Sheet № 63 · Foundation + Higher · AQA · Edexcel · OCR
Mean Median Mode and Range –
Mean, median, mode and range are the four key statistical measures you must know for GCSE Maths. They appear on every exam board — AQA, Edexcel and OCR — and crop up in both Foundation and Higher papers. Whether the data is presented as a list, a table or a grouped frequency chart, you need to be confident selecting the right average and
§Key definitions
Question:
A pupil scored the following marks in seven spelling tests: 6, 9, 3, 7, 9, 5, 8. Find the mean, median, mode and range.
Mean:
Total = 6 + 9 + 3 + 7 + 9 + 5 + 8 = 47. Number of values = 7. Mean = 47 ÷ 7 = 6.71 (to 2 d.p.).
Median:
Arrange in order: 3, 5, 6, 7, 8, 9, 9. Position = (7 + 1) ÷ 2 = 4th value. The 4th value is 7.
Mode:
The value 9 appears twice; all others appear once. Mode = 9.
Range:
9 − 3 = 6.
§Formulas to memorise
Mean = Sum of all values ÷ Number of values
Position of median = (n + 1) ÷ 2, where n is the number of data values
Range = Highest value − Lowest value
Total = 0 + 6 + 10 + 9 + 8 = 33. Total frequency = 4 + 6 + 5 + 3 + 2 = 20.
Mean = 33 ÷ 20 = 1.65 goals.
Worked example
A pupil scored the following marks in seven spelling tests: 6, 9, 3, 7, 9, 5, 8. Find the mean, median, mode and range.
Working:
⚠ Common mistakes
- ✗Forgetting to order the data before finding the median. The median only works when values are in ascending order.
- ✗Confusing the position with the value for the median. If the formula gives position 4, the median is the value at position 4, not the number 4.
- ✗Dividing by the wrong number when calculating the mean from a frequency table — you must divide by the total frequency, not the number of rows.
- ✗Saying there is no mode when two values share the highest frequency — the data set is bimodal and both values are modes.
- ✗Including outliers carelessly when asked which average best represents the data — mention that the mean is affected by outliers while the median is not.
✦ Exam tips
- →Show every step — write down the sum and the count separately before dividing for the mean. This earns method marks even if your final answer is wrong.
- →Use the (n + 1) ÷ 2 rule to find the median position. Examiners expect to see this working.
- →Read the question carefully — if it says "estimate the mean", you are likely dealing with grouped data and should use midpoints. See our guide on frequency tables and grouped data.
- →Check units and rounding — the question may specify "to 1 decimal place" or "to 2 significant figures".
- →For formula reminders, see our GCSE Maths formulas list.