Representing a quantitative variable with histograms and stem plots
A statistician for a basketball team tracked the number of points that each of the 12 players on the team had in one game. And then made a stem-and-leaf plot to show the data. And sometimes it's called a stem-plot. How many points did the team score? And when you first look at this plot right over here, it seems a little hard to understand. Understand we have 0, 1, 2 under leaf you have all of these digits here. How does this relate to the number of points each student, or each player, actually scored? And the way to interpret a stem-and-leaf plot is the leafs contain-- at least the way that this statistician used it-- the leaf contains the smallest digit, or the ones digit, in the number of points that each player scored. And the stem contains the tens digits. And usually the leaf will contain the rightmost digit, or the ones digit, and then the stem will contain all of the other digits. And what's useful about this is it gives kind of a distribution of where the players were. You see that most of the players scored points that started with a 0. Then a few more scored points that started with a 1. And then only one score scored points to started with a 2, and it was actually 20 points. So I'm going to actually write down all of this data in a way that maybe you're a little bit more used to understanding it. So I'm going to write the 0's in purple. So there's, let's see, 1, 2, 3, 4, 5, 6, 7 players had 0 as the first digit. So 1, 2, 3, 4, 5, 6, 7. I wrote seven 0's. And then this player also had a 0 in his ones digit. This player, I'm going to try to do all the colors, this player also had a 0 in his ones digit. This player right here had a 2 in his ones digit, so he scored a total of 2 points. This player, let me do orange, this player had 4 for his ones digit. This player had 7 for his ones digit. Then this player had 7 for his ones digit. And then, let me see, I'm almost using all the colors, this player had 9 for his ones digit. So the way to read this is, you had one player with 0 points. 0, 2, 4, 7, 9 and 9. But you can see, and it's kind of silly saying the zero was a tens digit, you could have even put a blank there. But the 0 lets us know that they didn't score anything in the tens place. But these are the actual scores for those seven players. Now let's go to the next row in the stem-and-leaf plot. So over here, all of the digits start with, or all of the points start with 1, for each of the players. And there's four of them. So 1, 1, 1, and 1. And then we have this player over here, his ones digit, or her ones digit, is a 1. So this player, this represents 11. 1 in the tens place, 1 in the ones place. This player over here also got 11. 1 in the tens place, 1 in the ones place. This player, let me do orange, this player has 3 in the ones place. So he or she scored 13 points. 1 in the tens place, 3 in the ones place. 13 points. And then I will do this in purple. This player has 8 in their ones place. So he or she scored 18 points. 1 in the tens place, 8 in the ones place. 18 points. And then finally, you have this player that has the tens digit is a 2. And then the ones digit is a 0. I'll circle that in yellow. It is a 0. So he or she scored 20 points. So looking at the stem-and-leaf plot, we were able to extract out all of the number of points that all of the players scored. And once again, what was useful about this, is you see how many players scored between 0 and 9 points, including 9 points. How many scored between 10 and 19 points, and then how many scored 20 points or over. And you see the distribution right over here. But let's actually answer the question that they're asking us to answer. How many points did the team score? So here we just have to add up all of these numbers right over here. So we're going to add up, I'll start with the largest, so 20 plus 18 plus 13 plus 11 plus 11-- 13, 11, 11-- plus 9 plus 7 plus 7 again plus 4 plus 2. Did I do that right? We have two 11's, then a 9, then two 7's, then a 4 then a 2, and then these two characters didn't score anything. So let's add up all of these together. So 0 plus 8 is 8, plus 3 is 11, plus 1 is 12, plus 1 is 13, plus 9 is 22, plus 7 is 27, 34, 38, 40. So that gets us to 40. Let me do that one more time. 8, 11, 11, 12, 13, 22, 29, 29, and then 29, 36, 40, and 42. Looks like I actually might have messed-- let me do that one more time. This is the hardest part, adding these up. So let me try that one last time. I'm just going to state where my sum is. So 0, 8, add 3, 11, 12, 13, 22, 29, 36, 40, 42. So it's a good thing that I double checked that. I made a mistake the first time. 4 plus 2 is 6, 7, 8, 9, 10. So we get to 102 points. The team, in total, scored 102 points.
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