows, 00:26:20.400 --> 00:26:24.390 align:middle line:84% you can actually have one window with different little subplots 00:26:24.390 --> 00:26:26.000 align:middle line:90% within. 00:26:26.000 --> 00:26:28.370 align:middle line:84% OK, so the first thing we're going to see 00:26:28.370 --> 00:26:33.860 align:middle line:84% is how to customize the data to have a certain line 00:26:33.860 --> 00:26:35.790 align:middle line:90% style and a certain color. 00:26:35.790 --> 00:26:39.110 align:middle line:84% So there's a shorthand notation to do this. 00:26:39.110 --> 00:26:43.220 align:middle line:84% Instead of actually passing in the parameter name in the plot 00:26:43.220 --> 00:26:45.128 align:middle line:84% command, we can do a shorthand notation. 00:26:45.128 --> 00:26:47.420 align:middle line:84% So you might have already noticed this little extra bit 00:26:47.420 --> 00:26:48.240 align:middle line:90% here. 00:26:48.240 --> 00:26:52.000 align:middle line:84% So the more you use it, the more you'll get used to it. 00:26:52.000 --> 00:26:54.330 align:middle line:84% But this basically tells Python that I 00:26:54.330 --> 00:26:57.780 align:middle line:84% would like this plot, this line corresponding to this data 00:26:57.780 --> 00:27:00.750 align:middle line:84% to be blue, that's what the b stands for, 00:27:00.750 --> 00:27:03.390 align:middle line:90% and to be a solid line. 00:27:03.390 --> 00:27:05.280 align:middle line:84% That's what that little dash means. 00:27:05.280 --> 00:27:07.800 align:middle line:84% The Phoenix one, you may have guessed, 00:27:07.800 --> 00:27:11.520 align:middle line:84% tells Python that I would like this one to be red, r for red, 00:27:11.520 --> 00:27:13.450 align:middle line:90% and to be a dashed line. 00:27:13.450 --> 00:27:16.380 align:middle line:84% And then the last one, I'm going to add one more temperature 00:27:16.380 --> 00:27:18.510 align:middle line:84% here, temperature data for Minneapolis-- 00:27:18.510 --> 00:27:24.450 align:middle line:84% I would like this one to be green and a dash-dot-dash line. 00:27:24.450 --> 00:27:26.550 align:middle line:90% So we can run that. 00:27:26.550 --> 00:27:35.410 align:middle line:90% 00:27:35.410 --> 00:27:38.800 align:middle line:84% And it looks something like this. 00:27:38.800 --> 00:27:41.530 align:middle line:84% All right, so I've got my solid blue line for Boston, 00:27:41.530 --> 00:27:45.100 align:middle line:84% my dashed line for Phoenix, and my dash-dot-dash line 00:27:45.100 --> 00:27:46.300 align:middle line:90% for Minneapolis. 00:27:46.300 --> 00:27:48.910 align:middle line:90% 00:27:48.910 --> 00:27:49.840 align:middle line:90% Very nice. 00:27:49.840 --> 00:27:53.350 align:middle line:84% Now, instead of doing that shorthand notation 00:27:53.350 --> 00:27:56.020 align:middle line:84% where we've got this one parameter that just somehow 00:27:56.020 --> 00:27:59.410 align:middle line:84% magically knows the color and the style 00:27:59.410 --> 00:28:01.750 align:middle line:84% based on just being passed in, we 00:28:01.750 --> 00:28:08.530 align:middle line:84% can actually tell Python the parameter values that 00:28:08.530 --> 00:28:10.480 align:middle line:84% correspond to the color, so here I've 00:28:10.480 --> 00:28:13.840 align:middle line:84% got color equals b for blue, and then that correspond 00:28:13.840 --> 00:28:14.870 align:middle line:90% to the line style. 00:28:14.870 --> 00:28:16.390 align:middle line:84% So here line style equals-- and then 00:28:16.390 --> 00:28:20.090 align:middle line:84% you explicitly pass in the line style that you'd like. 00:28:20.090 --> 00:28:23.410 align:middle line:84% So this may be more intuitive, according 00:28:23.410 --> 00:28:24.370 align:middle line:90% to what we've learned. 00:28:24.370 --> 00:28:29.050 align:middle line:84% But Python does allow you the option to do it all in one. 00:28:29.050 --> 00:28:32.710 align:middle line:84% So if we do-- if we run it with these specific, 00:28:32.710 --> 00:28:35.740 align:middle line:84% explicit parameters, then we'll get the exact same graph 00:28:35.740 --> 00:28:36.640 align:middle line:90% as before-- 00:28:36.640 --> 00:28:39.480 align:middle line:90% no surprise. 00:28:39.480 --> 00:28:42.100 align:middle line:84% So there's a lot of options that we can have here. 00:28:42.100 --> 00:28:44.530 align:middle line:84% So these are all the line style options. 00:28:44.530 --> 00:28:46.980 align:middle line:84% So you can also add a dotted line, which I didn't show. 00:28:46.980 --> 00:28:49.470 align:middle line:84% These are all the color options plus many more. 00:28:49.470 --> 00:28:53.070 align:middle line:84% You could also pass in the RGB values or maybe the hex values 00:28:53.070 --> 00:28:56.680 align:middle line:84% if you want a very specific shade of magenta or something. 00:28:56.680 --> 00:29:01.110 align:middle line:84% And then we can also add markers to our lines. 00:29:01.110 --> 00:29:04.270 align:middle line:84% We haven't seen this yet, but let's do that next. 00:29:04.270 --> 00:29:08.430 align:middle line:84% So let's say that I would like to have the actual data 00:29:08.430 --> 00:29:11.790 align:middle line:84% points that I've plotted show up in my lines. 00:29:11.790 --> 00:29:14.310 align:middle line:84% Right now, the lines just get connected-- 00:29:14.310 --> 00:29:17.040 align:middle line:84% or the data points just get connected with our lines, 00:29:17.040 --> 00:29:18.960 align:middle line:84% dashed or dotted or whatever we chose, 00:29:18.960 --> 00:29:21.390 align:middle line:84% but the marker-- the data points themselves 00:29:21.390 --> 00:29:23.010 align:middle line:90% don't show up with markers. 00:29:23.010 --> 00:29:25.170 align:middle line:84% So again, in shorthand notation, we 00:29:25.170 --> 00:29:27.840 align:middle line:84% can tell Python, hey, let's add these markers. 00:29:27.840 --> 00:29:29.790 align:middle line:84% So here I'm telling Python to just do 00:29:29.790 --> 00:29:32.820 align:middle line:90% a dot for this blue solid line. 00:29:32.820 --> 00:29:34.920 align:middle line:84% Here I'm telling Python to do a larger 00:29:34.920 --> 00:29:37.530 align:middle line:90% dot for this red dashed line. 00:29:37.530 --> 00:29:41.440 align:middle line:84% And here I'm telling it to do a star for the green dash dot 00:29:41.440 --> 00:29:44.770 align:middle line:90% dash dot line. 00:29:44.770 --> 00:29:47.990 align:middle line:90% All right, so that's down here. 00:29:47.990 --> 00:29:50.140 align:middle line:90% Run it. 00:29:50.140 --> 00:29:52.080 align:middle line:84% And now we see nice little markers 00:29:52.080 --> 00:29:54.120 align:middle line:84% for every one of our data points. 00:29:54.120 --> 00:29:57.180 align:middle line:84% So we can also do triangles, we can do squares. 00:29:57.180 --> 00:29:59.160 align:middle line:84% There's lots of other marker options, 00:29:59.160 --> 00:30:04.410 align:middle line:84% and they all exist in the documentation for matplotlib. 00:30:04.410 --> 00:30:08.660 align:middle line:90% So this is what we got, perfect. 00:30:08.660 --> 00:30:14.090 align:middle line:84% The last thing that we can do is to add thickness to our lines. 00:30:14.090 --> 00:30:16.820 align:middle line:84% So oftentimes, it's good to, first of all, 00:30:16.820 --> 00:30:20.420 align:middle line:84% delineate the lines using dashes or dots 00:30:20.420 --> 00:30:22.830 align:middle line:84% and things like that but also width. 00:30:22.830 --> 00:30:26.413 align:middle line:84% So here another parameter passed in, the line width, this 00:30:26.413 --> 00:30:27.830 align:middle line:84% is going to be a skinny line, this 00:30:27.830 --> 00:30:30.020 align:middle line:84% is going to be maybe a thicker line, 00:30:30.020 --> 00:30:32.690 align:middle line:84% and this one's going to be unreasonably thick. 00:30:32.690 --> 00:30:35.930 align:middle line:84% So let's see exactly what this will look like. 00:30:35.930 --> 00:30:37.970 align:middle line:90% It's going to look super weird. 00:30:37.970 --> 00:30:43.890 align:middle line:90% 00:30:43.890 --> 00:30:46.200 align:middle line:84% As I said, unreasonably thick line. 00:30:46.200 --> 00:30:47.190 align:middle line:90% But there it is. 00:30:47.190 --> 00:30:50.070 align:middle line:84% And then you can see that the legend itself also 00:30:50.070 --> 00:30:55.515 align:middle line:84% adjusted to whatever you chose for your line styles. 00:30:55.515 --> 00:31:01.420 align:middle line:90% 00:31:01.420 --> 00:31:05.090 align:middle line:84% So yeah, that's exactly what I said. 00:31:05.090 --> 00:31:05.900 align:middle line:90% Cool. 00:31:05.900 --> 00:31:09.000 align:middle line:84% Last thing I want to talk about is subplots. 00:31:09.000 --> 00:31:12.290 align:middle line:84% So right now, the only things that we've kind of learned 00:31:12.290 --> 00:31:15.440 align:middle line:84% about plotting is you either plot every line 00:31:15.440 --> 00:31:19.460 align:middle line:84% that you have on one figure, or you create a new figure 00:31:19.460 --> 00:31:21.590 align:middle line:84% and then it becomes a new window that you 00:31:21.590 --> 00:31:26.960 align:middle line:84% have to switch between for whatever you'd like to plot. 00:31:26.960 --> 00:31:29.300 align:middle line:84% Oftentimes, what's really nice to do 00:31:29.300 --> 00:31:32.600 align:middle line:90% is to create only one figure. 00:31:32.600 --> 00:31:37.760 align:middle line:84% So you have only one thing that pops up, like one window. 00:31:37.760 --> 00:31:41.660 align:middle line:84% And within that window with some name here-- 00:31:41.660 --> 00:31:43.820 align:middle line:84% and within that window, you can create 00:31:43.820 --> 00:31:46.640 align:middle line:90% a bunch of different subplots. 00:31:46.640 --> 00:31:52.920 align:middle line:84% So here I've created six different subplots. 00:31:52.920 --> 00:31:55.520 align:middle line:90% So we can tell that to Python. 00:31:55.520 --> 00:31:58.350 align:middle line:84% And we do that using the subplot command. 00:31:58.350 --> 00:32:00.740 align:middle line:84% So in this particular case, I've told 00:32:00.740 --> 00:32:06.750 align:middle line:84% Python to create for me a subplot with two rows, that's 00:32:06.750 --> 00:32:10.440 align:middle line:84% what the first parameter says, and one column. 00:32:10.440 --> 00:32:12.420 align:middle line:84% That's what the second parameter says. 00:32:12.420 --> 00:32:16.620 align:middle line:84% So here, this is one window with two positions in it. 00:32:16.620 --> 00:32:20.340 align:middle line:84% The third parameter tells Python which one of these positions 00:32:20.340 --> 00:32:25.240 align:middle line:84% to open for adding lines to or data to. 00:32:25.240 --> 00:32:28.140 align:middle line:84% So 1 means this is the one that you're opening, 00:32:28.140 --> 00:32:30.840 align:middle line:84% and 2 means this is the second one that you're opening. 00:32:30.840 --> 00:32:34.290 align:middle line:84% So you can see here the very top subplot 00:32:34.290 --> 00:32:40.140 align:middle line:84% command tells Python to open up this one for editing, 00:32:40.140 --> 00:32:40.680 align:middle line:90% basically. 00:32:40.680 --> 00:32:43.150 align:middle line:84% So we're going to add to it the Boston temperature. 00:32:43.150 --> 00:32:45.930 align:middle line:84% So this is all the plotting commands and all the labels 00:32:45.930 --> 00:32:50.040 align:middle line:84% and everything after it belong to this top subplot here. 00:32:50.040 --> 00:32:53.250 align:middle line:84% And then subplot command down here tells Python 00:32:53.250 --> 00:32:56.910 align:middle line:84% that on this figure with two rows and one column 00:32:56.910 --> 00:32:59.970 align:middle line:84% I would like to now open position number 2 for editing. 