WAEC 2018 · Paper 2 · Q12

The data show the production of mobile phones per day over a thirty-day period by a company.

53 26 21 28 38 46 35 31 51 35 23 38 46 24 44 36 39 40 45 33 32 54 51 49 20 42 46 38 39 40

(a)

Construct a frequency distribution table for the data using 7 class intervals of equal widths of 5.

Model answer

Start at the smallest value, 20, and take classes of width 5 up to 50–54, which holds the largest value, 54.

(b)
Draw a histogram for the distribution.
Model answer
Draw bars on the class boundaries, not the class limits (19.5, 24.5, …, 54.5), with no gaps between them. The height of each bar is the frequency, and each axis is labelled.

To estimate the mode, take the tallest bar. Join its top-left corner to the top-left corner of the bar on its right, and its top-right corner to the top-right corner of the bar on its left. Read down from where the two lines cross: the mode is about 37.3.
(c)
Use the histogram to estimate the mode.
(d)
Find, correct to two decimal places, the percentage of production above the modal class.

Histogram with the crossed lines that locate the mode.

Worked solution (try it first)

Tally the 30 values into 20–24, 25–29, …, 50–54: frequencies $4, 2, 3, 8, 4, 5, 4$ .

The modal class is 35–39.
Mode $= 34.5 + \dfrac{8 - 3}{(8 - 3) + (8 - 4)} \times 5$
$= 34.5 + \dfrac59 \times 5$
$\approx 37.3$ .

Above the modal class: $4 + 5 + 4 = 13$ of 30 days, which is $\dfrac{13}{30} \times 100 \approx 43.33\%$ .