WAEC 2022 · Paper 2 · Q11

1. Use an assumed mean of 5 years, with $d = x - 5$:

2. Age $x$	1	2	3	4	5	6	7	8	9	10	Total
   $f$	12	14	20	45	36	20	23	16	8	6	200
   $d$	$-4$	$-3$	$-2$	$-1$	0	1	2	3	4	5
   $fd$	$-48$	$-42$	$-40$	$-45$	0	20	46	48	32	30	1
   $fd^2$	192	126	80	45	0	20	92	144	128	150	977

(a)

1. Mean $= 5 + \frac{1}{200} = 5.005 \approx 5.0$ years.

(b)

1. Standard deviation $= \sqrt{\frac{\sum fd^2}{\sum f} - \left(\frac{\sum fd}{\sum f}\right)^2}$
   $= \sqrt{\frac{977}{200} - \left(\frac{1}{200}\right)^2}$
   $= \sqrt{4.885}$
   $\approx 2.2$ years.