Sheet № 180 · Foundation + Higher · AQA · Edexcel · OCR
Finding the Median –
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 an
§Key definitions
Question:
Find the median of: 7, 3, 9, 1, 5, 8, 4.
Answer:
The median is 5.
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.
§Formulas to memorise
Median position = (n + 1) ÷ 2, where n is the number of values
n = 7. Median position = (7 + 1) ÷ 2 = 4th value.
n = 8. Median position = (8 + 1) ÷ 2 = 4.5th value.
n = 30. Median position = (30 + 1) ÷ 2 = 15.5th value.
Worked example
Find the median of: 7, 3, 9, 1, 5, 8, 4.
Working:
⚠ 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.