WAEC 2017 · Paper 2 · Q13

Statistics & correlation

Age (years)	17–19	20–22	23–28	29–34	35–43
Number of patients	6	9	12	18	18

The table shows the frequency distribution of the ages of patients in a clinic.

(a)
Draw a histogram for the distribution.
Model answer
The classes have unequal widths (3, 3, 6, 6, 9), so the bar heights are frequency densities, frequency ÷ width: $2, 3, 2, 3, 2$ . Each bar stands on its class boundaries, so the bars touch and each bar’s area is its frequency.
(b)
Find, correct to two decimal places, the mean age of the patients.

Try it on a graph

Histogram with unequal class widths: heights are frequency densities.

Worked solution (try it first)

(a)

Class widths (from the boundaries): $3, 3, 6, 6, 9$ .
Frequency densities: $\frac63 = 2$ , $\frac93 = 3$ , $\frac{12}{6} = 2$ , $\frac{18}{6} = 3$ , $\frac{18}{9} = 2$ .
Draw each bar with this height over its class boundaries.

(b)

Class marks $18, 21, 25.5, 31.5, 39$ .
$\sum fx = 108 + 189 + 306 + 567 + 702$
$= 1872$ and $\sum f = 63$ .
Mean $= \dfrac{1872}{63} \approx 29.71$ years.

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