Stem-and-leaf diagrams and frequency tables

Ordered data makes averages easy to find. Stem-and-leaf diagrams and frequency tables are two neat ways to organise it.

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Stem-and-leaf diagrams

The stem shows the tens and the leaf shows the units. Always give a key.
The data stays in order, so you can read off the median, mode and range.
Key: 3 | 1 means 31 marks
StemLeaf
12 5 8
20 3 3 7
31 4 6 9
42 5

Averages from a frequency table

Goals scored in 20 matches:
Goals01234
Frequency58421

Reading the table

Mode: the value with the highest frequency: 1 goal.
Median: with 20 values it lies between the 10th and 11th. Running totals 5, 13, ... so both are 1 goal. Median = 1.
Range: largest value − smallest value = 4 − 0 = 4. Use the values, not the frequencies.
Comparing: give an average and the range, in context: 'Group A scored more on average, but Group B was more consistent.'
Worked example

Find the median of the marks in the stem-and-leaf diagram.

  1. There are 13 values
  2. The median is the 7th value: (13 + 1) ÷ 2 = 7
  3. Count along: 12, 15, 18, 20, 23, 23, 27

Answer: 27 marks

Key idea

Stem-and-leaf diagrams keep data in order and need a key. In a frequency table, the mode has the highest frequency, and the range uses the values, not the frequencies.

Key words
Frequency
How many times something happens or a value appears in a set of data.
Mode
The value that appears most often. There can be more than one mode.
Range
The largest value minus the smallest value. It measures how spread out the data is.
Median
The middle value when the data is in order. With an even number of values, it is halfway between the middle two.

All KS3 Mathematics key terms and definitions →

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  1. A stem-and-leaf diagram shows these marks: 1 | 4 6 9; 2 | 1 1 5 8; 3 | 0 2 7; 4 | 3 (Key: 2 | 1 means 21). Find the median mark.

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    Answer: 25

    There are 11 values. The median is the 6th: 25.

  2. A stem-and-leaf diagram shows these marks: 1 | 4 6 9; 2 | 1 1 5 8; 3 | 0 2 7; 4 | 3 (Key: 2 | 1 means 21). Find the mode.

    Show the answer

    Answer: 21

    21 appears 2 times, more than any other mark.

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Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

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