EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
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Statistics & Probability · Foundation & Higher

Mean, median, mode & range

Averages summarise a data set with a single representative value. The range measures spread.

Revising mean, median, mode & range the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Mean, median, mode & range GCSE” on the site for the complete guide.

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Key facts to remember

  • 1Mean = sum of all values ÷ number of values.
  • 2Median = middle value when data is ordered (or mean of middle two for even-sized data).
  • 3Mode = most frequently occurring value (there can be more than one).
  • 4Range = largest value − smallest value.
  • 5The mean is affected by outliers; the median is not.
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Formulas

Mean
x̄ = Σx / n

Σx = sum of all values, n = count

Range
Range = Max − Min
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Worked examples

Example 1

Find the mean, median, mode and range of: 3, 7, 7, 2, 9, 4, 7

Working

  1. Order: 2, 3, 4, 7, 7, 7, 9
  2. Mean = (2+3+4+7+7+7+9) ÷ 7 = 39 ÷ 7 = 5.57 (2 d.p.)
  3. Median = 4th value = 7
  4. Mode = 7 (appears 3 times)
  5. Range = 9 − 2 = 7
AnswerMean ≈ 5.57, Median = 7, Mode = 7, Range = 7
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Common mistakes

✗Forgetting to sort the data before finding the median.
✗Finding the median position incorrectly for even-sized data (should average the two middle values).
✗Confusing mode (most common) with mean (average).
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Exam tips

✓Always sort the data first — write the ordered list out clearly.
✓For n data points, the median is at position (n+1)/2.

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