WAEC 2013 · Paper 2 · Q7

1. Use the assumed mean $A = 85$ and the deviations $d$.
2. There are $n = 9$ numbers.
3. Add the deviations: $\sum d = -6 - 4 - 2 + 1 + 2 + 3 + 4 + 5 + 8$
   $= 11$.

(a)

1. Mean $= A + \dfrac{\sum d}{n}$, so the mean is $85 + \dfrac{11}{9}$.
2. That is $85 + 1.222 \approx 86.22$.

(b)

1. Square and add the deviations: $\sum d^2 = 36 + 16 + 4 + 1 + 4 + 9 + 16 + 25 + 64$
   $= 175$.
2. Variance $= \dfrac{\sum d^2}{n} - \left(\dfrac{\sum d}{n}\right)^2$, so it is $\dfrac{175}{9} - \left(\dfrac{11}{9}\right)^2$.
3. Work it out: $19.444 - 1.494 \approx 17.95$.
4. The mean is 86.22 and the variance is 17.95.