Practice Maths

L48 — Stem-and-Leaf Plots

Key Ideas

Key Terms

stem
The leading digit(s) in a stem-and-leaf plot, representing the higher place value. Usually the tens digit. Written in a column on the left side of the plot.
leaf
The final digit of a value in a stem-and-leaf plot, representing the units digit. Written to the right of the corresponding stem.
stem-and-leaf plot
A display that organises numerical data by splitting each value into a stem and leaf. All original values remain visible while the overall distribution is shown.
back-to-back stem-and-leaf plot
A display comparing two datasets using a shared central stem. One group's leaves go to the right, the other group's leaves go to the left.
key
A note that explains how to read the plot. For example, "2 | 3 = 23" tells the reader that stem 2 and leaf 3 represent the value 23.
distribution
How data values are spread across a range — where they cluster, where there are gaps, and the overall shape of the data.

Reading and Creating Stem-and-Leaf Plots

A stem-and-leaf plot organises numerical data using the tens digit as the stem (written on the left) and the units digit as the leaf (written on the right).

  • Stems are listed vertically in order (smallest to largest)
  • Leaves are listed horizontally, one digit per value, in order from smallest to largest
  • To read a value: combine stem and leaf — stem 3, leaf 5 gives the number 35
  • Back-to-back plots compare two datasets: leaves for one group go left, leaves for the other go right, sharing the same stems

Key: Always include a key (e.g. 3 | 5 = 35) so the reader knows what the stem represents.

Hot Tip: Always order the leaves from smallest to largest within each stem. If you write them in the order you find them, go back and sort them before your final answer!

Worked Example

Create a stem-and-leaf plot for: 23, 31, 45, 23, 38, 42, 51, 35, 28, 47, 33, 50

Step 1: Identify stems (tens digits): 2, 3, 4, 5

Step 2: Sort leaves (units digits) under each stem:

StemLeaves
23   3   8
31   3   5   8
42   5   7
50   1

Key: 2 | 3 = 23

Min = 23, Max = 51, Count = 12 values

What Is a Stem-and-Leaf Plot?

A stem-and-leaf plot is a clever way to organise numbers so you can see every individual value AND get an overall picture of how the data is spread. Instead of just listing numbers in a random order, you split each number into two parts: the stem (the leading digits, usually tens) and the leaf (the final digit, usually units). For example, the number 47 has a stem of 4 and a leaf of 7.

The stems are written in a column on the left, in order from smallest to largest. The leaves are written to the right of each stem, one digit per value. This display keeps all the original values visible — that's what makes it special compared to a bar graph, which only shows totals.

How to Build a Stem-and-Leaf Plot

Follow these steps every time:

Step 1: Find the smallest and largest values to work out which stems you need. For example, if data ranges from 23 to 58, you need stems 2, 3, 4, and 5.

Step 2: Write all stems in order down the left side, with a vertical line next to them.

Step 3: Go through the original data one value at a time. For each value, write its leaf next to the correct stem. Don't worry about order yet — just get all the leaves recorded.

Step 4: Go back and reorder the leaves in each row from smallest to largest.

Step 5: Write a key — for example, "2 | 3 = 23" — so the reader knows how to interpret the plot.

Reading Data from a Stem-and-Leaf Plot

To read a value from the plot, combine the stem with each of its leaves. A stem of 3 with leaves "1, 5, 8" gives the values 31, 35, and 38. You can find the minimum (first leaf of the first stem) and maximum (last leaf of the last stem) straight away. You can also count how many values are in each row, and spot which range of values has the most data.

Back-to-Back Stem-and-Leaf Plots

When you want to compare two groups side by side, you can use a back-to-back stem-and-leaf plot. The stems go down the middle. One group's leaves go to the right (read left to right as usual). The other group's leaves go to the left (but you still read them from the stem outward, so the smallest leaf is closest to the stem). This layout makes it easy to compare the two groups directly — you can see at a glance which group has higher values, which is more spread out, and whether there's any overlap.

Key tip — always sort the leaves: The most common mistake in stem-and-leaf plots is forgetting to sort the leaves in order within each row. If the leaves are jumbled (e.g. "7, 2, 5" instead of "2, 5, 7"), the plot still contains the right data, but you can't find the median or minimum/maximum quickly. Always sort before writing your final answer.

  1. Create Stem-and-Leaf Plots

    For each dataset: (i) draw the stem-and-leaf plot with leaves in order, (ii) state the minimum and maximum, (iii) count how many values fall in each stem group.

    1. Dataset A: 34, 27, 41, 35, 29, 38, 42, 27, 51, 33, 46, 39   (use stems 2, 3, 4, 5)
    2. Dataset B: 12, 8, 15, 19, 7, 14, 11, 18, 6, 13, 16, 9, 20   (use stems 0, 1, 2)
    3. Dataset C: 62, 74, 68, 83, 71, 79, 65, 88, 76, 69, 84, 72, 81   (use stems 6, 7, 8)

  2. Reading Stem-and-Leaf Plots

    Use the stem-and-leaf plots below to answer each set of questions.

    Plot 1 — Daily maximum temperatures (°C) in April:

    StemLeaves
    18   9
    20   2   3   5   5   7   8
    30   1   4

    Key: 2 | 3 = 23°C

    1. How many days are recorded?
    2. What was the highest temperature recorded?
    3. How many days had a temperature in the 20s?
    4. What was the most common temperature (mode)?

