How do I show decimals or three-digit numbers?

The last digit is still the leaf and the key says what it means. For 4.7 seconds use $4 \mid 7 = 4.7$; for 125 grams use $12 \mid 5 = 125$.

What is the difference between a stem-and-leaf plot and a histogram?

Both show how many values fall in each interval. A histogram shows only the counts, while a stem-and-leaf plot keeps every single value, so you can still find the exact median, mode and range.

When should I use split stems?

When nearly all the data shares only two or three stems, the rows get very long. Splitting each stem into leaves 0-4 and 5-9 doubles the number of rows and shows the shape more clearly.

Teacher Resources

Stem and Leaf Plots

Q: What is the stem of a one-digit number like 7?

The stem is 0 and the leaf is 7, so 7 is written as $0 \mid 7$. That way one-digit values fit in the same plot as two-digit values.

Learn to build and read stem-and-leaf plots, find the median, mode and range from them, and compare two groups with a back-to-back plot.

Intermediate25 minLesson

Printable worksheet

Definition

A stem-and-leaf plot shows every value of a data set while also showing its shape. Each number is split into two parts:

The stem is every digit except the last one (for two-digit numbers, the tens digit)
The leaf is the last digit (the ones digit)

Stems are written once, in a column from smallest to largest. The leaves of each stem are written in a row to the right, in order from smallest to largest. A key tells the reader how to read one entry.

Here are the quiz scores of 15 students: 52, 58, 61, 63, 67, 67, 70, 74, 75, 78, 81, 84, 86, 90, 95.

\begin{array}{r|l} \text{Stem} & \text{Leaves} \\ \hline 5 & 2~8 \\ 6 & 1~3~7~7 \\ 7 & 0~4~5~8 \\ 8 & 1~4~6 \\ 9 & 0~5 \end{array}

Key:

5 \mid 2 = 52

Every leaf is one data value, so the number of leaves is the number of data values (here 15). Turned on its side, the plot looks like a histogram with intervals 50-59, 60-69 and so on, but unlike a histogram you can still read every single score.

Worked Examples

Make a stem-and-leaf plot of these quiz scores: 74, 58, 86, 61, 90, 67, 52, 78, 70, 84, 63, 95, 67, 75, 81.

Choose the stems

The smallest score is 52 and the largest is 95, so the tens digits go from 5 to 9 → Stems: 5, 6, 7, 8, 9

Write each ones digit as a leaf next to its stem

74 gives leaf 4 on stem 7, 58 gives leaf 8 on stem 5, and so on for all 15 scores → 15 leaves written

Put the leaves of every row in order

\begin{array}{r|l} 5 & 2~8 \\ 6 & 1~3~7~7 \\ 7 & 0~4~5~8 \\ 8 & 1~4~6 \\ 9 & 0~5 \end{array}

→ Ordered stem-and-leaf plot

Add a key and check the count

Key:

5 \mid 2 = 52

. Count the leaves:

2 + 4 + 4 + 3 + 2 = 15

→ 15 leaves for 15 scores

Answer: The plot has stems 5 to 9 with ordered leaves 2 8 / 1 3 7 7 / 0 4 5 8 / 1 4 6 / 0 5 and the key $5 \mid 2 = 52$ .

Common Mistakes

Writing the leaves in the order the data was given (for example 6 | 7 1 7 3)

Why it's wrong: The plot still shows the shape, but counting to the median or spotting repeated values only works when each row is in order.

Correct: Always rewrite each row with the leaves from smallest to largest: 6 | 1 3 7 7.

Leaving out the key or ignoring it

Why it's wrong: The same entry $4 \mid 7$ can mean 47, 4.7 or 470. Without the key the reader has to guess.

Correct: Always write a key such as $4 \mid 7 = 4.7$ seconds and read every value with it.

Skipping a stem that has no leaves

Why it's wrong: If no value is between 30 and 39 and the row for stem 3 is left out, the gap in the data disappears and the shape looks wrong.

