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WAEC 2022 · Paper 2 · Q10

Age (years) 3 4 5 6 7 8 9 10
Number of children 2 6 5 xx 6 9 8 5

The table shows the distribution of ages of a number of children in a school. If the mean of the distribution is 7, find the:

  1. (a)

    value of xx;

  2. (b)

    standard deviation of their ages (3 d.p.).

Worked solution (try it first)

(a)

  1. ∑f=2+6+5+x+6+9+8+5\sum f = 2 + 6 + 5 + x + 6 + 9 + 8 + 5
    =41+x= 41 + x and ∑fx=6+24+25+6x+42+72+72+50\sum fx = 6 + 24 + 25 + 6x + 42 + 72 + 72 + 50
    =291+6x= 291 + 6x.
  2. The mean is 7: 291+6x41+x=7\frac{291 + 6x}{41 + x} = 7.
  3. So 291+6x=287+7x291 + 6x = 287 + 7x, which gives x=4x = 4.
  4. Check: ∑f=45\sum f = 45, ∑fx=315\sum fx = 315, and 31545=7\frac{315}{45} = 7.

(b)

  1. With the mean 7:
  2. Age xx 3 4 5 6 7 8 9 10 Total
    ff 2 6 5 4 6 9 8 5 45
    (x−7)2(x - 7)^2 16 9 4 1 0 1 4 9
    f(x−7)2f(x - 7)^2 32 54 20 4 0 9 32 45 196
  3. Standard deviation =19645= \sqrt{\frac{196}{45}}
    =4.3556= \sqrt{4.3556}
    ≈2.087\approx 2.087 years.

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