00:32:59.970 --> 00:33:03.120 align:middle line:84% And then everything that I have thereafter gets 00:33:03.120 --> 00:33:06.690 align:middle line:84% added to the subplot at this position. 00:33:06.690 --> 00:33:09.960 align:middle line:84% So the way that this is going to look is as follows. 00:33:09.960 --> 00:33:14.490 align:middle line:84% So I've got-- this is just one window that gets created. 00:33:14.490 --> 00:33:17.240 align:middle line:84% And you can see the top one has the Boston temperature, 00:33:17.240 --> 00:33:20.576 align:middle line:84% and the bottom one has the Phoenix temperature. 00:33:20.576 --> 00:33:23.900 align:middle line:90% 00:33:23.900 --> 00:33:28.050 align:middle line:84% At first glance, does this look right in terms of temperatures, 00:33:28.050 --> 00:33:30.560 align:middle line:84% if you were just to look at the pictures themselves? 00:33:30.560 --> 00:33:34.100 align:middle line:90% 00:33:34.100 --> 00:33:38.390 align:middle line:84% I don't know about you, but at first glance, 00:33:38.390 --> 00:33:40.640 align:middle line:84% I thought that the temperatures for Boston and Phoenix 00:33:40.640 --> 00:33:46.998 align:middle line:84% were the same because I didn't look closely at the y-axes. 00:33:46.998 --> 00:33:49.040 align:middle line:84% It kind of looked like, hey, they both bottom out 00:33:49.040 --> 00:33:51.165 align:middle line:84% in the same way, they both top out in the same way. 00:33:51.165 --> 00:33:52.770 align:middle line:90% So they look very similar to me. 00:33:52.770 --> 00:33:55.350 align:middle line:84% But if we inspect the y-axes closer, 00:33:55.350 --> 00:33:58.310 align:middle line:84% we see that the Boston temperature starts at 30, 00:33:58.310 --> 00:33:59.180 align:middle line:90% goes to 70. 00:33:59.180 --> 00:34:02.330 align:middle line:84% But the Phoenix one starts at, what is this, 50 00:34:02.330 --> 00:34:04.570 align:middle line:90% and goes to 90. 00:34:04.570 --> 00:34:08.550 align:middle line:84% So if we're presenting plots in one figure what 00:34:08.550 --> 00:34:11.400 align:middle line:84% would be really nice to do is to make sure 00:34:11.400 --> 00:34:14.980 align:middle line:84% that the axes are both bounded in a similar way, 00:34:14.980 --> 00:34:18.210 align:middle line:84% especially if we're plotting similar data, temperature 00:34:18.210 --> 00:34:21.179 align:middle line:90% in this particular case. 00:34:21.179 --> 00:34:26.159 align:middle line:84% So in our code what we'd also like to do 00:34:26.159 --> 00:34:30.420 align:middle line:84% is set limits on our axes, and just the y-axis 00:34:30.420 --> 00:34:32.130 align:middle line:90% because the x-axis is the same. 00:34:32.130 --> 00:34:37.770 align:middle line:84% So here I can limit the y-axis from 0 to 100, a reasonable set 00:34:37.770 --> 00:34:40.370 align:middle line:90% of temperatures in Fahrenheit. 00:34:40.370 --> 00:34:44.780 align:middle line:84% So if I fix these temperature limits from 0 to 100 00:34:44.780 --> 00:34:48.260 align:middle line:84% and now I plot, I get something that looks like this. 00:34:48.260 --> 00:34:52.630 align:middle line:84% And now at first glance, this makes a lot more sense to me. 00:34:52.630 --> 00:34:56.560 align:middle line:84% I've got-- the Phoenix temperatures seem 00:34:56.560 --> 00:35:00.730 align:middle line:84% to be on for this year, on average, higher 00:35:00.730 --> 00:35:02.240 align:middle line:90% than the Boston temperatures. 00:35:02.240 --> 00:35:07.430 align:middle line:90% 00:35:07.430 --> 00:35:11.640 align:middle line:84% So we can plot now multiple-- we can create multiple subplots. 00:35:11.640 --> 00:35:15.770 align:middle line:84% So here in the previous example, I just had two, top and bottom. 00:35:15.770 --> 00:35:18.020 align:middle line:84% But I can create as many subplots 00:35:18.020 --> 00:35:20.690 align:middle line:90% as I'd like within my window. 00:35:20.690 --> 00:35:25.100 align:middle line:84% So when I create them and I tell Python how many rows 00:35:25.100 --> 00:35:27.860 align:middle line:84% and columns I have-- in this particular example I just 00:35:27.860 --> 00:35:33.240 align:middle line:84% drew here, I have three rows and two columns. 00:35:33.240 --> 00:35:35.660 align:middle line:84% So the third parameter that I pass in 00:35:35.660 --> 00:35:39.230 align:middle line:84% will basically tell Python which one of these subplots 00:35:39.230 --> 00:35:40.990 align:middle line:90% to open up for processing. 00:35:40.990 --> 00:35:43.490 align:middle line:84% So this will be the first one, this will be the second one-- 00:35:43.490 --> 00:35:44.690 align:middle line:90% kind of the way we read-- 00:35:44.690 --> 00:35:48.470 align:middle line:90% third, fourth, fifth, and sixth. 00:35:48.470 --> 00:35:51.620 align:middle line:84% So that third parameter to these subplot commands 00:35:51.620 --> 00:35:53.930 align:middle line:84% will be either 1, 2, 3, 4, 5, or 6, 00:35:53.930 --> 00:35:56.600 align:middle line:84% telling Python which one of these sections 00:35:56.600 --> 00:35:59.300 align:middle line:90% I'm going to add plots to. 00:35:59.300 --> 00:36:02.210 align:middle line:84% In this particular case, I had a Boston, Phoenix, 00:36:02.210 --> 00:36:03.600 align:middle line:90% and Minneapolis temperature. 00:36:03.600 --> 00:36:06.810 align:middle line:84% So I'm just creating a two-by-two matrix. 00:36:06.810 --> 00:36:09.120 align:middle line:84% So here I just have this thing that 00:36:09.120 --> 00:36:12.090 align:middle line:84% looks like this, a figure with these four subplots. 00:36:12.090 --> 00:36:17.070 align:middle line:84% And I am going to add the Boston one over here, the Phoenix 00:36:17.070 --> 00:36:20.700 align:middle line:84% one over here, and then the Minneapolis 00:36:20.700 --> 00:36:28.470 align:middle line:84% down here, so 1, 2, and 3 as my subplots that I'm opening. 00:36:28.470 --> 00:36:32.220 align:middle line:84% Nothing in four, so that fourth spot will just be empty. 00:36:32.220 --> 00:36:34.390 align:middle line:84% So the plots will look something like this. 00:36:34.390 --> 00:36:37.420 align:middle line:84% And I haven't changed the line widths in this particular case. 00:36:37.420 --> 00:36:39.390 align:middle line:90% I didn't need to. 00:36:39.390 --> 00:36:42.810 align:middle line:84% And you can see everything's plotted with the heights, 00:36:42.810 --> 00:36:45.300 align:middle line:84% again, limited from 0 to 100 just 00:36:45.300 --> 00:36:46.680 align:middle line:90% so everything's comparable. 00:36:46.680 --> 00:36:48.523 align:middle line:84% And notice the empty spot here because I 00:36:48.523 --> 00:36:49.690 align:middle line:90% had nothing to fill in with. 00:36:49.690 --> 00:36:53.200 align:middle line:90% 00:36:53.200 --> 00:36:54.265 align:middle line:90% Questions about this? 00:36:54.265 --> 00:36:57.510 align:middle line:90% Is this interesting? 00:36:57.510 --> 00:37:00.000 align:middle line:90% OK. 00:37:00.000 --> 00:37:07.010 align:middle line:84% All right, so that finishes up just some really basic things 00:37:07.010 --> 00:37:12.000 align:middle line:84% that we can do with plotting, basic customizations. 00:37:12.000 --> 00:37:15.860 align:middle line:84% Now what I'd like to do is just open up a few different data 00:37:15.860 --> 00:37:18.950 align:middle line:90% sets for processing. 00:37:18.950 --> 00:37:22.610 align:middle line:84% We can start by just plotting the pure values 00:37:22.610 --> 00:37:24.080 align:middle line:90% on a regular plot. 00:37:24.080 --> 00:37:26.480 align:middle line:84% And then we can start to investigate things 00:37:26.480 --> 00:37:29.930 align:middle line:84% that we visualize, ask more questions, 00:37:29.930 --> 00:37:32.100 align:middle line:90% and see where we go from there. 00:37:32.100 --> 00:37:35.450 align:middle line:84% So the first thing I'd like to do is open up a file 00:37:35.450 --> 00:37:37.410 align:middle line:90% on the US population. 00:37:37.410 --> 00:37:44.220 align:middle line:84% So this particular file contains 40 different numbers. 00:37:44.220 --> 00:37:51.560 align:middle line:84% So it has a population value over about 400 years, every 10 00:37:51.560 --> 00:37:52.500 align:middle line:90% years. 00:37:52.500 --> 00:37:56.150 align:middle line:84% So that's 40 different values for the temperatures, 00:37:56.150 --> 00:38:00.170 align:middle line:84% starting from, I don't know, a really long time ago till about 00:38:00.170 --> 00:38:03.310 align:middle line:90% 2010 or something like that. 00:38:03.310 --> 00:38:06.250 align:middle line:84% So the file looks something like this. 00:38:06.250 --> 00:38:11.880 align:middle line:84% So it starts at 1610 and goes down to 2010. 00:38:11.880 --> 00:38:14.550 align:middle line:84% So this is 40 lines for 40 years-- 00:38:14.550 --> 00:38:19.660 align:middle line:90% 400 years, every 10 years. 00:38:19.660 --> 00:38:21.550 align:middle line:84% Then there's a space in the file. 00:38:21.550 --> 00:38:25.350 align:middle line:84% And then I've got the population value. 00:38:25.350 --> 00:38:30.640 align:middle line:84% So it starts at 350, increases, goes down to 300,000 in 2010. 00:38:30.640 --> 00:38:32.277 align:middle line:84% So that's what the file looks like. 00:38:32.277 --> 00:38:34.860 align:middle line:84% It's important to know what the file looks like because you're 00:38:34.860 --> 00:38:37.680 align:middle line:84% going to have to read in this data 00:38:37.680 --> 00:38:40.680 align:middle line:84% and save it in some sort of data structure 00:38:40.680 --> 00:38:42.400 align:middle line:90% that's easy to manipulate. 00:38:42.400 --> 00:38:44.845 align:middle line:84% So in our case, a data structure that's 00:38:44.845 --> 00:38:47.220 align:middle line:84% really easy to manipulate where you have a whole sequence 00:38:47.220 --> 00:38:50.100 align:middle line:90% of values is a list. 00:38:50.100 --> 00:38:52.230 align:middle line:84% So what we can do is we can open up 00:38:52.230 --> 00:38:56.370 align:middle line:84% this file for processing, read in the years as a list, 00:38:56.370 --> 00:39:01.740 align:middle line:84% and then read in the population values as a list as well. 00:39:01.740 --> 00:39:04.300 align:middle line:84% We could use a dictionary also if we wanted to. 00:39:04.300 --> 00:39:08.030 align:middle line:84% But in this case, I just used two lists. 00:39:08.030 --> 00:39:10.210 align:middle line:84% So let's look at the code to do that. 00:39:10.210 --> 00:39:13.070 align:middle line:84% It looks like a lot, but I'll go through it. 00:39:13.070 --> 00:39:17.290 align:middle line:84% So here is the function that's going to read in the file. 00:39:17.290 --> 00:39:20.500 align:middle line:84% It just opens up the file, creates two empty lists. 00:39:20.500 --> 00:39:22.240 align:middle line:90% One will contain the dates. 00:39:22.240 --> 00:39:23.980 align:middle line:84% The other will contain the populations. 00:39:23.980 --> 00:39:26.260 align:middle line:84% It iterates through each line in the file. 00:39:26.260 --> 00:39:28.690 align:middle line:84% So I've put up what a line in the file kind of looks 00:39:28.690 --> 00:39:29.440 align:middle line:90% like up here. 00:39:29.440 --> 00:39:34.250 align:middle line:84% So it's got some number, space, some other number. 