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WAEC 2014 · Paper 2 · Q12

Age (years) 15–19 20–24 25–29 30–34 35–39 40–44 45–49 50–54 55–59 60–64
Number of workers 5 22 30 32 25 36 32 30 21 2

The table shows the frequency distribution of the ages of workers in a factory. Using an assumed mean of 42, calculate, correct to one decimal place, the:

  1. (a)

    mean;

  2. (b)

    variance of the distribution.

Worked solution (try it first)
  1. Class marks 17,22,…,6217, 22, \ldots, 62 and d=x−42d = x - 42: −25,−20,−15,−10,−5,0,5,10,15,20-25, -20, -15, -10, -5, 0, 5, 10, 15, 20.
  2. ∑f=235\sum f = 235, ∑fd=−645\sum fd = -645 and ∑fd2=31 825\sum fd^2 = 31\,825.

(a)

  1. Mean =42+−645235= 42 + \dfrac{-645}{235}
    =42−2.745= 42 - 2.745
    ≈39.3\approx 39.3 years.

(b)

  1. Variance =31 825235−(−645235)2= \dfrac{31\,825}{235} - \left(\dfrac{-645}{235}\right)^2
    =135.43−7.53= 135.43 - 7.53
    ≈127.9\approx 127.9.

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