    Plot 2 — Scores on a spelling test (out of 50):

    StemLeaves
    24   6   9
    31   3   3   7   8
    40   2   5   5   8
    50

    Key: 3 | 7 = 37

    1. What was the lowest score?
    2. How many students scored 40 or above?
    3. What score appears most often?
    4. What is the range of scores?

    Plot 3 — Ages of people at a community event:

    StemLeaves
    12   4   5   9
    21   3   8
    30   5   5   6
    42   7
    53

    Key: 3 | 5 = 35

    1. How many people attended the event?
    2. What age group (decade) was most common?
    3. List all the ages in the 30s in order.
    4. What is the range of ages?

  3. Understanding the Plot Structure

    1. Using Dataset A from Q1 (34, 27, 41, 35, 29, 38, 42, 27, 51, 33, 46, 39), list all the values in order from smallest to largest.
    2. Compare listing data in a regular ordered list versus using a stem-and-leaf plot. What does the stem-and-leaf plot show that a plain list does not?
    3. A student creates a stem-and-leaf plot and writes the leaves out of order within each stem. Why is this a problem? Give an example of how it could cause an error when finding the median.
    4. For Dataset B from Q1, which stem group has the most values? What does this tell you about the data?

  4. Back-to-Back Stem-and-Leaf Plot

    The back-to-back stem-and-leaf plot below shows the test scores for Class A (leaves on the left) and Class B (leaves on the right).

    Class A (leaves) Stem Class B (leaves)
    9   6   2 5 3   7   8
    8   5   3   1 6 0   2   5   9
    7   4   2 7 1   4   6   8
    5   0 8 2   6

    Key: for Class A, read right to left: 5 | 2 = 52. For Class B, read left to right: 5 | 3 = 53.

    1. List all scores for Class A in order from smallest to largest.
    2. List all scores for Class B in order from smallest to largest.
    3. What is the highest score in each class?
    4. Which class had more students score in the 70s? How many in each class?
    5. What is the range of scores for each class?

  5. Interpret in Context

    1. A teacher records the number of correct answers (out of 20) for her class: 14, 17, 11, 18, 15, 12, 19, 16, 14, 17, 20, 13, 15, 16, 18. Create a stem-and-leaf plot and identify: the most common score, the highest score, and how many students scored more than 15.
    2. The heights (cm) of a basketball team are: 172, 185, 168, 191, 179, 183, 175, 188, 162, 176. Create a stem-and-leaf plot. What does the shape of the plot tell you about the spread of heights in the team?
    3. Using the stem-and-leaf plot from Q1, Dataset C (62, 74, 68, 83, 71, 79, 65, 88, 76, 69, 84, 72, 81): what is the middle value (median) of this dataset? Show how you found it.

  6. Read the key and decode values

    Use the stem-and-leaf plot below. Key: 4 | 3 = 43

    StemLeaves
    32   5   8
    40   1   4   7   9
    52   3   6
    60   5
    1. List all values from the plot.
    2. How many values are there in total?
    3. What is the minimum value?
    4. What is the maximum value?
    5. What is the range?
    6. Which stem group has the most values?
    7. What is the median value?

  7. Errors in stem-and-leaf plots

    The following stem-and-leaf plot was created by a student from the dataset: 31, 24, 38, 42, 26, 35, 48, 22, 39, 41.

    StemLeaves (student's version)
    24   6
    31   8   5   9
    42   8   1
    1. How many values should be in the plot? How many are shown?
    2. Identify one error the student made (other than missing values).
    3. Rewrite the corrected stem-and-leaf plot with leaves in order.
    4. Using the corrected plot, what is the median of the dataset?

  8. Create a back-to-back plot

    Two Year 7 classes recorded how long (minutes) they spent reading each evening.

    Class 7X: 15, 22, 30, 18, 25, 12, 28, 35, 20, 17

    Class 7Y: 20, 32, 14, 27, 36, 23, 19, 31, 25, 28

    1. Create a back-to-back stem-and-leaf plot using stems 1, 2, 3.
    2. Which class read for longer on average? Support your answer by referring to the plot.
    3. What is the range for each class?
    4. How many students in Class 7X read for 20 minutes or more?

  9. Stem-and-leaf to measures

    A physiotherapist records patients' recovery times (days) after knee surgery:

    45, 52, 38, 61, 49, 55, 43, 58, 47, 63, 50, 41, 56, 44, 53

    1. Create a stem-and-leaf plot for this data. Include a key.
    2. Find the median recovery time from the plot.
    3. Find the mode and range.
    4. The physiotherapist says "Most patients recover in 40 to 59 days." Does the plot support this claim? Count the values in the relevant stems.
    5. Two new patients recover in 28 and 71 days. Add these to your plot. Does this change the median? Find the new median.

  10. Comparing datasets with back-to-back plots

    A researcher compares the number of hours per week spent on screens by adults and teenagers.

    Adults: 22, 18, 25, 30, 19, 28, 21, 15, 23, 27

    Teenagers: 35, 42, 38, 45, 31, 40, 36, 48, 33, 44

    1. Create a back-to-back stem-and-leaf plot with appropriate stems.
    2. What is the range for adults? What is the range for teenagers?
    3. Write two comparison statements about the two groups using evidence from the plot.
    4. The researcher claims "Teenagers spend more than twice as many hours on screens as adults." Is this claim supported by the minimum and maximum values? Explain.
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