00:39:34.250 --> 00:39:36.370 align:middle line:90% But when we read and file-- 00:39:36.370 --> 00:39:38.800 align:middle line:84% when we read in a line from a file, 00:39:38.800 --> 00:39:42.020 align:middle line:84% Python actually reads it as a string. 00:39:42.020 --> 00:39:45.010 align:middle line:84% So what that means for us is we're 00:39:45.010 --> 00:39:48.220 align:middle line:84% going to have to take this string, each line 00:39:48.220 --> 00:39:54.160 align:middle line:84% being the string, "1640 space 26,634," something like that, 00:39:54.160 --> 00:39:58.510 align:middle line:84% and somehow separate it so that we have the date and then 00:39:58.510 --> 00:40:03.010 align:middle line:84% the number of the population and then somehow save 00:40:03.010 --> 00:40:05.120 align:middle line:90% those two pieces to lists. 00:40:05.120 --> 00:40:12.680 align:middle line:84% So the first thing to notice is that we have a pesky comma 00:40:12.680 --> 00:40:17.210 align:middle line:90% in our population values. 00:40:17.210 --> 00:40:20.300 align:middle line:84% Those values are human-readable, so it makes it easy 00:40:20.300 --> 00:40:26.600 align:middle line:84% for us to read, but the computer is not so happy about them. 00:40:26.600 --> 00:40:31.370 align:middle line:84% So if I have a number like 11,345, 00:40:31.370 --> 00:40:36.080 align:middle line:84% whatever, this is read in as a string, right? 00:40:36.080 --> 00:40:40.730 align:middle line:84% And if I just try to cast that as an integer, 00:40:40.730 --> 00:40:44.090 align:middle line:84% straight without doing any sort of processing on it, 00:40:44.090 --> 00:40:46.250 align:middle line:90% Python is very unhappy. 00:40:46.250 --> 00:40:50.150 align:middle line:84% So what we need to do is remove that comma. 00:40:50.150 --> 00:40:53.240 align:middle line:84% Because as long as I don't have a comma there, 00:40:53.240 --> 00:41:00.020 align:middle line:84% Python can convert that string number into a regular integer 00:41:00.020 --> 00:41:03.500 align:middle line:90% number for us to then plot. 00:41:03.500 --> 00:41:06.540 align:middle line:84% So that's what this bit of the code is doing. 00:41:06.540 --> 00:41:10.740 align:middle line:90% It's doing it in a weird way. 00:41:10.740 --> 00:41:14.760 align:middle line:84% It's saying, hey, take this entire line of characters 00:41:14.760 --> 00:41:19.980 align:middle line:84% and only keep characters that are either a digit or a space. 00:41:19.980 --> 00:41:22.830 align:middle line:84% So in doing so, it effectively removes the comma 00:41:22.830 --> 00:41:26.790 align:middle line:84% because it creates a new version of that line containing 00:41:26.790 --> 00:41:28.270 align:middle line:90% only digits and spaces. 00:41:28.270 --> 00:41:32.580 align:middle line:84% So it'll just take the 2, 6 and then the 6, 3, 4 right after. 00:41:32.580 --> 00:41:36.230 align:middle line:84% So it just creates this new line that looks like that. 00:41:36.230 --> 00:41:38.680 align:middle line:84% And then after it has this new line, 00:41:38.680 --> 00:41:40.780 align:middle line:84% we're going to split on the space 00:41:40.780 --> 00:41:44.530 align:middle line:84% because we note that every single-- 00:41:44.530 --> 00:41:47.260 align:middle line:84% after every date, every year, we've 00:41:47.260 --> 00:41:51.290 align:middle line:84% got a space that separates our population value and our date. 00:41:51.290 --> 00:41:54.580 align:middle line:84% So if we split on the space using the split command, 00:41:54.580 --> 00:41:58.750 align:middle line:84% the thing before the space, so the line at index 0, 00:41:58.750 --> 00:42:00.010 align:middle line:90% gives us the date. 00:42:00.010 --> 00:42:03.970 align:middle line:84% We'll just cast that to an int and append it to dates. 00:42:03.970 --> 00:42:08.560 align:middle line:84% And then the line at index 1 is the thing after the space, 00:42:08.560 --> 00:42:10.810 align:middle line:84% again without the comma because we did that trick. 00:42:10.810 --> 00:42:13.180 align:middle line:84% And then we cast that to an integer 00:42:13.180 --> 00:42:15.955 align:middle line:84% and append that to our populations value. 00:42:15.955 --> 00:42:18.165 align:middle line:90% 00:42:18.165 --> 00:42:19.290 align:middle line:90% So that's what we do there. 00:42:19.290 --> 00:42:20.670 align:middle line:90% And that's what we do there. 00:42:20.670 --> 00:42:22.590 align:middle line:84% And then, from there on out, we just 00:42:22.590 --> 00:42:24.540 align:middle line:84% return the dates and the populations. 00:42:24.540 --> 00:42:28.920 align:middle line:84% The dates become my x values for my plot, 00:42:28.920 --> 00:42:31.395 align:middle line:84% and the populations become the y values for my plot. 00:42:31.395 --> 00:42:33.900 align:middle line:90% 00:42:33.900 --> 00:42:37.030 align:middle line:84% And then we plot it, and it looks something like this. 00:42:37.030 --> 00:42:41.400 align:middle line:84% So much easier to read or to tell 00:42:41.400 --> 00:42:44.460 align:middle line:84% what's going on than just looking at pure numbers. 00:42:44.460 --> 00:42:46.980 align:middle line:84% Always nicer to visualize things than to just read 00:42:46.980 --> 00:42:49.380 align:middle line:84% a whole bunch of numbers, even if it's just 40. 00:42:49.380 --> 00:42:52.200 align:middle line:84% And in fact, we can tell a couple things 00:42:52.200 --> 00:42:54.030 align:middle line:90% that we weren't able to tell-- 00:42:54.030 --> 00:42:56.910 align:middle line:84% we definitely couldn't have been able to tell from just 00:42:56.910 --> 00:42:59.110 align:middle line:90% pure looking at pure numbers. 00:42:59.110 --> 00:43:02.850 align:middle line:84% The first is that we notice a little bump 00:43:02.850 --> 00:43:06.910 align:middle line:90% right here in the population. 00:43:06.910 --> 00:43:09.880 align:middle line:84% This is the impact of World War II on the population. 00:43:09.880 --> 00:43:12.780 align:middle line:84% Second, a little harder to tell is another little bump 00:43:12.780 --> 00:43:13.770 align:middle line:90% down here. 00:43:13.770 --> 00:43:17.220 align:middle line:84% And that's the impact of the Civil War on the population. 00:43:17.220 --> 00:43:19.710 align:middle line:90% So nicer to visualize. 00:43:19.710 --> 00:43:22.180 align:middle line:84% It exposes some interesting things. 00:43:22.180 --> 00:43:24.330 align:middle line:84% The other thing to notice is, well, 00:43:24.330 --> 00:43:27.290 align:middle line:90% what's going on down here? 00:43:27.290 --> 00:43:29.870 align:middle line:84% It kind of looks like the population is not really 00:43:29.870 --> 00:43:32.750 align:middle line:90% growing much. 00:43:32.750 --> 00:43:35.240 align:middle line:84% And then maybe from 1750 onward, it 00:43:35.240 --> 00:43:36.650 align:middle line:90% starts to grow exponentially. 00:43:36.650 --> 00:43:42.040 align:middle line:84% It's hard to tell what exactly is going on in that lower part. 00:43:42.040 --> 00:43:46.870 align:middle line:84% So let's think about a different way of showing this data. 00:43:46.870 --> 00:43:50.590 align:middle line:84% Instead of having a linear scale on our y-axis, 00:43:50.590 --> 00:43:56.040 align:middle line:84% let's see about doing it in a logarithmic scale. 00:43:56.040 --> 00:43:59.250 align:middle line:84% So we're going to add a command that 00:43:59.250 --> 00:44:04.230 align:middle line:84% tells Python to make our y-axis a logarithmic scale, instead 00:44:04.230 --> 00:44:06.060 align:middle line:90% of linear. 00:44:06.060 --> 00:44:08.940 align:middle line:84% So if we do that, then that means 00:44:08.940 --> 00:44:15.150 align:middle line:84% that every regular increment in our y-- on our y-axis 00:44:15.150 --> 00:44:20.670 align:middle line:84% is going to imply an exponential increase in the population. 00:44:20.670 --> 00:44:24.850 align:middle line:90% OK, so let's plot that. 00:44:24.850 --> 00:44:28.140 align:middle line:84% And if we plot that, we get something that looks like this. 00:44:28.140 --> 00:44:30.220 align:middle line:90% The x-axis remains unchanged. 00:44:30.220 --> 00:44:33.150 align:middle line:84% We're still incrementing the years linearly. 00:44:33.150 --> 00:44:37.670 align:middle line:84% But the y-axis is now logarithmic. 00:44:37.670 --> 00:44:39.970 align:middle line:90% So what do we notice? 00:44:39.970 --> 00:44:47.730 align:middle line:84% Well, I see a line here, and I see another line here. 00:44:47.730 --> 00:44:52.240 align:middle line:90% 00:44:52.240 --> 00:44:53.950 align:middle line:84% Again, linear growth on a log scale 00:44:53.950 --> 00:44:58.580 align:middle line:84% means exponential growth on a linear scale. 00:44:58.580 --> 00:45:01.750 align:middle line:84% So what we notice is that there's these two time 00:45:01.750 --> 00:45:03.580 align:middle line:90% periods of exponential growth. 00:45:03.580 --> 00:45:08.170 align:middle line:84% And in fact, those early years actually seem to be growing-- 00:45:08.170 --> 00:45:10.540 align:middle line:84% the population seems to be growing at a faster 00:45:10.540 --> 00:45:13.270 align:middle line:90% rate than the later years. 00:45:13.270 --> 00:45:17.050 align:middle line:84% And that was not readily visible on the previous graph 00:45:17.050 --> 00:45:18.610 align:middle line:90% that we had. 00:45:18.610 --> 00:45:20.070 align:middle line:90% So the question-- 00:45:20.070 --> 00:45:21.240 align:middle line:90% I have a question for you. 00:45:21.240 --> 00:45:23.410 align:middle line:84% Which one of those did you find more informative? 00:45:23.410 --> 00:45:25.320 align:middle line:84% Well, it kind of depends on what we're 00:45:25.320 --> 00:45:26.970 align:middle line:90% interested in finding out. 00:45:26.970 --> 00:45:30.480 align:middle line:84% If we're interested in big trends in the data, where 00:45:30.480 --> 00:45:35.010 align:middle line:84% in the top left one we spotted here the impacts of wars 00:45:35.010 --> 00:45:37.320 align:middle line:84% on the population, well, then the top 00:45:37.320 --> 00:45:39.310 align:middle line:90% left one is the one to look at. 00:45:39.310 --> 00:45:42.060 align:middle line:84% But if we visualize the data in a slightly different way, 00:45:42.060 --> 00:45:44.250 align:middle line:84% it gives us different insights into what's 00:45:44.250 --> 00:45:45.570 align:middle line:90% happened to the population. 00:45:45.570 --> 00:45:48.550 align:middle line:84% That wasn't as apparent in the previous graph. 00:45:48.550 --> 00:45:50.730 align:middle line:84% So it really kind of just depends 00:45:50.730 --> 00:45:55.890 align:middle line:84% on what you're interested in finding out 00:45:55.890 --> 00:45:59.130 align:middle line:84% which one of these plots you find more informative. 00:45:59.130 --> 00:46:04.410 align:middle line:84% And sometimes both are probably necessary to figure out 00:46:04.410 --> 00:46:06.710 align:middle line:90% exactly what happened. 00:46:06.710 --> 00:46:11.990 align:middle line:84% OK, so that finishes our example on the US population. 00:46:11.990 --> 00:46:15.850 align:middle line:84% Now let's look at a slightly different file. 00:46:15.850 --> 00:46:17.950 align:middle line:84% In this particular file, we're going 00:46:17.950 --> 00:46:20.810 align:middle line:90% to look at country populations. 