Stem-and-Leaf Plot Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Stem-and-Leaf Plot.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

A stem-and-leaf plot displays numerical data by splitting each value into a stem and a leaf. It shows the distribution of the data while keeping the original values visible.

A stem-and-leaf plot is like a sorted list and a graph at the same time. You can see clusters, gaps, and repeated values without losing the exact numbers.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Stem-and-Leaf Plot organizes data so the right pattern is visible without distorting the counts or scale.

Common stuck point: Students often know a procedure related to stem-and-leaf plot but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?

Worked Examples

Example 1

medium

Build a stem-and-leaf plot for:

34, 28, 41, 35, 29, 42, 33, 47

(key

2|8 = 28

). List the rows.

Completed plot for: 34, 28, 41, 35, 29, 42, 33, 47.

Answer

2|8\ 9;\ 3|3\ 4\ 5;\ 4|1\ 2\ 7

First step

Sort the data:

28, 29, 33, 34, 35, 41, 42, 47

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Example 2

medium

Plot:

1\,|\,2\ 4\ 4\ 8

;

2\,|\,1\ 3\ 7

;

3\,|\,0\ 5

(key

1|2 = 12

). Find the mean.

Find the mean of these 9 values.

Example 3

hard

Plot:

1\,|\,2\ 5\ 8

;

2\,|\,0\ 1\ 3\ 7

;

3\,|\,4

(key

1|2 = 12

). Find the IQR.

Find the IQR (Q3 − Q1).

Example 4

hard

Test scores:

72, 85, 91, 68, 77, 85, 79, 88, 92, 73, 80, 85

. Build a stem-and-leaf plot (key

6|8 = 68

Completed stem-and-leaf plot for the 12 test scores.

Example 5

hard

A back-to-back stem-and-leaf for two classes shows that Class A leaves are mostly on stem

7

–

8

while Class B's are spread across stems

5

–

9

. What does this say about the two distributions?

Example 6

challenge

A stem-and-leaf plot of

20

exam scores shows:

5|7\ 9

;

6|1\ 2\ 4\ 8\ 9

;

7|0\ 3\ 5\ 5\ 6\ 8

;

8|1\ 2\ 4\ 5\ 9

;

9|0\ 5

(key

5|7 = 57

). Find the median, the mean, and identify any outliers using the

1.5 \times \text{IQR}

rule.

Find the median, mean, and check for outliers.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A stem-and-leaf plot has stem 3 with leaves 1, 4, 7 (key: 3|1 = 31). List the data values for stem 3.

What are the data values for stem 3?

Example 2

easy

A stem-and-leaf plot row reads 5 | 2 3 3 8 (key 5|2 = 52). How many values are in this row?

How many values are in this row?

Example 3

easy

A stem-and-leaf plot has stems 1, 2, 3 with 4, 6, and 2 leaves respectively. How many data values total?

Example 4

easy

A stem-and-leaf plot's smallest value is in stem 2 with leaf 1 (key 2|1 = 21) and largest in stem 6 with leaf 5. What is the range?

Find the range: max minus min.

Example 5

easy

A stem-and-leaf plot has stem 4 with leaves 2 2 2 5 (key 4|2 = 42). Which value appears most often in this row?

Example 6

easy

A stem-and-leaf plot keeps original values visible. Stem 7 has leaves 0 4 (key 7|0 = 70). What are the exact values?

What are the exact values shown?

Example 7

easy

Is a stem-and-leaf plot best for (A) two-digit test scores of 20 students, or (B) the favorite colors of a class?

Example 8

easy

A stem-and-leaf plot row is 8 | 1 3 9 (key 8|1 = 81). What is the largest value in this row?

Example 9

medium

A stem-and-leaf plot: 1|2 5; 2|0 3 8; 3|1 (key 1|2 = 12). Find the median of all values.

Find the median of all six values.

Example 10

medium

A stem-and-leaf plot: 4|1 1 6; 5|2 9; 6|0 (key 4|1 = 41). What is the mean of all values?

Find the mean of all values.

Example 11

medium

A stem-and-leaf plot: 2|3 7; 3|1 1 4 8; 4|2 (key 2|3 = 23). What is the mode?

Example 12

medium

A stem-and-leaf plot has 12 values. Stems 1,2,3 hold 5, 4, 3 leaves. The 7th value when ordered is 24. Which stem contains the median position values for an even count, and what is needed to find the median?

Example 13

medium

A stem-and-leaf plot: 5|0 4; 6|1 3 7; 7|2 8 (key 5|0 = 50). Find Q1 (the median of the lower half).

Find Q1 (median of the lower half).

Example 14

medium

A stem-and-leaf plot row for stem 9 reads 9 | 0 0 5 (key 9|0 = 90). What fraction of a 10-value dataset is in the 90s?

What fraction of the dataset is in the 90s?

Example 15

medium

A back-to-back stem-and-leaf plot compares two classes on stem 7. Class A leaves: 2 5 8; Class B leaves: 0 3. How many more students scored in the 70s in Class A than Class B?

