WAEC 2024 · Paper 2 · Q7

The table shows the ages of 20 children in a household.

Age (years)	5	6	7	8	9	10
Frequency	2	$2x - 1$	$y + 2$	4	2	$y - 1$

Given that $x : y = 1 : 2$ , find the:

Worked solution (try it first)

There are 20 children: $2 + (2x - 1) + (y + 2) + 4 + 2 + (y - 1) = 20$ , so $8 + 2x + 2y = 20$ and $x + y = 6$ .
$x : y = 1 : 2$ means $y = 2x$ .
Then $x + 2x = 6$ , so $x = 2$ and $y = 4$ .

The frequencies are $2, 3, 6, 4, 2, 3$ (total 20).
$\sum fx = 5(2) + 6(3) + 7(6) + 8(4) + 9(2) + 10(3)$
$= 10 + 18 + 42 + 32 + 18 + 30$
$= 150$ .
Mean age $= \frac{150}{20} = 7.5$ years.