JAMB 1995 · UME · Q45

Find the standard deviation of the data in the table below.

Class	1–3	4–6	7–9
Frequency	5	8	5

Worked solution (try it first)

Use the class mid-points 2, 5 and 8.
The total is $5 \times 2 + 8 \times 5 + 5 \times 8 = 90$ over 18 values, so the mean is $\frac{90}{18} = 5$ .
The deviations are $-3$ , 0 and 3, so $\sum f d^2 = 5 \times 9 + 0 + 5 \times 9$
$= 90$ .
The variance is $\frac{90}{18} = 5$ , so the standard deviation is $\sqrt5$ , option D.