Correct: Write every stem from the smallest to the largest, even when a row stays empty.

Reading the left side of a back-to-back plot in the wrong direction (reading $3 \mid 7$ as 37)

Why it's wrong: On the left side the leaf stands before the stem, but the stem is still the tens digit.

Correct: Read left leaves outward from the stem: leaf 3 next to stem 7 is 73. The key of a back-to-back plot shows this.

Interactive Visual

Quiz scores of 15 students: sort the leaves

Stem	Leaf
5
6
7
8
9

Key: 7 | 4 = 74

Tap a leaf to see its value.

Values: 15
Median: 74
Mode: 67
Range: 95 − 52 = 43

Back-to-back plot: Class A and Class B

Class A	Stem	Class B
	4
	5
	6
	7
	8
	9

Key: 7 | 2 = 72Left side: 3 | 7 = 73

Tap a leaf to see its value.

Class A

Values: 10
Median: 63
Mode: 64
Range: 80 − 48 = 32

Class B

Values: 10
Median: 75
Mode: none
Range: 91 − 57 = 34

Commute times of 14 workers (minutes) with split stems

Stem	Leaf
2
2*
3
3*

Key: 2 | 1 = 21Split stems: the first row of a stem holds leaves 0 to 4, the row with * holds 5 to 9.

Tap a leaf to see its value.

Values: 14
Median: 28.5
Mode: 27
Range: 38 − 21 = 17

Histogram

Same quiz scores grouped by stem (the plot turned on its side)

50-59(2)

60-69(4)

70-79(4)

80-89(3)

90-99(2)

Interactive Sandbox

Expression Calculator

Try these:

History

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Practice Problems

18 problems

Problem 1 of 18

Easy

In a stem-and-leaf plot the key is

4 \mid 7 = 47

. Which value does stem 6 with leaf 3 stand for?

