WAEC 2017 · Paper 2 · Q6

Height (cm)	36–40	41–45	46–50	51–55	56–60
Frequency	3	9	21	12	5

The table shows the heights, in cm, of some seedlings in a certain garden.

(a)
Draw a cumulative frequency curve for the distribution.
Model answer
Plot the cumulative frequencies $3, 12, 33, 45, 50$ against the upper class boundaries $40.5, \ldots, 60.5$ , starting from $(35.5, 0)$ , and join them with a smooth S-shaped curve. For (b): reading across from 12.5 and 37.5 gives $Q_1 \approx 45.6$ and $Q_3 \approx 52.4$ . Readings from a hand-drawn curve vary a little; examiners accept a small range.
(b)
Using the curve, find the semi-interquartile range.

The ogive with the quartile readings.

Worked solution (try it first)

Plot the cumulative frequencies $3, 12, 33, 45, 50$ at the upper boundaries $40.5, 45.5, 50.5, 55.5, 60.5$ , starting from $(35.5, 0)$ , and join with a smooth curve.