Main content

## Statistics and probability

### Course: Statistics and probability > Unit 2

Lesson 1: Displaying quantitative data with graphs- Representing data
- Frequency tables & dot plots
- Creating frequency tables
- Creating dot plots
- Reading dot plots & frequency tables
- Dot plots and frequency tables review
- Creating a histogram
- Histograms
- Interpreting a histogram
- Create histograms
- Read histograms
- Histograms review
- Stem-and-leaf plots
- Reading stem and leaf plots
- Reading stem and leaf plots
- Stem and leaf plots review

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# Stem and leaf plots review

## Stem and leaf plots

A stem and leaf plot displays numerical data by splitting each data point into a "leaf" (usually the last digit) and a "stem" (the leading digit or digits).

For example, the buyer for a chain of department stores counted the number of pairs of boots at each of the stores and made a stem and leaf plot for the data. Here is the dataset and the stem and leaf plot:

Dataset: 17, 18, 20, 25, 28, 34, 34, 37, 38, 50

Stem and leaf plot:

$\begin{aligned}
&1~~|~~7~~8\\
&2~~|~~0~~5~~8\\
&3~~|~~4~~4~~7~~8\\
&4~~|\\
&5~~|~~0\\
\end{aligned}$

Key: 1, space, vertical bar, space, 8 represents a store that had 18 pairs of boots.

Key: 1, space, vertical bar, space, 8 represents a store that had 18 pairs of boots.

*Want to learn more about reading stem and leaf plots? Check out this video.*

## Creating a stem and leaf plot

Here's how to make a stem and leaf plot step by step. We'll use the same dataset as before. Here it is again:

17, 18, 20, 25, 28, 34, 34, 37, 38, 50

**Step 1:**Split each data point into a stem and a leaf. The stem is everything before the final digit, and the leaf is the final digit. Write the stems in a vertical column and don't skip stems just because they don't have any data.

start color #11accd, 1, end color #11accd, vertical bar, 7, start color #11accd, 1, end color #11accd, vertical bar, 8, start color #11accd, 2, end color #11accd, vertical bar, 0, start color #11accd, 2, end color #11accd, vertical bar, 5, start color #11accd, 2, end color #11accd, vertical bar, 8, start color #11accd, 3, end color #11accd, vertical bar, 4, start color #11accd, 3, end color #11accd, vertical bar, 4, start color #11accd, 3, end color #11accd, vertical bar, 7, start color #11accd, 3, end color #11accd, vertical bar, 8, start color #11accd, 5, end color #11accd, vertical bar, 0

Our start color #11accd, start text, s, t, e, m, s, end text, end color #11accd are the tens digits:

$\begin{aligned}
&1~~|\\
&2~~|\\
&3~~|\\
&4~~|\\
&5~~|\\
\end{aligned}$

**Step 2:**Write each leaf next to its corresponding stem. The start color #1fab54, start text, l, e, a, v, e, s, end text, end color #1fab54 should go from smallest to largest. Our leaves are the ones digits.1, vertical bar, start color #1fab54, 7, end color #1fab54, 1, vertical bar, start color #1fab54, 8, end color #1fab54, 2, vertical bar, start color #1fab54, 0, end color #1fab54, 2, vertical bar, start color #1fab54, 5, end color #1fab54, 2, vertical bar, start color #1fab54, 8, end color #1fab54, 3, vertical bar, start color #1fab54, 4, end color #1fab54, 3, vertical bar, start color #1fab54, 4, end color #1fab54, 3, vertical bar, start color #1fab54, 7, end color #1fab54, 3, vertical bar, start color #1fab54, 8, end color #1fab54, 5, vertical bar, start color #1fab54, 0, end color #1fab54

$\begin{aligned}
&1~~|~~7~~8\\
&2~~|~~0~~5~~8\\
&3~~|~~4~~4~~7~~8\\
&4~~|\\
&5~~|~~0\\
\end{aligned}$

**Step 3:**Give a key that explains what a stem and leaf represent.$\begin{aligned}
&1~~|~~7~~8\\
&2~~|~~0~~5~~8\\
&3~~|~~4~~4~~7~~8\\
&4~~|\\
&5~~|~~0\\
\end{aligned}$

Key: 1, space, vertical bar, space, 8 represents a store that had 18 pairs of boots.

Key: 1, space, vertical bar, space, 8 represents a store that had 18 pairs of boots.

*Want to learn more about creating stem and leaf plots? Check out this video.*

## Example: Reading stem and leaf plots

A zookeeper published the following stem-and-leaf plot showing the number of bears at each major zoo in the country:

$\begin{aligned}
&0~~|\\
&1~~|~~8~~8\\
&2~~|~~1~~3~~6~~6~~7~~7~~9\\
&3~~|~~1~~7\\
&4~~|~~1~~4~~5~~7\\
&5~~|~~0~~3\\
\end{aligned}$

Key: 1, space, vertical bar, space, 8 represents a zoo that has 18 bears.

Key: 1, space, vertical bar, space, 8 represents a zoo that has 18 bears.

*Want to practice more problems like this? Check out this exercise on reading stem and leaf plots.*

## Want to join the conversation?

- If one of the observations was 0, how would this be recorded? Would it be:

0 ¦ 0

?(5 votes)- Yes, precisely so.

It would be interpreted as 0 tens + 0 ones, which equals 0.(5 votes)

- It's easier than I thought(7 votes)
- When should I use this kind of representation?

What is the pros?(0 votes)- This is good for very variant things, I'd say. If you have data that is jumping all over the place in the Tens place, I would definitely use a Stem and Leaf plot.(9 votes)

- Can you do stem and leaf plots with decimals and negative numbers?(3 votes)
- Yes, you can actually. You make the Stem negative If you want the number negative such as -2 | 3 = -23. Now with Decimals, the only way I know how to do it is to edit the key, for example, 2 | 4 = 2.4 that line could instead mean where to place the decimal point instead of separating the 10s place value. Or 1.2 | 3 = 1.23 which is dividing the whole number and the 10ths place value from the hundredths place value from the ones. (I know this question was asked some time ago but hopefully this still helps anyone with the same question.)(2 votes)

- Is spacetime four dimensional?

If not, does compactification work?(2 votes) - It looks confusing at first, but is actually very simple.(2 votes)
- what happens when we have a three digit number like 345(0 votes)
- The stem is everything before the final digit and the leaf is the final digit.(4 votes)

- In which board and which class do we get questions like this.(1 vote)
- Add me on fn TurtleSloth550(1 vote)
- How do you find the circumference(1 vote)