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## AP®︎/College Statistics

### Unit 2: Lesson 2

Representing a quantitative variable with histograms and stem plots# Stem-and-leaf plots

AP.STATS:

UNC‑1 (EU)

, UNC‑1.G (LO)

, UNC‑1.G.2 (EK)

A stem and leaf is a table used to display data. The 'stem' is on the left displays the first digit or digits. The 'leaf' is on the right and displays the last digit. For example, 543 and 548 can be displayed together on a stem and leaf as 54 | 3,8. Created by Sal Khan.

## Video transcript

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.