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Median of grouped data sheet
5-mark answer frame

The median of the marks of 50 students is 50. Find p and q. Marks: 0-20: 6, 20-40: p, 40-60: 16, 60-80: q, 80-100: 8.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. Given: n = 50, median = 50, five classes of size 20. To find: p and q.
  2. 2 · Use the total. 6 + p + 16 + q + 8 = 50, so p + q = 20.
  3. 3 · Make the cumulative frequency column. cf: 6, 6 + p, 22 + p, 22 + p + q, 50.
  4. 4 · Find the median class. The median 50 lies in 40-60. So l = 40, h = 20, f = 16, cf = 6 + p, and n/2 = 25.
  5. 5 · Write the formula and substitute. Median = l + ((n/2 − cf) ÷ f) × h, so 50 = 40 + ((25 − 6 − p) ÷ 16) × 20.
  6. 6 · Solve.
    • 10 = (19 − p) × 20 ÷ 16, so 19 − p = 8.
    • p = 11 and q = 20 − 11 = 9.
  7. 7 · Check and box the answer. cf: 6, 17, 33, 42, 50. Median = 40 + ((25 − 17) ÷ 16) × 20 = 50. Box: p = 11, q = 9.

Scoring tip: Always write the check with the new cf column. If the median comes back right, your values are correct.