Maths Olympiad · topic 27 of 33 · free

Data handling: mean, median, mode — Maths Olympiad practice

The mean shares the total equally, the median is the middle value once the list is in order, and the mode is the most common value. When a number is added or removed, do not guess — rebuild the total.

How to solve it

Work with totals — “mean × how many = total, and totals are easy to add to”

  1. Mean = total ÷ how many; so total = mean × how many.
  2. Median: put the numbers in order and take the middle one.
  3. Mode: the number that appears most often.
  4. A number added: new mean = (old total + the number) ÷ (how many + 1).

Use it for: Marks, scores, heights and data-table questions in Class 6–10 Olympiad papers and the statistics chapter.

Worked example: The mean of 4 numbers is 15. When the number 25 is added to them, what is the new mean? → 17

  1. Old total: 4 × 15 = 60. Add 25: 60 + 25 = 85.
  2. Now there are 5 numbers: 85 ÷ 5 = 17.

Check: 5 × 17 = 85 = 60 + 25 ✓

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🏁 Topic 27 test

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🖨️ Mean Median Mode Worksheet for Maths Olympiad

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