Practice Problems: Stem and Leaf Plots

1. In a stem-and-leaf plot the key is 4 \mid 7 = 47. Which value does stem 6 with leaf 3 stand for?
2. The heights of some plants in cm are shown in this stem-and-leaf plot (key: 2 \mid 3 = 23 cm): \begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array} How many plants were measured?
3. The value 58 goes into a stem-and-leaf plot with the key 5 \mid 2 = 52. What is its leaf?
4. The heights of some plants in cm are shown in this stem-and-leaf plot (key: 2 \mid 3 = 23 cm): \begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array} How tall is the shortest plant, in cm?
5. The heights of some plants in cm are shown in this stem-and-leaf plot (key: 2 \mid 3 = 23 cm): \begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array} Find the range of the plant heights.
6. Make an ordered stem-and-leaf plot of these ages: 34, 27, 41, 29, 36, 22, 38, 45 (key: 2 \mid 2 = 22).
7. The heights of some plants in cm are shown in this stem-and-leaf plot (key: 2 \mid 3 = 23 cm): \begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array} Find the median plant height.
8. The heights of some plants in cm are shown in this stem-and-leaf plot (key: 2 \mid 3 = 23 cm): \begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array} What is the mode of the plant heights (in cm)?
9. This stem-and-leaf plot shows how many minutes some people exercised on one day (key: 4 \mid 2 = 42 minutes): \begin{array}{r|l} 3 & 5~8 \\ 4 & 0~2~2~6~9 \\ 5 & 1~3~7 \\ 6 & 0~4 \end{array} How many people exercised for 50 minutes or more?
10. This stem-and-leaf plot shows how many minutes some people exercised on one day (key: 4 \mid 2 = 42 minutes): \begin{array}{r|l} 3 & 5~8 \\ 4 & 0~2~2~6~9 \\ 5 & 1~3~7 \\ 6 & 0~4 \end{array} Find the median number of minutes.
11. How are the values 7, 12 and 15 written in a stem-and-leaf plot with the key 1 \mid 2 = 12?
12. The 100 m times of 8 runners in seconds are shown here (key: 13 \mid 5 = 13.5 seconds): \begin{array}{r|l} 12 & 4~8 \\ 13 & 1~1~5~9 \\ 14 & 2~6 \end{array} What is the range of the times, in seconds? Give a decimal number.
13. Five friends recorded how many push-ups they could do (key: 2 \mid 4 = 24): \begin{array}{r|l} 2 & 4~6 \\ 3 & 0~5~5 \end{array} Find the mean number of push-ups.
14. The 100 m times of 8 runners in seconds are shown here (key: 13 \mid 5 = 13.5 seconds): \begin{array}{r|l} 12 & 4~8 \\ 13 & 1~1~5~9 \\ 14 & 2~6 \end{array} Find the median time.
15. This back-to-back plot shows the points two basketball teams scored per game (key: 2 \mid 1 = 12 for Team A, 1 \mid 5 = 15 for Team B): \begin{array}{r|c|l} \text{Team A} & \text{Stem} & \text{Team B} \\ \hline 7~2 & 1 & 5 \\ 8~5~4~1 & 2 & 0~3~6 \\ 3~0 & 3 & 1~4~4~8 \\ & 4 & 2~5 \end{array} By how many points is Team B's median higher than Team A's?
16. This back-to-back plot shows the points two basketball teams scored per game (key: 2 \mid 1 = 12 for Team A, 1 \mid 5 = 15 for Team B): \begin{array}{r|c|l} \text{Team A} & \text{Stem} & \text{Team B} \\ \hline 7~2 & 1 & 5 \\ 8~5~4~1 & 2 & 0~3~6 \\ 3~0 & 3 & 1~4~4~8 \\ & 4 & 2~5 \end{array} Which team's points have the larger range?
17. This back-to-back plot shows the points two basketball teams scored per game (key: 2 \mid 1 = 12 for Team A, 1 \mid 5 = 15 for Team B): \begin{array}{r|c|l} \text{Team A} & \text{Stem} & \text{Team B} \\ \hline 7~2 & 1 & 5 \\ 8~5~4~1 & 2 & 0~3~6 \\ 3~0 & 3 & 1~4~4~8 \\ & 4 & 2~5 \end{array} In how many games did Team B score more than 30 points?
18. The scores of 11 players in a video game level are 41, 42, 44, 46, 47, 47, 48, 52, 53, 55, 58. They are shown with split stems: the first row of each stem holds the leaves 0-4, the second row the leaves 5-9 (key: 4 \mid 1 = 41). \begin{array}{r|l} 4 & 1~2~4 \\ 4 & 6~7~7~8 \\ 5 & 2~3 \\ 5 & 5~8 \end{array} Answer the questions about the plot.

Why It Matters

Stem-and-leaf plots are a quick way to organize a small or medium data set by hand:

No data is lost: unlike a histogram or a box plot, every original value can be read back from the plot
Shape at a glance: the length of each row shows where the data is crowded and where it is thin
Ordering for free: once the leaves are in order, the data is sorted, so the median, the mode and the range are easy to find
Comparing groups: a back-to-back plot puts two data sets on the same stems, for example the test scores of two classes or the temperatures of two towns

Sports reporters use them for points per game, doctors for pulse rates, and timetables in many countries still list departure minutes next to each hour, which is exactly the stem-and-leaf idea.

Real World Applications

Points per Game in Basketball

Coaches and sports reporters use stem-and-leaf plots to show a player's scoring over a season without losing any game.

Example:

A player's points in 12 games:

\begin{array}{r|l} 0 & 8~9 \\ 1 & 2~4~4~7 \\ 2 & 0~1~5~6 \\ 3 & 3~8 \end{array}

Key:

1 \mid 2 = 12

points (the stem 0 holds the one-digit scores 8 and 9).

1Try It Yourself

Use the plot of the player's 12 games above.

What is the median number of points per game?

