Stem and Leaf Diagrams
A stem-and-leaf diagram displays numerical data by splitting each value into a stem, usually all the digits except the last, and a leaf, the final digit, arranged in order so the shape of the distribution can be seen while every original data value stays visible. It is used in the Processing and Representing Data strand of GCSE Statistics as a compact alternative to a plain list of raw data.
Before you start
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Method
- Decide on the stem: usually all the digits of a value except the last one, so for 23 the stem is 2 and the leaf is 3.
- Write the stems in a column in ascending order, with a vertical line separating stems from leaves.
- Add each data value's leaf next to its stem, working through the data set in the order given.
- Redraw the diagram with the leaves in each row sorted in ascending order, and add a key such as '2 | 3 means 23'.
- Read off values by combining a stem with each of its leaves, and count leaves to find the frequency for a row or the whole diagram.
- Use the ordered diagram to find the median, mode or range directly, since the data is already sorted.
Worked example
The times, in minutes, taken by 11 runners to finish a race are: 32, 28, 35, 41, 28, 30, 45, 33, 29, 38, 41. Draw an ordered stem-and-leaf diagram with stems 2, 3 and 4, and use it to find the median time.
- Stems are the tens digit: 2, 3, 4.
- Stem 2 has leaves 8, 8, 9 (from 28, 28, 29).
- Stem 3 has leaves 0, 2, 3, 5, 8 (from 30, 32, 33, 35, 38).
- Stem 4 has leaves 1, 1, 5 (from 41, 41, 45), with key '3 | 2 means 32 minutes'.
- There are 11 values, so the median is the 6th value in order: 28, 28, 29, 30, 32, 33, ...
- Final answer: median = 33 minutes.
Practice questions
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Q1A stem-and-leaf diagram has the row '1 | 4 7 9' with key '1|4 means 14'. What three data values does this row represent?Show answer
Answer: 14, 17, 19
Q2A stem-and-leaf diagram has rows: 0|5 8, 1|2 2 6, 2|1. How many data values are there in total?Show answer
Answer: 6 values
Q3Using the diagram from the question above, what is the mode?Show answer
Answer: 12 (appears twice in row 1)
Q4Using the same diagram (0|5 8, 1|2 2 6, 2|1), what is the range?Show answer
Answer: 16 (21 - 5)
Q5A stem-and-leaf row, with key '3|1 means 31', is '3|0 2 4 4 7 9'. Find the median of these six values.Show answer
Answer: 34 (average of the 3rd and 4th values, 34 and 34)
Q6A back-to-back stem-and-leaf diagram compares two classes' test scores. For stem 7, Class A (left side) has 3 leaves and Class B (right side) has 4 leaves. Which class had more students scoring in the 70s?Show answer
Answer: Class B (4 students compared with 3)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
An unordered stem-and-leaf diagram has key '2|3 means 23' and the row '2 | 7 1 9 4'. Write the four data values in ascending order.
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The ages, in years, of 9 people at a club are recorded in an ordered stem-and-leaf diagram, key '1|5 means 15': 1 | 5 8 9, 2 | 0 3 3 6, 3 | 2 4. (a) Write down the mode. (b) Find the median age.
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The heights, in cm, of 12 plants are recorded in an ordered stem-and-leaf diagram, key '4|2 means 42 cm': 4 | 1 3 5 8 9, 5 | 0 2 2 6, 6 | 1 4 5. (a) Find the median height. (b) Find the range of the heights.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the stem and leaf diagrams worksheet pack - 16 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 18 of GCSE Statistics Foundation Workbook 1 and chapter 22 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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