00:46:20.810 --> 00:46:23.950 align:middle line:84% So these are the populations in a whole bunch 00:46:23.950 --> 00:46:25.690 align:middle line:84% of different countries-- or sorry, 00:46:25.690 --> 00:46:30.220 align:middle line:84% all the countries, ordered from countries with the highest 00:46:30.220 --> 00:46:33.790 align:middle line:84% population up at the top of the file down to the countries 00:46:33.790 --> 00:46:36.380 align:middle line:84% with the lowest population at the bottom of the file. 00:46:36.380 --> 00:46:38.440 align:middle line:84% So they are basically ranked in this order. 00:46:38.440 --> 00:46:41.170 align:middle line:84% So I know that this order is correct. 00:46:41.170 --> 00:46:46.250 align:middle line:84% So there's 237 lines in this file. 00:46:46.250 --> 00:46:47.760 align:middle line:84% What do we notice about the data? 00:46:47.760 --> 00:46:49.927 align:middle line:84% So we need to know what the data looks like in order 00:46:49.927 --> 00:46:50.870 align:middle line:90% to read the file in. 00:46:50.870 --> 00:46:56.540 align:middle line:84% And again, we're going to be interested in extracting 00:46:56.540 --> 00:46:57.470 align:middle line:90% certain parts of it. 00:46:57.470 --> 00:47:01.100 align:middle line:84% For the particular analysis I'm going to do next, 00:47:01.100 --> 00:47:03.900 align:middle line:84% I'm actually only interested in the population itself. 00:47:03.900 --> 00:47:05.900 align:middle line:90% So I don't care about the rank. 00:47:05.900 --> 00:47:09.890 align:middle line:84% And I don't actually care about the country either. 00:47:09.890 --> 00:47:12.220 align:middle line:90% So all that my-- 00:47:12.220 --> 00:47:14.510 align:middle line:84% the code that's going to read in the file 00:47:14.510 --> 00:47:17.390 align:middle line:84% will only be interested in extracting the population 00:47:17.390 --> 00:47:18.300 align:middle line:90% value. 00:47:18.300 --> 00:47:22.760 align:middle line:84% And notice, once again, we've got our commas here 00:47:22.760 --> 00:47:24.470 align:middle line:90% in the population values right. 00:47:24.470 --> 00:47:28.430 align:middle line:84% So we're going to use the same trick to get rid of those. 00:47:28.430 --> 00:47:31.640 align:middle line:84% Again, nice human-readable format here but not 00:47:31.640 --> 00:47:35.300 align:middle line:84% so good for reading in the file and dealing with the data 00:47:35.300 --> 00:47:35.900 align:middle line:90% itself. 00:47:35.900 --> 00:47:39.520 align:middle line:84% So we're going to have to take care of that when we read in. 00:47:39.520 --> 00:47:42.850 align:middle line:84% So here's the function that reads in the file. 00:47:42.850 --> 00:47:44.580 align:middle line:84% It's going to have a very similar feel 00:47:44.580 --> 00:47:46.020 align:middle line:90% to the previous one. 00:47:46.020 --> 00:47:48.120 align:middle line:84% Again, I've got a little sample of our file 00:47:48.120 --> 00:47:51.250 align:middle line:84% up here just to remind ourselves what it looks like. 00:47:51.250 --> 00:47:54.510 align:middle line:84% So this particular file, I'm only interested in grabbing 00:47:54.510 --> 00:47:56.080 align:middle line:90% the population value. 00:47:56.080 --> 00:47:59.440 align:middle line:84% And it's actually a tab-separated file. 00:47:59.440 --> 00:48:04.890 align:middle line:84% So I've got rank, tab, country, tab, population, tab, and then 00:48:04.890 --> 00:48:06.250 align:middle line:90% the date. 00:48:06.250 --> 00:48:12.060 align:middle line:84% So when I take a line of code what I'm first going to do 00:48:12.060 --> 00:48:14.730 align:middle line:84% is split it on the tab character. 00:48:14.730 --> 00:48:18.530 align:middle line:84% And the tab character is this backslash t thing. 00:48:18.530 --> 00:48:23.090 align:middle line:84% So once I split it on the tab character, the thing at index 0 00:48:23.090 --> 00:48:25.740 align:middle line:84% is my rank, the thing at index 1 is my country, 00:48:25.740 --> 00:48:28.040 align:middle line:84% and the thing at index 2 is my population. 00:48:28.040 --> 00:48:31.050 align:middle line:90% The thing at index 3 is my date. 00:48:31.050 --> 00:48:33.590 align:middle line:84% So if I'm only interested in grabbing the population, 00:48:33.590 --> 00:48:36.350 align:middle line:84% I'm going to look at the thing at index 2, 00:48:36.350 --> 00:48:40.130 align:middle line:84% and this gives me the population as a string here. 00:48:40.130 --> 00:48:41.870 align:middle line:84% And then we do the exact same trick 00:48:41.870 --> 00:48:45.560 align:middle line:84% as before to eliminate the commas. 00:48:45.560 --> 00:48:47.600 align:middle line:84% There's no space in this particular case 00:48:47.600 --> 00:48:52.370 align:middle line:84% because I've just got the number saved because of my tab split. 00:48:52.370 --> 00:48:55.610 align:middle line:84% So all I need to do is keep digits. 00:48:55.610 --> 00:48:58.070 align:middle line:84% And then if I keep the digits, then I'm 00:48:58.070 --> 00:49:00.950 align:middle line:84% just going to keep that number as a population. 00:49:00.950 --> 00:49:02.810 align:middle line:84% Again, I cast it to an integer because I 00:49:02.810 --> 00:49:05.600 align:middle line:84% would like to work with numbers in my lists as opposed 00:49:05.600 --> 00:49:06.620 align:middle line:90% to strings. 00:49:06.620 --> 00:49:07.670 align:middle line:90% That would be very weird. 00:49:07.670 --> 00:49:12.230 align:middle line:84% And at the end of this function, I've got all of the populations 00:49:12.230 --> 00:49:15.380 align:middle line:84% in the same order that they were in that file read 00:49:15.380 --> 00:49:19.010 align:middle line:84% in as a list, numbers not strings. 00:49:19.010 --> 00:49:22.370 align:middle line:84% And so if we plot the populations, just 00:49:22.370 --> 00:49:26.000 align:middle line:84% pure populations, I'm going to have something like this. 00:49:26.000 --> 00:49:32.980 align:middle line:90% 00:49:32.980 --> 00:49:34.990 align:middle line:84% If I plot just the pure populations, 00:49:34.990 --> 00:49:37.120 align:middle line:84% I see something that looks like this. 00:49:37.120 --> 00:49:38.480 align:middle line:90% Kind of hard to tell-- 00:49:38.480 --> 00:49:40.240 align:middle line:84% I mean, it's a big exponential decrease, 00:49:40.240 --> 00:49:43.430 align:middle line:90% but is that really what it is? 00:49:43.430 --> 00:49:47.560 align:middle line:84% So again, we'll do a little semi-log plot on the y-axis 00:49:47.560 --> 00:49:51.025 align:middle line:84% to see exactly if there's any sort of linear action going on 00:49:51.025 --> 00:49:52.480 align:middle line:90% on that log plot. 00:49:52.480 --> 00:49:57.760 align:middle line:84% And unsurprisingly, it kind of matches our intuition. 00:49:57.760 --> 00:50:00.100 align:middle line:84% There are very few countries that 00:50:00.100 --> 00:50:02.060 align:middle line:90% have a really high population. 00:50:02.060 --> 00:50:05.620 align:middle line:84% There are very few countries that have a low population. 00:50:05.620 --> 00:50:08.920 align:middle line:84% And then a bunch of countries that are kind of in the middle 00:50:08.920 --> 00:50:12.370 align:middle line:84% here where the population just exponentially decreases. 00:50:12.370 --> 00:50:15.230 align:middle line:90% 00:50:15.230 --> 00:50:18.950 align:middle line:84% All right, but that's not the analysis 00:50:18.950 --> 00:50:24.990 align:middle line:84% I would like to do on this data because that's kind of boring. 00:50:24.990 --> 00:50:27.720 align:middle line:84% So instead what we're going to analyze 00:50:27.720 --> 00:50:32.910 align:middle line:84% is actually just the first digits from every country's 00:50:32.910 --> 00:50:35.010 align:middle line:90% population. 00:50:35.010 --> 00:50:39.630 align:middle line:84% So what I'd like to do from that data set is once I've grabbed 00:50:39.630 --> 00:50:42.810 align:middle line:84% a list of all of the country populations, 00:50:42.810 --> 00:50:46.150 align:middle line:84% I am going to extract that first digit. 00:50:46.150 --> 00:50:50.340 align:middle line:84% So the way we do it is if we have a population, 00:50:50.340 --> 00:50:58.500 align:middle line:84% I don't know, 2542136, whatever, I'm going to take this number, 00:50:58.500 --> 00:51:00.090 align:middle line:90% cast it to a string. 00:51:00.090 --> 00:51:03.510 align:middle line:84% That's what this one line of code is doing all in one. 00:51:03.510 --> 00:51:06.150 align:middle line:84% It casts it to a string, extracts 00:51:06.150 --> 00:51:08.190 align:middle line:90% the element at index 0. 00:51:08.190 --> 00:51:10.470 align:middle line:90% This becomes the string 2. 00:51:10.470 --> 00:51:17.370 align:middle line:84% And then we cast that to an integer to give us 2. 00:51:17.370 --> 00:51:20.490 align:middle line:84% So that line of code does all of those steps in order. 00:51:20.490 --> 00:51:25.500 align:middle line:84% So at the end of this loop, I've got this first digits list 00:51:25.500 --> 00:51:28.680 align:middle line:84% that contains all of the first digits of every single one 00:51:28.680 --> 00:51:32.030 align:middle line:90% of those country populations. 00:51:32.030 --> 00:51:33.880 align:middle line:84% So I'll print that for you, just to give you 00:51:33.880 --> 00:51:35.450 align:middle line:90% a sense of what it looks like. 00:51:35.450 --> 00:51:37.240 align:middle line:90% So we see this. 00:51:37.240 --> 00:51:40.330 align:middle line:84% So we had two countries up at the top 00:51:40.330 --> 00:51:42.310 align:middle line:90% that had 1 billion people-- 00:51:42.310 --> 00:51:43.510 align:middle line:90% 1 billion people. 00:51:43.510 --> 00:51:46.720 align:middle line:84% Then the next country down had 300 million people, 00:51:46.720 --> 00:51:48.980 align:middle line:84% then 200 million, then 200 million, then 200 million, 00:51:48.980 --> 00:51:50.890 align:middle line:90% 100 million, and so on. 00:51:50.890 --> 00:51:52.960 align:middle line:84% So just extracting that first digit, 00:51:52.960 --> 00:51:58.580 align:middle line:90% we see this pattern of values. 00:51:58.580 --> 00:52:00.980 align:middle line:90% So if we plot that-- 00:52:00.980 --> 00:52:02.760 align:middle line:84% so that's exactly what we do down here, 00:52:02.760 --> 00:52:04.250 align:middle line:84% and I'll just do it in the slides. 00:52:04.250 --> 00:52:07.790 align:middle line:84% If we plot that list in that order, 00:52:07.790 --> 00:52:11.520 align:middle line:84% we get a plot that looks something like this. 00:52:11.520 --> 00:52:15.680 align:middle line:84% It's a nice little sawtooth pattern. 00:52:15.680 --> 00:52:20.210 align:middle line:84% And if we stare at it a bit, it makes sense because the numbers 00:52:20.210 --> 00:52:25.310 align:middle line:84% that we got right from the file were already in ranked order 00:52:25.310 --> 00:52:29.050 align:middle line:84% highest population to the lowest population. 00:52:29.050 --> 00:52:34.540 align:middle line:90% So down here, we had-- 00:52:34.540 --> 00:52:36.180 align:middle line:84% sorry, down here, this little dot right 00:52:36.180 --> 00:52:40.080 align:middle line:84% here had two countries that were 1 billion, so 1, 1, 00:52:40.080 --> 00:52:43.080 align:middle line:84% and then had one country that had 300 million. 00:52:43.080 --> 00:52:45.780 align:middle line:84% And then it had three countries that had 200 million, 00:52:45.780 --> 00:52:49.890 align:middle line:84% then a bunch of countries that had 100 million something, so 00:52:49.890 --> 00:52:51.390 align:middle line:90% 1, 1, 1, 1, 1, 1. 