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WAEC 2013 · Paper 2 · Q6

Age (years) 12–14 15–17 18–20 21–23 24–26
Frequency 6 10 3 2 1

The table shows the distribution of ages of 22 students in a school. Using an assumed mean of 19, calculate, correct to three significant figures, the:

  1. (a)

    mean age;

  2. (b)

    standard deviation of the distribution.

Worked solution (try it first)
  1. Class marks 13,16,19,22,2513, 16, 19, 22, 25.
  2. d=x−19d = x - 19: −6,−3,0,3,6-6, -3, 0, 3, 6.
  3. Frequencies 6,10,3,2,16, 10, 3, 2, 1.
  4. ∑fd=−36−30+0+6+6=−54\sum fd = -36 - 30 + 0 + 6 + 6 = -54 and ∑fd2=216+90+0+18+36=360\sum fd^2 = 216 + 90 + 0 + 18 + 36 = 360.

(a)

  1. xˉ=19+−5422\bar x = 19 + \dfrac{-54}{22}
    =19−2.4545= 19 - 2.4545
    ≈16.5\approx 16.5 years.

(b)

  1. σ=36022−2.45452\sigma = \sqrt{\dfrac{360}{22} - 2.4545^2}
    =16.3636−6.0248= \sqrt{16.3636 - 6.0248}
    ≈3.22\approx 3.22 years.

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