WAEC 2023 · Paper 2 · Q9

Height (m)	3	4	5	6	7	8
Number of trees	4	6	4	5	6	2

The table shows the heights of teak trees harvested by a farmer.

(a)
Find the median height.
(b)
Calculate, correct to one decimal place, the (i) mean; (ii) standard deviation.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

There are $4 + 6 + 4 + 5 + 6 + 2 = 27$ trees, so the median is the $\frac{27 + 1}{2} = 14$ th height.
Running totals: $4, 10, 14, \ldots$ .
The 11th to 14th trees are 5 m, so the median height is 5 m.

(b)(i)

$\sum fx = 12 + 24 + 20 + 30 + 42 + 16$
$= 144$ , so the mean is $\frac{144}{27} \approx 5.3$ m.

(ii)

$\sum fx^2 = 4(9) + 6(16) + 4(25) + 5(36) + 6(49) + 2(64)$
$= 36 + 96 + 100 + 180 + 294 + 128$
$= 834$ .
Standard deviation $= \sqrt{\frac{\sum fx^2}{\sum f} - \bar x^2}$
$= \sqrt{\frac{834}{27} - \left(\frac{144}{27}\right)^2}$
$= \sqrt{30.889 - 28.444}$
$= \sqrt{2.444}$
$\approx 1.6$ m.

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