WAEC 2022 · Paper 2 · Q12

(a)
The mean and the standard deviation of marks scored by eight people in an interview are 7 and $\sqrt3$ respectively. If six of the marks are 6, 7, 9, 5, 5 and 6, find the two remaining marks.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

The mean is 7, so the eight marks add to $8 \times 7 = 56$ .
The six known marks add to 38, so the missing ones satisfy $a + b = 18$ .
$\sigma^2 = 3 = \dfrac{\sum x^2}{8} - 7^2$ , so $\sum x^2 = 8 \times 52 = 416$ .
The six known squares add to 252, so $a^2 + b^2 = 164$ .
Substitute $b = 18 - a$ : $a^2 + (18 - a)^2 = 164$ , so $2a^2 - 36a + 160 = 0$ , that is $a^2 - 18a + 80 = 0$ .
Factorise: $(a - 8)(a - 10) = 0$ .
The two marks are 8 and 10.