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WAEC 2023 · Paper 2 · Q11✱✱

The table shows the frequency distribution of the ages of fifty members of a family.

Ages (years) 1–5 6–10 11–15 16–20 21–25 26–30
Frequency 7 12 4 6 11 10

Calculate, correct to two decimal places, the:

  1. (a)

    mean;

  2. (b)

    mean deviation of the distribution.

Worked solution (try it first)

(a)

  1. The class marks are 3,8,13,18,23,283, 8, 13, 18, 23, 28.
  2. Ages 1–5 6–10 11–15 16–20 21–25 26–30 Total
    ff 7 12 4 6 11 10 50
    xx 3 8 13 18 23 28
    fxfx 21 96 52 108 253 280 810
  3. Mean =81050=16.20= \frac{810}{50} = 16.20 years.

(b)

  1. The distances of the class marks from 16.2 are ∣x−16.2∣=13.2,8.2,3.2,1.8,6.8,11.8|x - 16.2| = 13.2, 8.2, 3.2, 1.8, 6.8, 11.8.
  2. Multiply by the frequencies: 92.4,98.4,12.8,10.8,74.8,11892.4, 98.4, 12.8, 10.8, 74.8, 118, which add up to 407.2.
  3. Mean deviation =∑f∣x−xˉ∣∑f= \frac{\sum f|x - \bar x|}{\sum f}
    =407.250= \frac{407.2}{50}
    =8.144= 8.144
    ≈8.14\approx 8.14 years.

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