WAEC 2017 · Paper 2 · Q5

Marks	40	41	42	43	44	45	46
Frequency	7	4	6	2	4	2	6

The table shows the distribution of marks of students in a test.

(a)
Represent this information on a bar chart.
Model answer
Put the marks on the horizontal axis and the frequency on the vertical axis, and draw bars of equal width with equal gaps between them. The bar heights are $7, 4, 6, 2, 4, 2, 6$ ; the tallest bar is at mark 40.
(b)
Find the median mark.
(c)
Calculate, correct to three decimal places, the probability that a student selected at random scored less than the median mark.

Worked solution (try it first)

(a)

The marks are separate whole numbers, so draw a bar chart: one bar for each mark from 40 to 46, equal widths, with gaps between them, of heights $7, 4, 6, 2, 4, 2, 6$ .
Label the axes and state the scale.

(b)

There are $7 + 4 + 6 + 2 + 4 + 2 + 6 = 31$ students, so the median is the $\frac{31 + 1}{2} = 16$ th mark.
Running totals: $7, 11, 17, \ldots$ .
The 12th to 17th students scored 42, so the median is 42.

(c)

Less than the median means 40 or 41: $7 + 4 = 11$ students.
The probability is $\frac{11}{31} \approx 0.355$ .

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