1 00:00:00,740 --> 00:00:02,990 A statistician for a basketball team 2 00:00:02,990 --> 00:00:04,800 tracked the number of points that each 3 00:00:04,800 --> 00:00:07,600 of the 12 players on the team had in one game. 4 00:00:07,600 --> 00:00:12,010 And then made a stem-and-leaf plot to show the data. 5 00:00:12,010 --> 00:00:14,040 And sometimes it's called a stem-plot. 6 00:00:14,040 --> 00:00:16,102 How many points did the team score? 7 00:00:16,102 --> 00:00:18,310 And when you first look at this plot right over here, 8 00:00:18,310 --> 00:00:19,950 it seems a little hard to understand. 9 00:00:19,950 --> 00:00:22,444 Understand we have 0, 1, 2 under leaf 10 00:00:22,444 --> 00:00:23,860 you have all of these digits here. 11 00:00:23,860 --> 00:00:26,190 How does this relate to the number of points 12 00:00:26,190 --> 00:00:29,260 each student, or each player, actually scored? 13 00:00:29,260 --> 00:00:31,750 And the way to interpret a stem-and-leaf plot 14 00:00:31,750 --> 00:00:33,910 is the leafs contain-- at least the way 15 00:00:33,910 --> 00:00:38,470 that this statistician used it-- the leaf contains the smallest 16 00:00:38,470 --> 00:00:41,400 digit, or the ones digit, in the number of points 17 00:00:41,400 --> 00:00:42,860 that each player scored. 18 00:00:42,860 --> 00:00:45,250 And the stem contains the tens digits. 19 00:00:45,250 --> 00:00:48,870 And usually the leaf will contain the rightmost digit, 20 00:00:48,870 --> 00:00:50,700 or the ones digit, and then the stem 21 00:00:50,700 --> 00:00:52,840 will contain all of the other digits. 22 00:00:52,840 --> 00:00:54,480 And what's useful about this is it 23 00:00:54,480 --> 00:00:57,070 gives kind of a distribution of where the players were. 24 00:00:57,070 --> 00:00:59,310 You see that most of the players scored 25 00:00:59,310 --> 00:01:01,440 points that started with a 0. 26 00:01:01,440 --> 00:01:04,209 Then a few more scored points that started with a 1. 27 00:01:04,209 --> 00:01:07,980 And then only one score scored points to started with a 2, 28 00:01:07,980 --> 00:01:09,450 and it was actually 20 points. 29 00:01:09,450 --> 00:01:11,977 So I'm going to actually write down all of this data 30 00:01:11,977 --> 00:01:13,810 in a way that maybe you're a little bit more 31 00:01:13,810 --> 00:01:15,420 used to understanding it. 32 00:01:15,420 --> 00:01:18,920 So I'm going to write the 0's in purple. 33 00:01:18,920 --> 00:01:23,020 So there's, let's see, 1, 2, 3, 4, 5, 6, 7 players 34 00:01:23,020 --> 00:01:25,070 had 0 as the first digit. 35 00:01:25,070 --> 00:01:28,462 So 1, 2, 3, 4, 5, 6, 7. 36 00:01:31,330 --> 00:01:33,040 I wrote seven 0's. 37 00:01:33,040 --> 00:01:37,090 And then this player also had a 0 in his ones digit. 38 00:01:37,090 --> 00:01:39,800 This player, I'm going to try to do all the colors, 39 00:01:39,800 --> 00:01:43,600 this player also had a 0 in his ones digit. 40 00:01:43,600 --> 00:01:46,220 This player right here had a 2 in his ones digit, 41 00:01:46,220 --> 00:01:48,710 so he scored a total of 2 points. 42 00:01:48,710 --> 00:01:51,793 This player, let me do orange, this player 43 00:01:51,793 --> 00:01:54,330 had 4 for his ones digit. 44 00:01:54,330 --> 00:01:58,580 This player had 7 for his ones digit. 45 00:01:58,580 --> 00:02:02,480 Then this player had 7 for his ones digit. 46 00:02:02,480 --> 00:02:05,960 And then, let me see, I'm almost using all the colors, 47 00:02:05,960 --> 00:02:08,530 this player had 9 for his ones digit. 48 00:02:08,530 --> 00:02:11,460 So the way to read this is, you had one player with 0 points. 49 00:02:11,460 --> 00:02:14,850 0, 2, 4, 7, 9 and 9. 50 00:02:14,850 --> 00:02:16,870 But you can see, and it's kind of silly 51 00:02:16,870 --> 00:02:18,407 saying the zero was a tens digit, 52 00:02:18,407 --> 00:02:19,990 you could have even put a blank there. 53 00:02:19,990 --> 00:02:21,615 But the 0 lets us know that they didn't 54 00:02:21,615 --> 00:02:24,700 score anything in the tens place. 55 00:02:24,700 --> 00:02:27,940 But these are the actual scores for those seven players. 56 00:02:27,940 --> 00:02:31,700 Now let's go to the next row in the stem-and-leaf plot. 57 00:02:31,700 --> 00:02:34,060 So over here, all of the digits start with, 58 00:02:34,060 --> 00:02:37,760 or all of the points start with 1, for each of the players. 