00:52:51.390 --> 00:52:54.300 align:middle line:84% And then, since we're going in decreasing order in terms 00:52:54.300 --> 00:52:56.790 align:middle line:84% of rank, once we've finished going 00:52:56.790 --> 00:52:58.715 align:middle line:84% to that significant digit, when we move down, 00:52:58.715 --> 00:53:00.840 align:middle line:84% then we're going to start looking at countries that 00:53:00.840 --> 00:53:04.980 align:middle line:84% have 90 million, 90 million, 90 million, 80 million, 00:53:04.980 --> 00:53:06.280 align:middle line:90% 80 million, and so on. 00:53:06.280 --> 00:53:10.470 align:middle line:84% So just the order of all of these values, the first digits 00:53:10.470 --> 00:53:12.900 align:middle line:84% of every one of these values, it makes sense 00:53:12.900 --> 00:53:14.700 align:middle line:84% to have that sawtooth pattern, right? 00:53:14.700 --> 00:53:19.340 align:middle line:84% We basically have 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 00:53:19.340 --> 00:53:20.400 align:middle line:90% 3, 2, 1, and so on. 00:53:20.400 --> 00:53:24.220 align:middle line:90% 00:53:24.220 --> 00:53:26.970 align:middle line:90% So we get this pattern. 00:53:26.970 --> 00:53:32.940 align:middle line:84% What I'd like to do is ask how many countries 00:53:32.940 --> 00:53:36.180 align:middle line:90% have their first digit a 1? 00:53:36.180 --> 00:53:37.830 align:middle line:84% It seems like there's a lot, right? 00:53:37.830 --> 00:53:41.220 align:middle line:84% If we count how many of these countries are down here, 00:53:41.220 --> 00:53:42.540 align:middle line:90% it seems to be a lot. 00:53:42.540 --> 00:53:44.850 align:middle line:84% How many countries have a first digit of 2? 00:53:44.850 --> 00:53:46.500 align:middle line:84% So again, we count how many countries 00:53:46.500 --> 00:53:48.600 align:middle line:90% are on this step of my sawtooth. 00:53:48.600 --> 00:53:51.450 align:middle line:84% How many countries have the first digit 3? 00:53:51.450 --> 00:53:52.470 align:middle line:90% And so on. 00:53:52.470 --> 00:53:55.110 align:middle line:84% And it kind of looks like, I don't know, 00:53:55.110 --> 00:53:58.230 align:middle line:84% maybe there are more countries that have a first digit of 1 00:53:58.230 --> 00:54:01.260 align:middle line:84% than there are countries that have a first digit of 9, right? 00:54:01.260 --> 00:54:03.870 align:middle line:84% There's only a couple here, maybe like five here, 00:54:03.870 --> 00:54:05.790 align:middle line:84% maybe one here, a couple here, a couple 00:54:05.790 --> 00:54:08.520 align:middle line:84% here, whereas the number of countries that have a 1 00:54:08.520 --> 00:54:10.470 align:middle line:90% are actually a lot. 00:54:10.470 --> 00:54:14.770 align:middle line:84% So let's try to plot this data, the values here. 00:54:14.770 --> 00:54:18.820 align:middle line:84% So what I'm interested in doing is creating a histogram. 00:54:18.820 --> 00:54:23.730 align:middle line:84% So a histogram on the x-axis has a bunch of bins. 00:54:23.730 --> 00:54:27.090 align:middle line:84% In this particular case, the way I'd like to bin my data 00:54:27.090 --> 00:54:29.700 align:middle line:84% is by saying my bins are going to be the 00:54:29.700 --> 00:54:33.800 align:middle line:84% digits 1, 2, 3, 4, 5, 6, 7, 8, and 9. 00:54:33.800 --> 00:54:34.940 align:middle line:90% That's the x-axis. 00:54:34.940 --> 00:54:38.840 align:middle line:84% And the y-axis is going to be a count, a frequency of how 00:54:38.840 --> 00:54:41.870 align:middle line:84% many of my countries have the number 00:54:41.870 --> 00:54:44.630 align:middle line:84% 1 as their first digit, how many countries have the number 00:54:44.630 --> 00:54:46.860 align:middle line:90% 2 as my first digit, and so on. 00:54:46.860 --> 00:54:49.670 align:middle line:84% So in terms of this list containing 00:54:49.670 --> 00:54:52.370 align:middle line:84% all of the first digits of the countries, 00:54:52.370 --> 00:54:54.320 align:middle line:90% I'm essentially have-- 00:54:54.320 --> 00:54:57.290 align:middle line:84% I essentially have one bin that counts how many ones I 00:54:57.290 --> 00:55:00.370 align:middle line:84% have in this list, another bin that counts how many twos 00:55:00.370 --> 00:55:02.870 align:middle line:84% I have in this list, another bin that counts how many threes 00:55:02.870 --> 00:55:06.920 align:middle line:90% I have in this list, and so on. 00:55:06.920 --> 00:55:12.060 align:middle line:84% So if I plot that histogram, it looks like this. 00:55:12.060 --> 00:55:15.470 align:middle line:84% Now, I would have expected this histogram 00:55:15.470 --> 00:55:18.680 align:middle line:90% to be about even, right? 00:55:18.680 --> 00:55:22.310 align:middle line:84% Why does it matter the first digit? 00:55:22.310 --> 00:55:24.870 align:middle line:84% It seems like in this particular case, 00:55:24.870 --> 00:55:28.790 align:middle line:84% the first digit has a higher probability of being a 1 00:55:28.790 --> 00:55:29.720 align:middle line:90% than being a 9. 00:55:29.720 --> 00:55:33.080 align:middle line:84% But intuitively, I would've expected every digit 00:55:33.080 --> 00:55:37.580 align:middle line:84% to come out with equal probability, 11%, 1 over 9. 00:55:37.580 --> 00:55:40.890 align:middle line:84% But instead what we get is this really surprising result, 00:55:40.890 --> 00:55:46.538 align:middle line:84% which is that the first digit seems to be about 30%. 00:55:46.538 --> 00:55:48.830 align:middle line:84% To have the first-- sorry, to have the first digit of 1 00:55:48.830 --> 00:55:51.170 align:middle line:90% seems to be about 30%. 00:55:51.170 --> 00:55:53.870 align:middle line:84% To have the first digit being a 2 00:55:53.870 --> 00:55:58.100 align:middle line:84% seems to be about 18 or something percent, 00:55:58.100 --> 00:55:59.400 align:middle line:90% and so on and so on. 00:55:59.400 --> 00:56:02.100 align:middle line:84% And then the first digit being a 9 is pretty low. 00:56:02.100 --> 00:56:07.710 align:middle line:84% It's going to be about, what is this, 12 out of 200 countries. 00:56:07.710 --> 00:56:10.850 align:middle line:90% So pretty low probability. 00:56:10.850 --> 00:56:14.080 align:middle line:84% So as it turns out, this graph actually 00:56:14.080 --> 00:56:17.820 align:middle line:84% follows something called Benford's law. 00:56:17.820 --> 00:56:20.110 align:middle line:90% And this is a well-proven law. 00:56:20.110 --> 00:56:22.440 align:middle line:84% It applies to a bunch of different data sets 00:56:22.440 --> 00:56:23.970 align:middle line:84% that we find in nature, data sets 00:56:23.970 --> 00:56:26.940 align:middle line:84% that don't really have upper or lower bounds, 00:56:26.940 --> 00:56:29.650 align:middle line:90% like country populations. 00:56:29.650 --> 00:56:33.780 align:middle line:84% So Benford's law effectively says the probability 00:56:33.780 --> 00:56:40.350 align:middle line:84% of the first digit in some big set of numbers being a 1, a 2, 00:56:40.350 --> 00:56:44.720 align:middle line:84% a 3, whatever-- this d being the 1, a 2, or 3, or whatever-- 00:56:44.720 --> 00:56:45.990 align:middle line:90% is according to this formula. 00:56:45.990 --> 00:56:49.700 align:middle line:84% So if we find the probability of that first digit being a 1, 00:56:49.700 --> 00:56:55.920 align:middle line:84% we basically find log base 10 of 2, which is about 0.28. 00:56:55.920 --> 00:56:59.070 align:middle line:84% Probability of that first digit being a 2 is log base 00:56:59.070 --> 00:57:03.000 align:middle line:84% 10 of 1 and 1/2, which is about 0.17. 00:57:03.000 --> 00:57:07.650 align:middle line:84% So our data, the country populations, 00:57:07.650 --> 00:57:10.810 align:middle line:84% if we look at just the first digit of our data, 00:57:10.810 --> 00:57:16.120 align:middle line:84% it also follows this law, which is pretty neat. 00:57:16.120 --> 00:57:20.470 align:middle line:84% So a lot of data that we deal with on a daily basis 00:57:20.470 --> 00:57:24.190 align:middle line:84% follows this law, number of social media followers, 00:57:24.190 --> 00:57:27.820 align:middle line:84% number of posts people make, stock values, grocery prices, 00:57:27.820 --> 00:57:32.260 align:middle line:84% sports statistics, building heights, income taxes, things 00:57:32.260 --> 00:57:38.270 align:middle line:84% like that all follow this law, which is pretty cool. 00:57:38.270 --> 00:57:43.760 align:middle line:84% As an aside, one of the ways that people figure out 00:57:43.760 --> 00:57:48.590 align:middle line:84% tax fraud on income taxes is by applying Benford's law 00:57:48.590 --> 00:57:50.600 align:middle line:90% to income taxes submitted. 00:57:50.600 --> 00:57:53.300 align:middle line:84% People, when they submit fraudulent numbers, 00:57:53.300 --> 00:57:55.850 align:middle line:84% they tend to make every number come up 00:57:55.850 --> 00:57:57.320 align:middle line:90% with an equal probability. 00:57:57.320 --> 00:57:59.190 align:middle line:90% They forget about Benford's law. 00:57:59.190 --> 00:58:03.920 align:middle line:84% And so they run this Benford's law on potentially fraudulent 00:58:03.920 --> 00:58:05.630 align:middle line:90% tax submissions. 00:58:05.630 --> 00:58:08.898 align:middle line:84% And they figure out that whatever those people submitted 00:58:08.898 --> 00:58:10.190 align:middle line:90% don't actually follow this law. 00:58:10.190 --> 00:58:11.930 align:middle line:90% And hence, it's fraudulent. 00:58:11.930 --> 00:58:18.830 align:middle line:84% So if you're making up numbers, just remember Benford's law. 00:58:18.830 --> 00:58:19.580 align:middle line:90% Cool. 00:58:19.580 --> 00:58:24.380 align:middle line:84% So yeah, that's a really interesting thing 00:58:24.380 --> 00:58:26.240 align:middle line:90% that can come out of some data. 00:58:26.240 --> 00:58:31.130 align:middle line:84% And again, we got to visualize it and see the law in action. 00:58:31.130 --> 00:58:34.460 align:middle line:84% OK, one last example I want to go through. 00:58:34.460 --> 00:58:39.145 align:middle line:84% This one will show a bunch of different things. 00:58:39.145 --> 00:58:40.520 align:middle line:84% It's going to have a lot of code. 00:58:40.520 --> 00:58:42.187 align:middle line:84% I'm just going to briefly talk about it. 00:58:42.187 --> 00:58:43.850 align:middle line:90% But the code is in the slides-- 00:58:43.850 --> 00:58:45.710 align:middle line:84% or sorry, in the Python file if you want 00:58:45.710 --> 00:58:48.210 align:middle line:90% to look at it more in depth. 00:58:48.210 --> 00:58:51.540 align:middle line:84% I'm going to compare city temperatures again, 00:58:51.540 --> 00:58:54.230 align:middle line:84% but we're going to do a more in-depth analysis dealing 00:58:54.230 --> 00:58:56.370 align:middle line:90% with a whole bunch more data. 00:58:56.370 --> 00:58:58.940 align:middle line:84% So this particular data set, I've 00:58:58.940 --> 00:59:06.030 align:middle line:84% got daily temperatures for 55 years for 21 different cities. 00:59:06.030 --> 00:59:08.870 align:middle line:84% So the amount of data that I have here 00:59:08.870 --> 00:59:14.370 align:middle line:84% is going to be 365 times 55 times 21. 00:59:14.370 --> 00:59:18.300 align:middle line:84% So that's how many rows would exist in my data set. 00:59:18.300 --> 00:59:21.870 align:middle line:84% So that's a lot of numbers to look at manually. 00:59:21.870 --> 00:59:25.250 align:middle line:84% So instead, we're going to rely on aggregating it 00:59:25.250 --> 00:59:27.620 align:middle line:84% with averages and things like that to make 00:59:27.620 --> 00:59:30.170 align:middle line:90% sense of all of this data. 00:59:30.170 --> 00:59:32.170 align:middle line:84% So this is what the file would look like. 00:59:32.170 --> 00:59:34.870 align:middle line:84% I've got three columns, effectively, 00:59:34.870 --> 00:59:36.530 align:middle line:90% separated by commas. 