WAEC 2019 · Paper 2 · Q12

Statistics & correlation

Marks	50–54	55–59	60–64	65–69	70–74	75–79	80–84	85–89
Frequency	5	15	20	28	12	9	7	4

The table shows the distribution of marks obtained by students in an examination. Using an assumed mean of 67, calculate, correct to one decimal place, the:

(a)
mean;
(b)
standard deviation of the distribution.

Worked solution (try it first)

Class marks $52, 57, \ldots, 87$ and $d = x - 67$ : $-15, -10, -5, 0, 5, 10, 15, 20$ .
$\sum f = 100$ , $\sum fd = 10$ and $\sum fd^2 = 7500$ .

(a)

Mean $= 67 + \dfrac{10}{100} = 67.1$ .

(b)

$\sigma = \sqrt{\dfrac{7500}{100} - 0.1^2}$
$= \sqrt{74.99}$
$\approx 8.7$ .

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