Example 16

medium

A stem-and-leaf plot: 1|5; 2|0 4 4; 3|1 6; 4|9 (key 1|5 = 15). What is the range, and is 49 an outlier by the 'far from the rest' eye test?

Find the range. Is 49 an outlier?

Example 17

medium

A stem-and-leaf plot: 3|2 8; 4|0 5 5 9; 5|1 (key 3|2 = 32). What value is at the 4th position when ordered?

What value is at the 4th position when ordered?

Example 18

challenge

A stem-and-leaf plot has stems 2, 3, 4 with the same number of leaves each, totaling 9 values, and a median of 35. The stem-3 leaves are 1, 5, 9. What is the median, and which value is it?

Example 19

challenge

A stem-and-leaf plot of 8 values has IQR 20. The values are 2|2 5; 3|0 8; 4|1 7; 5|3 6 (key 2|2 = 22). Verify the IQR.

Verify the IQR (Q3 − Q1).

Example 20

challenge

A stem-and-leaf plot of 10 quiz scores (out of 100) has stems 6,7,8,9. Stem 8 holds leaves 0 0 5 5 5. If the overall mean is 79, what is the sum of the values NOT in the 80s?

Example 21

easy

A stem-and-leaf plot row reads

6 \,|\, 0\ 2\ 5\ 9

(key

6|0 = 60

). List the data values in this row.

List the data values in this row.

Example 22

easy

A stem-and-leaf plot row is

9 \,|\, 1\ 1\ 5

(key

9|1 = 91

). How many values are in this row?

How many values are in this row?

Example 23

easy

A stem-and-leaf plot has stems

0, 1, 2

with

3, 5, 2

leaves respectively. How many values in total?

Example 24

easy

What is the smallest value in this plot?

1\,|\,4\ 9

;

2\,|\,2\ 5

;

3\,|\,0

(key

1|4 = 14

What is the smallest value in this plot?

Example 25

easy

What is the largest value in this plot?

4\,|\,2\ 6

;

5\,|\,1\ 3\ 8

;

6\,|\,0

(key

4|2 = 42

What is the largest value in this plot?

Example 26

medium

Plot:

1\,|\,0\ 5

;

2\,|\,2\ 4\ 9

;

3\,|\,1\ 8

(key

1|0 = 10

). What is the range?

Find the range (max − min).

Example 27

medium

Plot:

3\,|\,2\ 7

;

4\,|\,1\ 4\ 4\ 8

;

5\,|\,0

(key

3|2 = 32

). What is the median?

Example 28

medium

Plot:

2\,|\,1\ 3\ 6

;

3\,|\,2\ 5

;

4\,|\,0\ 7

(key

2|1 = 21

). What is the mode?

What is the mode? (Check for repeated leaves.)

Example 29

medium

Plot:

5\,|\,2\ 5\ 8

;

6\,|\,0\ 3\ 3\ 7

;

7\,|\,1

(key

5|2 = 52

). How many values are at least

63

How many values are at least 63?

Example 30

medium

Plot:

0\,|\,3\ 7

;

1\,|\,2\ 2\ 5

;

2\,|\,4

(key

0|3 = 3

). What is the median?

Example 31

medium

A back-to-back stem-and-leaf plot compares two groups. Group A leaves are read right-to-left from the stem, group B left-to-right. Why is this layout useful?

Example 32

hard

Plot:

4\,|\,1\ 3

;

5\,|\,0\ 5\ 8\ 8

;

6\,|\,2\ 7

;

7\,|\,1

(key

4|1 = 41

). Find

Q_1

and

Q_3

Find Q1 and Q3.

Example 33

hard

In the plot

2\,|\,3\ 8

;

3\,|\,1\ 5\ 9

;

4\,|\,2\ 6\ 7\ 7

;

5\,|\,0

(key

2|3 = 23

), what percent of values are at least

40

What percent of values are at least 40?

Example 34

hard

A truncated stem-and-leaf plot uses stem

12

with leaves

3, 5, 8

where the key reads

12|3 = 123

. List the values.

Example 35

hard

Plot:

0\,|\,5

;

1\,|\,0\ 3\ 9

;

2\,|\,2

(key

0|5 = 0.5

, decimals). What is the mean?

Find the mean (decimal scale: key 0|5 = 0.5).

Example 36

hard

Plot:

2\,|\,5

;

3\,|\,1\ 4

;

4\,|\,0\ 2\ 6\ 8

;

5\,|\,1\ 7

;

6\,|\,3

(key

2|5 = 25

). Describe the shape.

Describe the shape of this distribution.

Example 37

medium

Plot:

1\,|\,1

;

2\,|\,4\ 7

;

3\,|\,2\ 5\ 5\ 8

;

4\,|\,1\ 6

(key

1|1 = 11

). What is the mode?

Example 38

challenge

A stem-and-leaf plot has

25

values with median

46

and IQR

14

. A new value

90

is added, making

26

values. Which summary statistic is most affected: median, IQR, or mean?

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Related Concepts

Frequency Table Dot Plot Histogram Distribution Shape

Background Knowledge

These ideas may be useful before you work through the harder examples.

frequency tabledot plot