00:59:36.530 --> 00:59:39.220 align:middle line:84% So the first one corresponds to the city. 00:59:39.220 --> 00:59:43.660 align:middle line:84% Second one corresponds to the temperature in Celsius. 00:59:43.660 --> 00:59:46.940 align:middle line:84% And the third one is the date that it was taken. 00:59:46.940 --> 00:59:48.610 align:middle line:90% So it's nicely in order. 00:59:48.610 --> 00:59:52.250 align:middle line:84% The date is delineated like this. 00:59:52.250 --> 00:59:55.210 align:middle line:84% So it's got year, year, year, year, month, month, day, day. 00:59:55.210 --> 00:59:57.520 align:middle line:90% So this is 1961, January 4. 00:59:57.520 --> 00:59:58.990 align:middle line:90% That's how we would read that. 00:59:58.990 --> 01:00:03.580 align:middle line:84% So later, when we're trying to think about which one of-- 01:00:03.580 --> 01:00:07.360 align:middle line:84% grabbing particular temperatures for a specific year or things 01:00:07.360 --> 01:00:09.920 align:middle line:84% like that, then we can use the format-- 01:00:09.920 --> 01:00:11.440 align:middle line:84% keep the format in mind and use that 01:00:11.440 --> 01:00:14.410 align:middle line:84% to extract the relevant information. 01:00:14.410 --> 01:00:18.340 align:middle line:84% OK, so the first thing we want to do is to grab this data 01:00:18.340 --> 01:00:21.760 align:middle line:84% and save it again in a nice data structure that 01:00:21.760 --> 01:00:24.400 align:middle line:84% allows us to manipulate it to our heart's content. 01:00:24.400 --> 01:00:25.880 align:middle line:90% That is a list. 01:00:25.880 --> 01:00:29.620 align:middle line:84% So we're going to open up our file for reading. 01:00:29.620 --> 01:00:32.950 align:middle line:84% I'm creating two lists here, one for the temperatures, 01:00:32.950 --> 01:00:34.300 align:middle line:90% the other one for the dates. 01:00:34.300 --> 01:00:36.520 align:middle line:84% I'm going to loop through each line in my file. 01:00:36.520 --> 01:00:38.350 align:middle line:84% And I know it's comma-separated, so I'm 01:00:38.350 --> 01:00:39.970 align:middle line:90% going to split it on the comma. 01:00:39.970 --> 01:00:42.490 align:middle line:84% The thing at index 0 will be my date-- 01:00:42.490 --> 01:00:43.600 align:middle line:90% will be my city. 01:00:43.600 --> 01:00:46.210 align:middle line:84% The thing at index 1 will be my temperature value. 01:00:46.210 --> 01:00:49.180 align:middle line:84% The thing at index 2 will be my date. 01:00:49.180 --> 01:00:51.820 align:middle line:84% I would like to take the temperature value 01:00:51.820 --> 01:00:56.660 align:middle line:84% and save it as a number because I want to plot these numbers. 01:00:56.660 --> 01:01:01.040 align:middle line:84% This specific function will get a list 01:01:01.040 --> 01:01:03.870 align:middle line:84% of all of the temperatures for a particular city. 01:01:03.870 --> 01:01:06.360 align:middle line:84% So the city here is going to be a parameter. 01:01:06.360 --> 01:01:09.290 align:middle line:84% So as I'm reading the file, I would only 01:01:09.290 --> 01:01:12.450 align:middle line:84% like to grab the lines that match that city. 01:01:12.450 --> 01:01:14.580 align:middle line:84% So here I've got this if statement. 01:01:14.580 --> 01:01:17.640 align:middle line:84% So I'm only going to do this stuff inside this if statement 01:01:17.640 --> 01:01:20.870 align:middle line:84% if the city is matching what I'm interested in. 01:01:20.870 --> 01:01:22.380 align:middle line:90% And then what do we do? 01:01:22.380 --> 01:01:24.650 align:middle line:84% Well, we're going to take our temperature value, which 01:01:24.650 --> 01:01:28.800 align:middle line:84% is the thing at index 1, because I've split on the commas. 01:01:28.800 --> 01:01:29.940 align:middle line:90% Convert it to a float. 01:01:29.940 --> 01:01:33.340 align:middle line:84% There's no commas or anything weird like in that number. 01:01:33.340 --> 01:01:36.450 align:middle line:84% So it's just a pure float, 0.55 as a string. 01:01:36.450 --> 01:01:40.140 align:middle line:84% If we cast it to a float, Python will happily do that for us. 01:01:40.140 --> 01:01:45.630 align:middle line:84% Then we're going to run a Celsius to Fahrenheit function, 01:01:45.630 --> 01:01:49.320 align:middle line:84% throwback to lecture 1, to convert that Celsius 01:01:49.320 --> 01:01:50.730 align:middle line:90% to Fahrenheit value. 01:01:50.730 --> 01:01:53.400 align:middle line:84% And then we're going to append all of these temperatures 01:01:53.400 --> 01:01:55.248 align:middle line:90% in a nice list. 01:01:55.248 --> 01:01:56.790 align:middle line:84% And at the end of the function, we're 01:01:56.790 --> 01:01:58.332 align:middle line:84% going to return all the temperatures. 01:01:58.332 --> 01:02:01.470 align:middle line:84% So it's going to be 365 times 55. 01:02:01.470 --> 01:02:06.050 align:middle line:84% That's how many temperature values we have for one city. 01:02:06.050 --> 01:02:09.230 align:middle line:84% And what we'd like to do as a first step 01:02:09.230 --> 01:02:12.260 align:middle line:84% is to just get a sense of the average temperatures 01:02:12.260 --> 01:02:14.820 align:middle line:84% for each one of these different cities. 01:02:14.820 --> 01:02:17.660 align:middle line:84% So over every single data point that we 01:02:17.660 --> 01:02:21.650 align:middle line:84% have for a particular city, what is the average temperature 01:02:21.650 --> 01:02:23.940 align:middle line:84% over all these days for all of these years? 01:02:23.940 --> 01:02:26.120 align:middle line:84% So I would one number to represent 01:02:26.120 --> 01:02:28.600 align:middle line:90% the temperature per city. 01:02:28.600 --> 01:02:30.460 align:middle line:84% So that's what this code is doing. 01:02:30.460 --> 01:02:33.640 align:middle line:84% It's going to first get all of the cities that are in my file, 01:02:33.640 --> 01:02:35.360 align:middle line:90% so all the unique values. 01:02:35.360 --> 01:02:39.580 align:middle line:84% Then it's going to get the average temperature over all 01:02:39.580 --> 01:02:42.550 align:middle line:90% of those 365 times 55 years. 01:02:42.550 --> 01:02:45.490 align:middle line:84% Then it's going to grab the name of my city 01:02:45.490 --> 01:02:47.530 align:middle line:84% as just the first two characters, 01:02:47.530 --> 01:02:50.480 align:middle line:84% and then it's going to create a nice scatter plot. 01:02:50.480 --> 01:02:54.110 align:middle line:84% So I don't want to link all of these city values together. 01:02:54.110 --> 01:02:58.060 align:middle line:84% I would just like them to be dots in my plot. 01:02:58.060 --> 01:03:01.100 align:middle line:84% If we do that, we get something that looks like this. 01:03:01.100 --> 01:03:05.860 align:middle line:84% So this point here represents the temperature in Seattle 01:03:05.860 --> 01:03:08.510 align:middle line:90% over every day over 55 years. 01:03:08.510 --> 01:03:12.160 align:middle line:84% So one temperature point that represents the Seattle 01:03:12.160 --> 01:03:15.420 align:middle line:84% temperature for all of this data that I've got. 01:03:15.420 --> 01:03:16.990 align:middle line:90% What does this tell us? 01:03:16.990 --> 01:03:20.490 align:middle line:84% Well, not much that we didn't already know. 01:03:20.490 --> 01:03:23.250 align:middle line:84% I've got these cities down here that 01:03:23.250 --> 01:03:29.100 align:middle line:84% are super cold and those cities up there that are super warm. 01:03:29.100 --> 01:03:31.380 align:middle line:84% And then all the rest of my cities 01:03:31.380 --> 01:03:33.510 align:middle line:84% are somewhere in the middle on average. 01:03:33.510 --> 01:03:36.690 align:middle line:84% So nothing that we didn't really know, nothing groundbreaking 01:03:36.690 --> 01:03:37.870 align:middle line:90% here. 01:03:37.870 --> 01:03:40.090 align:middle line:84% What would be a nicer thing to look at 01:03:40.090 --> 01:03:43.570 align:middle line:84% is the temperature change over time. 01:03:43.570 --> 01:03:49.140 align:middle line:84% So here, my one data point tells me the temperature 01:03:49.140 --> 01:03:50.550 align:middle line:90% that represents that city. 01:03:50.550 --> 01:03:52.230 align:middle line:84% But what I would like to do is grab 01:03:52.230 --> 01:03:56.110 align:middle line:84% the temperature that represents that city for each year. 01:03:56.110 --> 01:03:59.490 align:middle line:84% So for each year, I would like to get the average temperature 01:03:59.490 --> 01:04:00.120 align:middle line:90% for that year. 01:04:00.120 --> 01:04:02.880 align:middle line:84% And maybe I could see a trend for the temperatures 01:04:02.880 --> 01:04:07.590 align:middle line:84% getting warmer over time or cooling over time or something 01:04:07.590 --> 01:04:10.120 align:middle line:84% like-- or not having any change at all. 01:04:10.120 --> 01:04:12.330 align:middle line:84% So this is the code that does that. 01:04:12.330 --> 01:04:15.360 align:middle line:84% I've got get temperatures by year for city. 01:04:15.360 --> 01:04:17.410 align:middle line:84% This is kind of the function that gets run. 01:04:17.410 --> 01:04:19.270 align:middle line:90% And it calls the one at the top. 01:04:19.270 --> 01:04:22.890 align:middle line:84% So here I've got the code from the previous slide. 01:04:22.890 --> 01:04:24.660 align:middle line:84% It gets a list of all the temperatures 01:04:24.660 --> 01:04:29.090 align:middle line:84% for a particular city, so over all those 55 years. 01:04:29.090 --> 01:04:32.610 align:middle line:84% And then I'm interested in all of these different years. 01:04:32.610 --> 01:04:34.250 align:middle line:84% So for each one of these years, I'm 01:04:34.250 --> 01:04:37.370 align:middle line:84% going to get a temperature value. 01:04:37.370 --> 01:04:40.220 align:middle line:84% This getTempsForYear is the function up there. 01:04:40.220 --> 01:04:44.090 align:middle line:84% And all it does is it looks at that third column and grabs 01:04:44.090 --> 01:04:44.840 align:middle line:90% the year. 01:04:44.840 --> 01:04:49.940 align:middle line:84% It matches those first four characters of the year entry. 01:04:49.940 --> 01:04:51.960 align:middle line:84% And as long as it matches that year, 01:04:51.960 --> 01:04:54.530 align:middle line:84% then it's going to get added to this running sum. 01:04:54.530 --> 01:05:00.470 align:middle line:84% And at the end, I'm going to get the average for the year. 01:05:00.470 --> 01:05:04.470 align:middle line:84% And let's say that I'm going to compare four different cities. 01:05:04.470 --> 01:05:09.050 align:middle line:84% So I've got 55 values for each city representing 01:05:09.050 --> 01:05:12.290 align:middle line:84% the average temperature in those 55 years. 01:05:12.290 --> 01:05:14.660 align:middle line:84% And I've got four cities to compare. 01:05:14.660 --> 01:05:17.630 align:middle line:84% So this is what one plot would look like for Boston-- 01:05:17.630 --> 01:05:19.910 align:middle line:84% sorry, so this is what the plot would look like. 01:05:19.910 --> 01:05:22.370 align:middle line:84% I've got one line for Boston, that's the blue; 01:05:22.370 --> 01:05:24.440 align:middle line:84% one line for San Diego, the red; one line 01:05:24.440 --> 01:05:29.710 align:middle line:84% for Phoenix, the orange; and one line for Miami, the green. 