WAEC 2023 · Paper 2 · Q5

1. Put the heights in order: $110, 120, 120, 125, 128, 130, 135, 140, 142, 145$.

(a)

1. Range $= 145 - 110 = 35$ cm.

(b)

1. $Q_1$ is at position $\frac{10}{4} = 2.5$: halfway between the 2nd and 3rd heights, $\frac{120 + 120}{2} = 120$.
2. $Q_3$ is at position $\frac{3 \times 10}{4} = 7.5$: halfway between the 7th and 8th heights, $\frac{135 + 140}{2} = 137.5$.
3. Interquartile range $= 137.5 - 120 = 17.5$ cm.

(c)

1. The heights add up to 1295, so the mean is $\frac{1295}{10} = 129.5$ cm.