JAMB 2011 · UTME · Q45

Class interval	0–2	3–5	6–8	9–11
Frequency	3	2	5	3

Find the mode of the distribution.

Worked solution (try it first)

The modal class is 6–8, with frequency 5.
Its lower class boundary is 5.5 and its width is 3.
Differences from the neighbours: $\Delta_1 = 5 - 2 = 3$ and $\Delta_2 = 5 - 3 = 2$ .
Mode $= 5.5 + \frac{3}{3 + 2} \times 3$
$= 5.5 + 1.8$ , which is 7.3.
So the mode is about 7, option D.