01:05:29.710 --> 01:05:30.740 align:middle line:90% What do we see? 01:05:30.740 --> 01:05:34.900 align:middle line:84% Well, yes, Boston on average is a lot colder 01:05:34.900 --> 01:05:36.610 align:middle line:84% than any of the three other cities. 01:05:36.610 --> 01:05:37.110 align:middle line:90% Cool. 01:05:37.110 --> 01:05:39.340 align:middle line:90% We knew that. 01:05:39.340 --> 01:05:42.550 align:middle line:84% Miami and Phoenix are nicely hot there. 01:05:42.550 --> 01:05:43.870 align:middle line:90% I'd like to be there right now. 01:05:43.870 --> 01:05:46.090 align:middle line:90% And what about trends? 01:05:46.090 --> 01:05:47.870 align:middle line:84% This is why we did this analysis. 01:05:47.870 --> 01:05:49.540 align:middle line:84% What do we see from the trends here? 01:05:49.540 --> 01:05:52.690 align:middle line:84% Well, the Boston temperature maybe increases a little bit 01:05:52.690 --> 01:05:54.430 align:middle line:90% slightly over time. 01:05:54.430 --> 01:05:57.490 align:middle line:84% San Diego, it seems to stay about steady. 01:05:57.490 --> 01:06:01.210 align:middle line:84% The Phoenix one seems to increase 01:06:01.210 --> 01:06:05.230 align:middle line:84% pretty dramatically as time has gone by, on average. 01:06:05.230 --> 01:06:09.680 align:middle line:84% And the Miami one maybe also slightly increased. 01:06:09.680 --> 01:06:12.660 align:middle line:84% But this only tells us average temperatures. 01:06:12.660 --> 01:06:17.870 align:middle line:84% So one thing that we can do is check out the extremes. 01:06:17.870 --> 01:06:20.600 align:middle line:84% In addition to plotting the average, 01:06:20.600 --> 01:06:23.990 align:middle line:84% let's also plot the minimum for Boston 01:06:23.990 --> 01:06:28.600 align:middle line:84% and the maximum for Boston and see exactly how 01:06:28.600 --> 01:06:30.250 align:middle line:90% close that average is. 01:06:30.250 --> 01:06:32.140 align:middle line:84% Is the average in the middle and then 01:06:32.140 --> 01:06:34.360 align:middle line:84% the minimum and maximums are super far away 01:06:34.360 --> 01:06:35.230 align:middle line:90% from the average? 01:06:35.230 --> 01:06:38.780 align:middle line:84% Or are they all pretty much close to the average? 01:06:38.780 --> 01:06:41.320 align:middle line:84% So this is the code that does that. 01:06:41.320 --> 01:06:45.790 align:middle line:84% The function here is exactly the same as on the previous slide. 01:06:45.790 --> 01:06:48.880 align:middle line:84% The only difference is instead of returning the average, 01:06:48.880 --> 01:06:51.850 align:middle line:84% we're also going to grab the max and the min 01:06:51.850 --> 01:06:56.060 align:middle line:90% for that list of temperatures. 01:06:56.060 --> 01:07:00.050 align:middle line:84% And then we've got all of the different cities 01:07:00.050 --> 01:07:01.490 align:middle line:90% to plot this for. 01:07:01.490 --> 01:07:05.870 align:middle line:84% So we get something that looks like this. 01:07:05.870 --> 01:07:11.470 align:middle line:84% Again, at first glance, I tend to ignore the y-axes 01:07:11.470 --> 01:07:12.460 align:middle line:90% at first glance. 01:07:12.460 --> 01:07:15.430 align:middle line:84% So at first glance again, it looks 01:07:15.430 --> 01:07:19.397 align:middle line:84% like, hey, the minimums are pretty much the same, 01:07:19.397 --> 01:07:20.980 align:middle line:84% the maximums are pretty much the same, 01:07:20.980 --> 01:07:22.790 align:middle line:84% averages are pretty much the same. 01:07:22.790 --> 01:07:24.770 align:middle line:84% So, misleading to think about that. 01:07:24.770 --> 01:07:28.840 align:middle line:84% So once again, let's help the reader 01:07:28.840 --> 01:07:32.500 align:middle line:90% and set limits on our y-axes. 01:07:32.500 --> 01:07:36.910 align:middle line:84% So here, I've got a limit to my function or to my code. 01:07:36.910 --> 01:07:39.820 align:middle line:84% It's going to have every one of my graphs start at 0 01:07:39.820 --> 01:07:42.660 align:middle line:90% and top out at 100. 01:07:42.660 --> 01:07:46.050 align:middle line:84% And now the plots are nicely comparable. 01:07:46.050 --> 01:07:49.030 align:middle line:84% So now I'm plotting the average temperature for each year. 01:07:49.030 --> 01:07:50.850 align:middle line:84% So there's 55 of these data points, 01:07:50.850 --> 01:07:52.770 align:middle line:84% the minimum temperature for each year 01:07:52.770 --> 01:07:54.760 align:middle line:84% and the maximum temperature for each year. 01:07:54.760 --> 01:07:58.300 align:middle line:90% So 55 data points being plotted. 01:07:58.300 --> 01:07:59.260 align:middle line:90% What can we tell? 01:07:59.260 --> 01:08:01.990 align:middle line:84% A lot easier to infer information from this, right? 01:08:01.990 --> 01:08:05.080 align:middle line:84% So we could see that the average temperature in Boston 01:08:05.080 --> 01:08:10.150 align:middle line:84% is the minimum temperature in Miami and San Diego. 01:08:10.150 --> 01:08:11.200 align:middle line:90% What else can we see? 01:08:11.200 --> 01:08:15.760 align:middle line:84% The variation in Boston is pretty high. 01:08:15.760 --> 01:08:19.420 align:middle line:84% The variation in Miami and San Diego is a lot lower. 01:08:19.420 --> 01:08:21.970 align:middle line:84% San Diego goes from 40 to 80, whereas Boston 01:08:21.970 --> 01:08:26.680 align:middle line:84% goes from 0 to 90, so pretty high variation. 01:08:26.680 --> 01:08:30.490 align:middle line:84% The average for Boston and San Diego 01:08:30.490 --> 01:08:34.210 align:middle line:84% seems to be almost the same, but that variation 01:08:34.210 --> 01:08:36.415 align:middle line:84% is very different between these two cities. 01:08:36.415 --> 01:08:42.819 align:middle line:90% 01:08:42.819 --> 01:08:43.575 align:middle line:90% Yeah, question. 01:08:43.575 --> 01:08:45.700 align:middle line:84% AUDIENCE: So what happens if there's a value that's 01:08:45.700 --> 01:08:47.260 align:middle line:90% lower than the minimum y value? 01:08:47.260 --> 01:08:49.990 align:middle line:84% ANA BELL: Oh, yeah, then it doesn't get plotted. 01:08:49.990 --> 01:08:54.729 align:middle line:84% Yeah, so that was a tenuous there, but it didn't go down. 01:08:54.729 --> 01:08:57.189 align:middle line:84% I could imagine the minimum in Boston 01:08:57.189 --> 01:08:58.732 align:middle line:90% being below 0 for one year. 01:08:58.732 --> 01:09:00.565 align:middle line:84% But yeah, then it just wouldn't get plotted. 01:09:00.565 --> 01:09:04.700 align:middle line:90% 01:09:04.700 --> 01:09:07.160 align:middle line:84% So you could use that to guide your limits. 01:09:07.160 --> 01:09:12.350 align:middle line:84% The code here could say y limit equals minimum of those three 01:09:12.350 --> 01:09:15.100 align:middle line:84% lists, and then you'll be sure to make sure 01:09:15.100 --> 01:09:18.979 align:middle line:84% to-- you'll ensure that that minimum will 01:09:18.979 --> 01:09:20.240 align:middle line:90% be hitting the limits. 01:09:20.240 --> 01:09:22.970 align:middle line:90% Great question. 01:09:22.970 --> 01:09:25.220 align:middle line:84% OK, so one other thing that we can look at 01:09:25.220 --> 01:09:28.350 align:middle line:84% is the distribution of temperatures. 01:09:28.350 --> 01:09:29.750 align:middle line:90% So this is a nice plot. 01:09:29.750 --> 01:09:32.450 align:middle line:84% It gives us sort of an overview look 01:09:32.450 --> 01:09:34.229 align:middle line:90% at what happens year by year. 01:09:34.229 --> 01:09:38.050 align:middle line:84% But what if we focus on one specific year? 01:09:38.050 --> 01:09:40.750 align:middle line:84% And now, for that year, let's think 01:09:40.750 --> 01:09:45.670 align:middle line:84% about what the temperature distribution looks like. 01:09:45.670 --> 01:09:49.330 align:middle line:84% So what I'm interested in plotting 01:09:49.330 --> 01:09:51.290 align:middle line:90% is something like this. 01:09:51.290 --> 01:09:55.660 align:middle line:84% So I've got on the x-axis maybe bins that 01:09:55.660 --> 01:09:58.690 align:middle line:84% correspond to different temperatures, so a temperature 01:09:58.690 --> 01:10:01.290 align:middle line:84% of 0, temperature of 1, temperature of 2, 01:10:01.290 --> 01:10:03.020 align:middle line:90% 3, 4, and so on. 01:10:03.020 --> 01:10:06.010 align:middle line:84% And then this is going to be pretty big because maybe my max 01:10:06.010 --> 01:10:07.630 align:middle line:90% temperature will be 100. 01:10:07.630 --> 01:10:12.280 align:middle line:84% So for one particular year, I would like to have 100 bins. 01:10:12.280 --> 01:10:15.280 align:middle line:84% And the height of each bin is going 01:10:15.280 --> 01:10:19.130 align:middle line:84% to be a count of how many days within that year 01:10:19.130 --> 01:10:22.820 align:middle line:84% we reached a temperature of 0, how many days within the year 01:10:22.820 --> 01:10:24.550 align:middle line:90% we reached a temperature of 1. 01:10:24.550 --> 01:10:27.700 align:middle line:84% And we can average things, or we can round temperatures 01:10:27.700 --> 01:10:30.430 align:middle line:84% because obviously the temperature would be like 20.6 01:10:30.430 --> 01:10:31.780 align:middle line:90% or something like that. 01:10:31.780 --> 01:10:36.210 align:middle line:84% And then we can just round it so it fits in one of these bins. 01:10:36.210 --> 01:10:38.860 align:middle line:84% So that's exactly what this code is doing. 01:10:38.860 --> 01:10:45.180 align:middle line:84% So here it's looping over every single one of the dates. 01:10:45.180 --> 01:10:49.320 align:middle line:84% And we're creating this list of the temperatures. 01:10:49.320 --> 01:10:51.790 align:middle line:84% And the list is for one specific year. 01:10:51.790 --> 01:10:54.460 align:middle line:84% So this year is my parameter here. 01:10:54.460 --> 01:10:56.760 align:middle line:84% So here, this is just going through the data 01:10:56.760 --> 01:10:59.610 align:middle line:84% and ensuring that I'm grabbing only the rows that 01:10:59.610 --> 01:11:02.080 align:middle line:90% match that year. 01:11:02.080 --> 01:11:05.230 align:middle line:84% And then down here is where I'm creating 01:11:05.230 --> 01:11:08.870 align:middle line:90% a list of 100 elements. 01:11:08.870 --> 01:11:16.330 align:middle line:84% So this down here, you can think of it as a list, like this. 01:11:16.330 --> 01:11:19.780 align:middle line:90% And the index nicely-- 01:11:19.780 --> 01:11:21.700 align:middle line:84% it worked out really nicely-- the index 01:11:21.700 --> 01:11:23.560 align:middle line:84% is going to correspond to a temperature 01:11:23.560 --> 01:11:25.510 align:middle line:90% value, which is weird to think. 01:11:25.510 --> 01:11:27.520 align:middle line:84% It only works in this particular scenario 01:11:27.520 --> 01:11:29.050 align:middle line:90% with Fahrenheit temperatures. 01:11:29.050 --> 01:11:33.020 align:middle line:84% But the index in this list corresponds to a temperature. 01:11:33.020 --> 01:11:36.760 align:middle line:84% So as I'm iterating through my list of temperatures 01:11:36.760 --> 01:11:39.670 align:middle line:84% over 365 days in a year, I'm going 01:11:39.670 --> 01:11:41.750 align:middle line:90% to round that temperature. 