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## AP®︎/College Statistics

### Course: AP®︎/College Statistics > Unit 2

Lesson 2: Representing a quantitative variable with histograms and stem plots# Reading stem and leaf plots

AP.STATS:

UNC‑1 (EU)

, UNC‑1.G (LO)

, UNC‑1.G.2 (EK)

A stem and leaf plot displays data by breaking each data point into two parts: the "stem" and the "leaf." Each stem represents a range of values (e.g. if the stem is 2, the corresponding leaves might be data points in the 20s). Each leaf typically represents the last digit of a data point (e.g. if the leaf is 6 next to a stem of 2, it could represent a data point whose value is 26). Created by Sal Khan.

## Want to join the conversation?

- how do you read a three digit number on a stem and leaf plot(13 votes)
- Three Digit Numbers:

10 : 1, 2, 3, 4, 5, 6, 7, 8, 9,

11 : 3, 7

12 : 8, 9

13 : 1, 5

14 : 2, 4

15 : 0, 5, 8(22 votes)

- So to put this all in a nutshell, this is what it is?

7 | 1 = 71? I'm just asking, just for clarification!(5 votes)- That's right for these examples. Sometimes you'll see other formats, such as 1|2 = 1.2, but they should have a "key" which tells you what format it is in.(4 votes)

- Wouldn't the answer of the coconut problem be 0?(5 votes)
- no, because there arent any digits in the second column, if it was zero ther'd be zero in that coulumn too(4 votes)

- Hey everyone! I've seen questions where they ask the median..how would you do that? Please and thank you!(3 votes)
- Once you understand how to read a stem and leaf plot, you would sort all the data points from least to greatest. Then, you would find the middle number of all the data points. This is the median. A way I like to do this is by writing down all the data on a piece of paper and then crossing off one number from the left, then one from the right, then repeating until you only have one number left. If you are left with 2 numbers, find the average of the two numbers to find your median.(6 votes)

- on the first example with turtle, why are there two 16s and two 23s ?

are they representing different zoos?(3 votes)- Yes, each number represents a zoo, so there are two different zoos with 16 turtles and two different zoos with 23 turtles.(5 votes)

- What would be the minimum data entry and the maximum data entry?(3 votes)
- I guess the minimum is 0 and there is no limit for maximum for 'stem and leaf' diagram.(4 votes)

- On the turtles equation: Since the question was asking how many zoo's have fewer than 46 turtles, why wasn't the 4 (which is 40 correct?) be included?(3 votes)
- Stem and leaf plots show for each category in the stem how many and which data points were measured that fall into this category.

In the turtles example the categories are number of turtles from 0 to 9, 10 to 19, 20 to 21 and so on.

If you want to add a data point to the plot, you'd look for the right place on the stem and add it on the right side as a leaf. For example to add 32, you'd go to category 3 (30 to 39 or numbers beginning with 3), then add a 2 to the right side.

An empty right side means that there are no data points in this category.

It does not mean, that there is a data point with a 0, like 40.

Sorry for the lengthy explanation.

In short: there is no 40 in the plot since adding a 40 would result in a 0 on the right to the "4" category. If a category has no elements, the right side is empty (= no leafs). See second example in the video for an example of 0 on the right side.(4 votes)

- What if the leaf unit is .01? and the chart has three columns.......(3 votes)
- This is only used for counting Whole numbers.

if you have fractions you would have to round them to the nearest whole number(2 votes)

- Ok so if they asked what is leaf 3a, would that be 1 or 31?

Is it normal to ask for a leaf name or do they call the leaf everything after the 3 so its 369?(3 votes) - why is this called as stem and leaf plots?(1 vote)
- Because the part on the left is called the stem, and the other numbers on the side are the leaves.(3 votes)

## Video transcript

The government created the
following stem-and-leaf plot showing the number of turtles at
each major zoo in the country. How many zoos have
fewer than 46 turtles? So what the
stem-and-leaf plot does is it gives us the first
digit in each number and essentially you could
call this the tens place. And then it gives
us the ones place. So there was only one zoo
that had four turtles. So you could view this
as 0, 0, 4, or 4 turtles. Then everything here,
the tens place, is a 1. So this number right
here is really an 11. This is a 14. This right over
here would be a 16. That's a 16, and
so forth and so on. This would be 17, 18. All of this is 23. This is 23. This is 26 because we have our
tens place right over here. This is the first digit. So let's answer the question. How many zoos have
fewer than 46 turtles? So there are no zoos that
had 40 anything turtles. And so all of these zoos
here-- so all of these had 30 something turtles,
these had 20 something turtles, these have in the teens,
this has single digits. So it's literally as many
zoos as we have listed here. So 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17. 17 zoos have fewer
than 46 turtles. Let's do another one. The buyer for a
chain of supermarkets created the following
stem-and-leaf plot showing the number of coconuts
at each of the stores. What was the smallest number
of coconuts at any one grocery store? So the buyer for a
chain of supermarkets created the following
stem-and-leaf plot showing the number of coconuts
at each of the stores. So at any one grocery store
the smallest number-- well, that's this one right over here. And remember, it's not two. We have our tens
places right over here. It's a one. So this right over
here represents 12 coconuts at that store. So we'll put 12 right over here. Let's try another one. A statistician for a
chain of department stores created the following
stem-and-leaf plot showing the number of watches
at each of the stores. How many department stores
have exactly seven watches? Well that's only this one
right over here-- 07 watches. This one, this, this,
and that one are not 7. This is representing 17
because it's in the row with 1 at the beginning. This right over
here represents 27 because it's in the row
with the 2 at the beginning. So there's only one store that
has exactly seven watches. Let's do one more. This is kind of fun. A zookeeper created the
following stem-and-leaf plot showing the number of tigers at
each major zoo in the country. How many zoos have
more than 24 tigers? So we can ignore the
zeros and the teens and we get in the 20s. This is 25. So that meets the criteria. And then you go to 28, 29. So all of these in the 30s and
all of these right over here. This 3, 0-- this
doesn't mean 0 tigers. This is 30 tigers. This is 40 tigers. So we count 1, 2, 3,
4, 5, 6, 7, 8, 9, 9 zoos have more than 24 tigers. 9 zoos. And we're done.