Step 1: Write the mathematical expression

Write the calculation for the median:

Comparing Temperatures of Two Towns

Weather services compare towns with back-to-back plots: the same stems in the middle, one town on each side.

Example:

Daily high temperatures in °C:

\begin{array}{r|c|l} \text{Town A} & \text{Stem} & \text{Town B} \\ \hline 9~6 & 0 & \\ 8~5~3~1 & 1 & 4~7 \\ 2~0 & 2 & 0~3~5~7~8 \\ & 3 & 1~2~4 \end{array}

Key:

6 \mid 0 = 6

°C for Town A,

1 \mid 4 = 14

°C for Town B. Town A has 8 days, Town B has 10 days.

2Try It Yourself

Use the back-to-back plot of the two towns above.

By how many degrees is the median of Town B higher than the median of Town A?

Step 1: Write the mathematical expression

Write median B minus median A:

Resting Pulse Rates

School nurses and doctors record pulse rates in stem-and-leaf plots to see at once which values are typical and which are unusual.

Example:

Resting pulse rates of 12 students in beats per minute:

\begin{array}{r|l} 6 & 2~5~8 \\ 7 & 0~1~4~4~9 \\ 8 & 3~6 \\ 9 & 0~7 \end{array}

Key:

7 \mid 4 = 74

beats per minute.

3Try It Yourself

Use the pulse rate plot above.

What is the range of the pulse rates?

Step 1: Write the mathematical expression

Write the calculation for the range:

Key Takeaways

1A stem-and-leaf plot splits each value into a stem (all digits but the last) and a leaf (the last digit)
2Stems go in a column from smallest to largest, leaves in each row are written in order, and every plot needs a key such as $5 \mid 2 = 52$
3Each leaf is one data value, so the number of leaves is the number of values and every value can be read back
4Because the data is in order, the median is found by counting leaves, the mode is a repeated leaf in one row and the range is last value minus first value
5A back-to-back plot shares the stems between two groups: leaves on the left are read outward from the stem
6Split stems (leaves 0-4 and 5-9 in separate rows) show the shape better when the data uses only a few stems

Frequently Asked Questions

The stem is 0 and the leaf is 7, so 7 is written as

0 \mid 7

. That way one-digit values fit in the same plot as two-digit values.

Glossary

Stem-and-leaf plot: A display that splits each value into a stem and a leaf so that every value is shown and the shape of the data is visible
Stem: All digits of a value except the last one, written once in the left column (in 74 the stem is 7)
Leaf: The last digit of a value, written in the row of its stem (in 74 the leaf is 4)
Key: A note that shows how to read an entry, for example $5 \mid 2 = 52$ or $5 \mid 2 = 5.2$
Back-to-back plot: Two stem-and-leaf plots that share one column of stems, with one group's leaves on the left and the other's on the right
Split stems: Each stem is used for two rows, the first with leaves 0 to 4 and the second with leaves 5 to 9

Formula Card

Reading an entry (key stem | leaf)

7 \mid 4 = 7 \times 10 + 4 = 74

For two-digit data the value is stem times 10 plus leaf. Always check the key: with $7 \mid 4 = 7.4$ the leaf is the tenths digit.

Position of the median

\text{position} = \frac{n + 1}{2}

Count leaves from the top until you reach this position. If it ends in .5, take the mean of the two values on either side.

Range

\text{range} = \text{last leaf value} - \text{first leaf value}

The largest value is the last leaf of the last stem and the smallest is the first leaf of the first stem.

Today's challengeOne problem, three tries

Stem and Leaf Plots

Definition

Worked Examples

Common Mistakes

Interactive Visual

Histogram

Same quiz scores grouped by stem (the plot turned on its side)

Interactive Sandbox

Expression Calculator

History

Practice Problems

Why It Matters

Real World Applications

Points per Game in Basketball

Comparing Temperatures of Two Towns

Resting Pulse Rates

Key Takeaways

Frequently Asked Questions

Glossary

Formula Card

Reading an entry (key stem | leaf)

Position of the median

Range

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