01:11:41.750 --> 01:11:44.440 align:middle line:84% And I'm going to add it to the index 01:11:44.440 --> 01:11:46.690 align:middle line:90% that I believe it belongs to. 01:11:46.690 --> 01:11:49.720 align:middle line:84% So in this way, I'm going to have-- 01:11:49.720 --> 01:11:53.860 align:middle line:84% if the temperature was 4 degrees, then that index 4, 01:11:53.860 --> 01:11:56.320 align:middle line:84% I'm going to increment my count by one. 01:11:56.320 --> 01:11:58.120 align:middle line:84% And if further on in the list I've 01:11:58.120 --> 01:12:01.087 align:middle line:84% got another temperature that's 4, at index 4, 01:12:01.087 --> 01:12:02.420 align:middle line:90% I'm going to increment it again. 01:12:02.420 --> 01:12:06.220 align:middle line:84% So I've got this nice list, these nice counts 01:12:06.220 --> 01:12:10.270 align:middle line:84% of all of the temperatures at different-- 01:12:10.270 --> 01:12:13.330 align:middle line:84% sorry, all of the counts at all of 01:12:13.330 --> 01:12:15.140 align:middle line:90% these different temperatures. 01:12:15.140 --> 01:12:17.660 align:middle line:84% So out of those 365 days, how many days 01:12:17.660 --> 01:12:19.450 align:middle line:90% had a temperature of 4? 01:12:19.450 --> 01:12:22.775 align:middle line:84% Out of 365 days, how many days had a temperature of 85? 01:12:22.775 --> 01:12:25.470 align:middle line:90% 01:12:25.470 --> 01:12:26.610 align:middle line:90% And then we can plot it. 01:12:26.610 --> 01:12:31.035 align:middle line:84% And we're not going to plot a regular plot, because we 01:12:31.035 --> 01:12:32.160 align:middle line:90% don't want these connected. 01:12:32.160 --> 01:12:34.035 align:middle line:84% We're not going to do a histogram, because we 01:12:34.035 --> 01:12:36.570 align:middle line:90% made our own histogram here. 01:12:36.570 --> 01:12:38.670 align:middle line:84% Instead, we're going to do a bar plot. 01:12:38.670 --> 01:12:43.500 align:middle line:84% And the bar plot takes in my x-axis and my y-axis, 01:12:43.500 --> 01:12:48.240 align:middle line:84% the x-axis being this list 0 through 100 01:12:48.240 --> 01:12:50.640 align:middle line:84% corresponding temperatures and the y-axis 01:12:50.640 --> 01:12:53.970 align:middle line:84% being the count of how many days had 01:12:53.970 --> 01:12:55.620 align:middle line:90% each one of those temperatures. 01:12:55.620 --> 01:12:58.620 align:middle line:84% And we get something that looks like this. 01:12:58.620 --> 01:13:00.860 align:middle line:90% So this is only for one year. 01:13:00.860 --> 01:13:06.380 align:middle line:84% So if we count the sum of all of these bars, how many times they 01:13:06.380 --> 01:13:10.380 align:middle line:84% appear, it should add up to 365 days. 01:13:10.380 --> 01:13:14.660 align:middle line:84% So this is the distribution, I think, in 1961. 01:13:14.660 --> 01:13:17.180 align:middle line:84% Left is Boston and right is San Diego. 01:13:17.180 --> 01:13:20.830 align:middle line:90% 01:13:20.830 --> 01:13:23.710 align:middle line:84% Already we can tell some pretty interesting things from this. 01:13:23.710 --> 01:13:26.890 align:middle line:84% So 1961, what does the distribution look 01:13:26.890 --> 01:13:28.038 align:middle line:90% like for these two cities? 01:13:28.038 --> 01:13:30.580 align:middle line:84% Well, it looks like-- this is something we could already tell 01:13:30.580 --> 01:13:32.170 align:middle line:90% from the minimum and maximum-- 01:13:32.170 --> 01:13:34.660 align:middle line:84% it looks like temperatures in Boston 01:13:34.660 --> 01:13:37.750 align:middle line:90% kind of went from about 0 to 85. 01:13:37.750 --> 01:13:39.760 align:middle line:84% But what the distribution tells us 01:13:39.760 --> 01:13:43.360 align:middle line:84% that the minimum and maximum couldn't tell 01:13:43.360 --> 01:13:46.690 align:middle line:84% us is how many days were that low, 01:13:46.690 --> 01:13:48.790 align:middle line:90% how many days were that high. 01:13:48.790 --> 01:13:54.040 align:middle line:84% Is it that we have some sort of nice-looking bell-curve-type 01:13:54.040 --> 01:13:56.380 align:middle line:84% distribution where most of our temperatures 01:13:56.380 --> 01:13:59.260 align:middle line:84% land comfortably in this middle range? 01:13:59.260 --> 01:14:00.970 align:middle line:90% That's one option. 01:14:00.970 --> 01:14:04.900 align:middle line:84% Or maybe there is some city out there 01:14:04.900 --> 01:14:09.280 align:middle line:84% where it just has an even distribution. 01:14:09.280 --> 01:14:12.680 align:middle line:84% So basically, they're going to have temperatures that-- 01:14:12.680 --> 01:14:15.510 align:middle line:90% 01:14:15.510 --> 01:14:18.400 align:middle line:84% sorry, the count of the temperatures basically is even. 01:14:18.400 --> 01:14:20.420 align:middle line:84% So it doesn't really matter what temperature 01:14:20.420 --> 01:14:22.550 align:middle line:84% you're talking about, there will be an even number 01:14:22.550 --> 01:14:25.190 align:middle line:84% of days throughout the year that are at that temperature. 01:14:25.190 --> 01:14:27.620 align:middle line:84% So this kind of graph can tell us this. 01:14:27.620 --> 01:14:30.470 align:middle line:84% So it looks like the temperature in Boston kind of maybe 01:14:30.470 --> 01:14:33.680 align:middle line:84% follows a very wide bell-shaped-curve kind 01:14:33.680 --> 01:14:36.785 align:middle line:90% of, maybe two bumps, a bimodal. 01:14:36.785 --> 01:14:41.250 align:middle line:84% The temperature in San Diego, again, much, 01:14:41.250 --> 01:14:45.050 align:middle line:84% much lower variability but also seems to follow this 01:14:45.050 --> 01:14:48.530 align:middle line:90% bell-type-curve here, where-- 01:14:48.530 --> 01:14:52.640 align:middle line:84% bimodal with two bumps here, one with temperatures that are just 01:14:52.640 --> 01:14:55.670 align:middle line:84% in the 55s, very few temperatures in the middle, 01:14:55.670 --> 01:14:59.280 align:middle line:84% and then a bunch of temperatures in the 70s. 01:14:59.280 --> 01:15:02.430 align:middle line:84% So this is the distribution for 1961. 01:15:02.430 --> 01:15:06.600 align:middle line:84% And then we can again ask what happens to the distribution 01:15:06.600 --> 01:15:08.740 align:middle line:90% in a later year. 01:15:08.740 --> 01:15:12.300 align:middle line:84% So if we take more than one year that we plot, 01:15:12.300 --> 01:15:15.840 align:middle line:84% here I'm going to plot 1961 and 2015. 01:15:15.840 --> 01:15:18.150 align:middle line:84% So just two years, not everything in between. 01:15:18.150 --> 01:15:21.420 align:middle line:84% That would be a very, very cluttered graph. 01:15:21.420 --> 01:15:27.030 align:middle line:84% I'm going to label the 1961 temperatures blue and the 2015 01:15:27.030 --> 01:15:29.770 align:middle line:90% temperatures red. 01:15:29.770 --> 01:15:33.100 align:middle line:84% So then I get something that looks like this. 01:15:33.100 --> 01:15:34.420 align:middle line:90% A little hard to tell. 01:15:34.420 --> 01:15:37.630 align:middle line:84% So what we can do for this graph is we can actually 01:15:37.630 --> 01:15:40.660 align:middle line:84% add something called an alpha value, so a transparency, 01:15:40.660 --> 01:15:43.660 align:middle line:84% so we can see what's behind the red. 01:15:43.660 --> 01:15:46.480 align:middle line:84% Does the blue go all the way down here? 01:15:46.480 --> 01:15:49.480 align:middle line:84% Is the blue just slightly below the red? 01:15:49.480 --> 01:15:50.920 align:middle line:90% Hard to tell from this. 01:15:50.920 --> 01:15:53.800 align:middle line:84% One thing we can do is to add that transparency, like I said. 01:15:53.800 --> 01:15:56.590 align:middle line:84% Another thing that we can do is to just plot them 01:15:56.590 --> 01:15:59.360 align:middle line:90% on two separate subplots. 01:15:59.360 --> 01:16:02.150 align:middle line:84% And then we can try to compare them 01:16:02.150 --> 01:16:06.350 align:middle line:84% to see exactly what happened from 1961 in terms 01:16:06.350 --> 01:16:09.110 align:middle line:84% of the distribution to 2015, again, 01:16:09.110 --> 01:16:10.490 align:middle line:90% in terms of the distribution. 01:16:10.490 --> 01:16:11.990 align:middle line:84% So you can, if you want, play around 01:16:11.990 --> 01:16:14.330 align:middle line:84% with different cities, your home city, 01:16:14.330 --> 01:16:16.970 align:middle line:84% and see exactly what happened to the temperatures 01:16:16.970 --> 01:16:18.140 align:middle line:90% over all those years. 01:16:18.140 --> 01:16:21.420 align:middle line:84% So it's kind of a cute thing to try. 01:16:21.420 --> 01:16:24.370 align:middle line:90% Any questions? 01:16:24.370 --> 01:16:27.490 align:middle line:90% OK, so that's the end. 01:16:27.490 --> 01:16:29.950 align:middle line:84% We've really just scratched the surface of the things 01:16:29.950 --> 01:16:31.730 align:middle line:84% that you can do with plotting today. 01:16:31.730 --> 01:16:33.950 align:middle line:84% We saw how to customize our graphs. 01:16:33.950 --> 01:16:36.880 align:middle line:84% We saw how to create labels, some really, really 01:16:36.880 --> 01:16:37.940 align:middle line:90% basic things. 01:16:37.940 --> 01:16:40.750 align:middle line:84% But I hope that sort of throughout all of this, 01:16:40.750 --> 01:16:44.650 align:middle line:84% you saw how useful it is to visualize the data. 01:16:44.650 --> 01:16:46.960 align:middle line:84% The commands are not so important, 01:16:46.960 --> 01:16:48.530 align:middle line:84% because you can always look those up. 01:16:48.530 --> 01:16:52.540 align:middle line:84% But what's important is to take some set of data, which you'll 01:16:52.540 --> 01:16:55.390 align:middle line:84% be working with in the real world, if you do a UROP, 01:16:55.390 --> 01:16:57.580 align:middle line:84% if you decide to take other computer science 01:16:57.580 --> 01:17:00.400 align:middle line:84% courses in other departments, computation courses. 01:17:00.400 --> 01:17:02.200 align:middle line:90% You'll be working with data. 01:17:02.200 --> 01:17:03.500 align:middle line:90% And as soon as you get it. 01:17:03.500 --> 01:17:04.960 align:middle line:84% It's important to just initialize 01:17:04.960 --> 01:17:08.570 align:middle line:84% it to see what it looks, get a general sense of it. 01:17:08.570 --> 01:17:10.660 align:middle line:84% And once you get a sense of it, it 01:17:10.660 --> 01:17:12.490 align:middle line:84% can lead to more questions, which 01:17:12.490 --> 01:17:14.830 align:middle line:84% will cause you to visualize the data in a slightly 01:17:14.830 --> 01:17:18.070 align:middle line:84% different way, which becomes more useful in answering 01:17:18.070 --> 01:17:21.940 align:middle line:84% questions and potentially posing new questions to investigate. 01:17:21.940 --> 01:17:24.210 align:middle line:90% OK, so that's it for today. 01:17:24.210 --> 01:17:26.660 align:middle line:84% Next lecture, we'll be just tying up some loose ends 01:17:26.660 --> 01:17:31.520 align:middle line:84% regarding dictionaries and some ideas on hash tables 01:17:31.520 --> 01:17:33.270 align:middle line:84% and how dictionaries are stored in memory, 01:17:33.270 --> 01:17:35.960 align:middle line:84% as well as doing a little bit of preview 01:17:35.960 --> 01:17:37.820 align:middle line:84% of simulations, which is something that's 01:17:37.820 --> 01:17:40.280 align:middle line:90% a really useful technique. 01:17:40.280 --> 01:17:43.190 align:middle line:84% Again, if you're going to do some more computation courses 01:17:43.190 --> 01:17:44.750 align:middle line:84% in other departments, a simulation 01:17:44.750 --> 01:17:47.950 align:middle line:84% is something that's going to be really, really helpful. 01:17:47.950 --> 01:17:54.000 align:middle line:90%