1 00:00:00,090 --> 00:00:02,490 The following content is provided under a Creative 2 00:00:02,490 --> 00:00:04,030 Commons license. 3 00:00:04,030 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,720 continue to offer high quality educational resources for free. 5 00:00:10,720 --> 00:00:13,320 To make a donation or view additional materials 6 00:00:13,320 --> 00:00:17,280 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,280 --> 00:00:20,640 at ocw.mit.edu. 8 00:00:20,640 --> 00:00:23,380 PROFESSOR: We've noticed a couple of things. 9 00:00:23,380 --> 00:00:25,230 Let me ask you a question-- 10 00:00:25,230 --> 00:00:27,180 in each one of these graphs, what 11 00:00:27,180 --> 00:00:29,390 is the total number of people represented? 12 00:00:33,205 --> 00:00:34,080 What was that, Steve? 13 00:00:34,080 --> 00:00:35,080 AUDIENCE: 29? 14 00:00:35,080 --> 00:00:36,620 PROFESSOR: 29. 15 00:00:36,620 --> 00:00:41,690 If I look here, I had 16 plus 13, that's 29-- 16 00:00:41,690 --> 00:00:42,470 or no? 17 00:00:42,470 --> 00:00:45,020 16 plus 13, yeah, that's 29. 18 00:00:45,020 --> 00:00:48,410 If I look at all of these, I have 2 plus 2 plus 1 plus 1 19 00:00:48,410 --> 00:00:49,610 plus 1 plus 1. 20 00:00:49,610 --> 00:00:52,550 You're all representing the same number of people, 21 00:00:52,550 --> 00:00:54,370 you're just representing it differently. 22 00:00:54,370 --> 00:00:57,050 Here, it's hard to tell. 23 00:00:57,050 --> 00:01:00,110 Which of these graphs can you easily tell 24 00:01:00,110 --> 00:01:04,008 what's the average of the number of calories eaten? 25 00:01:04,008 --> 00:01:04,591 AUDIENCE: 400. 26 00:01:04,591 --> 00:01:06,282 AUDIENCE: 400. 27 00:01:06,282 --> 00:01:07,490 PROFESSOR: Bin width the 400. 28 00:01:07,490 --> 00:01:08,841 Why do you say that, Chris? 29 00:01:08,841 --> 00:01:11,550 AUDIENCE: Because there's a big peak right there. 30 00:01:11,550 --> 00:01:12,260 PROFESSOR: OK. 31 00:01:12,260 --> 00:01:14,960 If we look at 400, it kind of goes down and up 32 00:01:14,960 --> 00:01:16,260 and then back down. 33 00:01:16,260 --> 00:01:18,830 If we look at 1,600 bin width, it's 34 00:01:18,830 --> 00:01:22,040 kind of like it drops off a little bit. 35 00:01:22,040 --> 00:01:24,170 But if we look at bin width 100, it's 36 00:01:24,170 --> 00:01:27,620 like up, down, down, down, up, down, up, down, up, 37 00:01:27,620 --> 00:01:31,730 down a little bit, so it's harder to tell. 38 00:01:31,730 --> 00:01:34,010 Where did most of the people have their calories? 39 00:01:34,010 --> 00:01:36,560 Because up here where most of the people had their calories, 40 00:01:36,560 --> 00:01:38,300 it's like three or four bins, so you're 41 00:01:38,300 --> 00:01:39,890 splitting the people out. 42 00:01:39,890 --> 00:01:44,255 Whereas here in the middle, you've got a wider bin. 43 00:01:44,255 --> 00:01:46,430 It's easy to compare nine to one. 44 00:01:46,430 --> 00:01:50,930 It's kind of hard to compare two to one, or two to zero. 45 00:01:50,930 --> 00:01:54,980 So in some cases you want lots of people in each bin. 46 00:01:54,980 --> 00:01:58,640 In some cases you want essentially lots of resolution 47 00:01:58,640 --> 00:02:02,090 for telling the difference between what people consumed. 48 00:02:02,090 --> 00:02:04,130 And in some cases you want things in the middle 49 00:02:04,130 --> 00:02:07,610 so you can see some patterns a little bit better. 50 00:02:07,610 --> 00:02:10,340 Picking the bin size for a histogram 51 00:02:10,340 --> 00:02:12,150 is kind of an art form. 52 00:02:12,150 --> 00:02:13,970 It depends on what you're looking for, 53 00:02:13,970 --> 00:02:16,370 because there's different ways to represent 54 00:02:16,370 --> 00:02:19,370 the exact same data, so it depends 55 00:02:19,370 --> 00:02:21,081 on what you're looking for. 56 00:02:21,081 --> 00:02:22,580 So we're actually going to think now 57 00:02:22,580 --> 00:02:25,960 about how could we represent light, 58 00:02:25,960 --> 00:02:28,900 or how could we represent measurements of light, 59 00:02:28,900 --> 00:02:30,370 with histograms.