WAEC 2021 · Paper 2 · Q5

Age	12	13	15	10	14	16
Frequency	2	3	3	9	6	2

The table shows the distribution of ages of some students in a school.

Worked solution (try it first)

Put the ages in order (the table in the question isn't) and find the mean first:
Age $x$ 10 12 13 14 15 16 Total

$f$ 9 2 3 6 3 2 25

$fx$ 90 24 39 84 45 32 314
Mean $= \frac{314}{25} = 12.56$ .

Age $x$	10	12	13	14	15	16	Total
$f$	9	2	3	6	3	2	25
$fx$	90	24	39	84	45	32	314

Age $x$	10	12	13	14	15	16	Total
$\lvert x - 12.56\rvert$	2.56	0.56	0.44	1.44	2.44	3.44
$f\lvert x - 12.56\rvert$	23.04	1.12	1.32	8.64	7.32	6.88	48.32

Mean deviation $= \frac{\sum f|x - \bar x|}{\sum f}$
$= \frac{48.32}{25}$
$= 1.9328$
$\approx 1.9$ .