JAMB 1998 · UME · Q43

Estimate the mode of the frequency distribution below.

Average hourly earnings (₦)	5–9	10–14	15–19	20–24
No. of workers	17	32	25	24

Worked solution (try it first)

The modal class is 10–14, with 32 workers.
Its class boundaries are 9.5 and 14.5, so $L = 9.5$ and $c = 5$ .
Differences from the neighbours: $\Delta_1 = 32 - 17 = 15$ and $\Delta_2 = 32 - 25 = 7$ .
Mode $= L + \frac{\Delta_1}{\Delta_1 + \Delta_2} \times c$
$= 9.5 + \frac{15}{22} \times 5$ , which is $9.5 + 3.41$ .
So the mode is about ₦12.9, option C.