WAEC 2009 · Paper 2 · Q14

The age distribution of final year students in a polytechnic is shown in the table below.

Age (years)	20–24	25–29	30–34	35–39	40–44
Number of students	40	45	36	14	5

Calculate, correct to one decimal place, the:

Worked solution (try it first)

Class marks: $22, 27, 32, 37, 42$ .
Multiply by the frequencies: $fx = 880, 1215, 1152, 518, 210$ .
$\sum f = 140$ and $\sum fx = 3975$ .
Mean $= \dfrac{\sum fx}{\sum f}$
$= \dfrac{3975}{140}$
$= 28.39$ , which is $28.4$ years (1 d.p.).

$fx^2 = 19\,360, 32\,805, 36\,864, 19\,166, 8820$ , so $\sum fx^2 = 117\,015$ .
Variance $= \dfrac{\sum fx^2}{\sum f} - \bar x^2$
$= \dfrac{117\,015}{140} - \left(\dfrac{3975}{140}\right)^2$
$= 835.82 - 806.15$
$= 29.67$ .
Standard deviation $= \sqrt{29.67} = 5.4$ years (1 d.p.).