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Mathematics · Topic

Averages from lists and frequency tables

A frequency table needs an fx column; the mean is a division you must show.

2 original questions in the bank, worth 5 marks · above the two-per-topic floor

Drill this topic All averages from lists and frequency tables questions

The questions, with the examiner reasoning

Estimate4 marksBGCSE

A tuck shop records bags of crisps sold each day: 0–4 bags on 6 days, 5–9 on 12 days, 10–14 on 8 days and 15–19 on 4 days. Estimate the mean number of bags sold per day.

Show the mark scheme and the examiner note

Answer: 8.67 bags (2 d.p.)

  1. Midpoints: 2, 7, 12, 17
  2. fx column: 12, 84, 96, 68 → total 260
  3. Frequency total: 30 days
  4. Mean = 260 ÷ 30 = 8.67

Examiner technique: The midpoints are estimated, so the answer is an estimate — say so if asked to comment. The fx column is not optional: the division is a marked step, and two marks belong to it.

Find1 markBoth boards

Find the median of 4, 7, 2, 9, 5, 7, 3.

Show the mark scheme and the examiner note

Answer: 5

  1. Order the list: 2, 3, 4, 5, 7, 7, 9
  2. Seven values, so the median is the 4th
  3. Median = 5
  • A. 5 — Correct: in order, 2, 3, 4, 5, 7, 7, 9 — the middle of seven values is the fourth.
  • B. 7 — That is the mode, the most frequent value. The median is about position, not frequency.
  • C. 4 — That is the value in the middle of the list as written, which is why the list must be ordered first.
  • D. 5.5 — Correct method for an even number of values, but there are seven values here.

Examiner technique: Order first, always. With an even count, take the mean of the two middle values — that is where 5.5 style answers come from.