The median is a key measure of average that appears on both Foundation and Higher GCSE Maths papers across AQA, Edexcel and OCR. Unlike the mean, the median is not affected by extreme values, making it especially useful for skewed data. You need to be able to order data, apply the position rule, find the median from even-numbered lists and from frequency tables. This guide explains each skill step by step. For an overview of every topic, see our complete GCSE Maths topics list.
What Is the Median?
The median is the middle value when data is arranged in order from smallest to largest. If there is an even number of values, the median is the mean of the two middle values.
Key Formulas
For an odd number of values, this gives a whole number — the position of the median. For an even number, it gives a position ending in .5, telling you to average the two values either side.
Median from a Frequency Table
Add a cumulative frequency column. Use (n + 1) ÷ 2 to find the position, then read across to find which value that position falls in.
Step-by-Step Method
- Arrange all data values in ascending order.
- Count the total number of values, n.
- Calculate the median position: (n + 1) ÷ 2.
- If n is odd, the median is the value at that position.
- If n is even, add the two middle values and divide by 2.
Worked Example 1 — Foundation Level
Question: Find the median of: 7, 3, 9, 1, 5, 8, 4.
Working:
Arrange in order: 1, 3, 4, 5, 7, 8, 9.
n = 7. Median position = (7 + 1) ÷ 2 = 4th value.
The 4th value is 5.
Answer: The median is 5.
Worked Example 2 — Higher Level
Question: Find the median of: 12, 6, 18, 3, 15, 9, 21, 24.
Working:
Arrange in order: 3, 6, 9, 12, 15, 18, 21, 24.
n = 8. Median position = (8 + 1) ÷ 2 = 4.5th value.
This means we average the 4th and 5th values: (12 + 15) ÷ 2 = 13.5.
Answer: The median is 13.5.
Worked Example 3 — Exam Style
Question: The table shows the number of pets owned by 30 pupils.
| Pets | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Frequency | 5 | 8 | 10 | 4 | 3 |
Find the median number of pets.
Working:
n = 30. Median position = (30 + 1) ÷ 2 = 15.5th value.
Cumulative frequencies: 5, 13, 23, 27, 30.
The 15th and 16th values both fall in the "2 pets" group (cumulative frequency reaches 23 at 2 pets).
Answer: The median number of pets is 2.
Common Mistakes
- Forgetting to order the data. The median requires data in ascending order — finding the middle of an unordered list gives a wrong answer.
- Using n ÷ 2 instead of (n + 1) ÷ 2. The correct position formula includes the +1. Without it, you may select the wrong value.
- Not averaging for even-numbered lists. When n is even, you must find the mean of the two middle values, not just pick one of them.
- Misreading cumulative frequency. When working from a frequency table, build the cumulative frequency carefully and check which group the median position falls in.
Exam Tips
- Always write the data in order before identifying the median — even if it looks roughly ordered already.
- For frequency tables, add a cumulative frequency column on the exam paper to keep your working clear.
- If asked to compare the median with the mean, note that the median is not affected by outliers and may better represent the "typical" value in skewed data.
- For related averages, see finding the mean and mode and range. For key formulas, visit our GCSE Maths formulas page.
Practice Questions
Q1 (Foundation): Find the median of 14, 8, 22, 11, 17.
Q2 (Foundation): Find the median of 5, 10, 2, 8, 6, 3.
Q3 (Higher): A frequency table shows scores 1 (freq 4), 2 (freq 7), 3 (freq 6), 4 (freq 3). Find the median score.
Practise finding the median and other averages free on GCSEMathsAI.
Related Topics
Summary
- The median is the middle value when data is arranged in order from smallest to largest.
- Use the position rule (n + 1) ÷ 2 to find which value is the median.
- For an even number of values, average the two middle values.
- For frequency tables, use cumulative frequency to locate the median position.
- The median is not affected by outliers, making it useful for skewed data.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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