59 00:02:37,760 --> 00:02:40,940 And there's four of them. 60 00:02:40,940 --> 00:02:44,710 So 1, 1, 1, and 1. 61 00:02:44,710 --> 00:02:46,600 And then we have this player over here, 62 00:02:46,600 --> 00:02:51,250 his ones digit, or her ones digit, is a 1. 63 00:02:51,250 --> 00:02:54,090 So this player, this represents 11. 64 00:02:54,090 --> 00:02:57,150 1 in the tens place, 1 in the ones place. 65 00:02:57,150 --> 00:02:59,370 This player over here also got 11. 66 00:02:59,370 --> 00:03:02,770 1 in the tens place, 1 in the ones place. 67 00:03:02,770 --> 00:03:06,080 This player, let me do orange, this player 68 00:03:06,080 --> 00:03:08,350 has 3 in the ones place. 69 00:03:08,350 --> 00:03:10,250 So he or she scored 13 points. 70 00:03:10,250 --> 00:03:14,070 1 in the tens place, 3 in the ones place. 71 00:03:14,070 --> 00:03:15,770 13 points. 72 00:03:15,770 --> 00:03:18,020 And then I will do this in purple. 73 00:03:18,020 --> 00:03:20,760 This player has 8 in their ones place. 74 00:03:20,760 --> 00:03:23,160 So he or she scored 18 points. 75 00:03:23,160 --> 00:03:25,710 1 in the tens place, 8 in the ones place. 76 00:03:25,710 --> 00:03:27,190 18 points. 77 00:03:27,190 --> 00:03:29,390 And then finally, you have this player 78 00:03:29,390 --> 00:03:33,220 that has the tens digit is a 2. 79 00:03:33,220 --> 00:03:37,296 And then the ones digit is a 0. 80 00:03:37,296 --> 00:03:38,420 I'll circle that in yellow. 81 00:03:38,420 --> 00:03:40,160 It is a 0. 82 00:03:40,160 --> 00:03:43,030 So he or she scored 20 points. 83 00:03:43,030 --> 00:03:45,370 So looking at the stem-and-leaf plot, 84 00:03:45,370 --> 00:03:48,179 we were able to extract out all of the number of points 85 00:03:48,179 --> 00:03:49,470 that all of the players scored. 86 00:03:49,470 --> 00:03:51,261 And once again, what was useful about this, 87 00:03:51,261 --> 00:03:54,110 is you see how many players scored between 0 and 9 points, 88 00:03:54,110 --> 00:03:55,700 including 9 points. 89 00:03:55,700 --> 00:03:58,210 How many scored between 10 and 19 points, 90 00:03:58,210 --> 00:04:00,450 and then how many scored 20 points or over. 91 00:04:00,450 --> 00:04:02,620 And you see the distribution right over here. 92 00:04:02,620 --> 00:04:04,360 But let's actually answer the question 93 00:04:04,360 --> 00:04:06,360 that they're asking us to answer. 94 00:04:06,360 --> 00:04:09,190 How many points did the team score? 95 00:04:09,190 --> 00:04:10,920 So here we just have to add up all 96 00:04:10,920 --> 00:04:12,530 of these numbers right over here. 97 00:04:12,530 --> 00:04:16,230 So we're going to add up, I'll start with the largest, so 20 98 00:04:16,230 --> 00:04:27,120 plus 18 plus 13 plus 11 plus 11-- 13, 11, 11-- plus 9 plus 7 99 00:04:27,120 --> 00:04:33,177 plus 7 again plus 4 plus 2. 100 00:04:33,177 --> 00:04:34,010 Did I do that right? 101 00:04:34,010 --> 00:04:38,570 We have two 11's, then a 9, then two 7's, then a 4 then a 2, 102 00:04:38,570 --> 00:04:40,770 and then these two characters didn't score anything. 103 00:04:40,770 --> 00:04:42,353 So let's add up all of these together. 104 00:04:46,440 --> 00:04:53,110 So 0 plus 8 is 8, plus 3 is 11, plus 1 is 12, plus 1 is 13, 105 00:04:53,110 --> 00:05:03,490 plus 9 is 22, plus 7 is 27, 34, 38, 40. 106 00:05:03,490 --> 00:05:05,060 So that gets us to 40. 107 00:05:05,060 --> 00:05:06,590 Let me do that one more time. 108 00:05:06,590 --> 00:05:22,232 8, 11, 11, 12, 13, 22, 29, 29, and then 29, 36, 40, and 42. 109 00:05:22,232 --> 00:05:23,940 Looks like I actually might have messed-- 110 00:05:23,940 --> 00:05:25,148 let me do that one more time. 111 00:05:25,148 --> 00:05:27,030 This is the hardest part, adding these up. 112 00:05:27,030 --> 00:05:28,404 So let me try that one last time. 113 00:05:28,404 --> 00:05:30,280 I'm just going to state where my sum is. 114 00:05:30,280 --> 00:05:40,660 So 0, 8, add 3, 11, 12, 13, 22, 29, 36, 40, 42. 115 00:05:40,660 --> 00:05:42,660 So it's a good thing that I double checked that. 116 00:05:42,660 --> 00:05:44,720 I made a mistake the first time. 117 00:05:44,720 --> 00:05:49,490 4 plus 2 is 6, 7, 8, 9, 10. 118 00:05:49,490 --> 00:05:52,200 So we get to 102 points. 119 00:05:52,200 --> 00:05:57,540 The team, in total, scored 102 points.