WAEC 2009 · Paper 2 · Q5

The table shows the marks obtained by a group of students.

Marks	0–9	10–19	20–29	30–39	40–49	50–59	60–69	70–79
Number of students	2	5	9	15	18	14	10	7

(a)
If a student is selected at random from the group, find the probability that this student scored at most 69 marks.
(b)
Calculate the median of the distribution.

Worked solution (try it first)

(a)

The total number of students is $2 + 5 + 9 + 15 + 18 + 14 + 10 + 7 = 80$ .
At most 69 marks means every class except 70–79: $80 - 7 = 73$ students.
Probability $= \dfrac{73}{80}$ .

(b)

The median is the $\frac{80}{2} = 40$ th mark.
Cumulative frequencies: $2, 7, 16, 31, 49, \ldots$ , so the median class is 40–49.
Median $= L_1 + \left(\dfrac{\frac{N}{2} - F}{f_m}\right)c$ with $L_1 = 39.5$ , $F = 31$ , $f_m = 18$ and $c = 10$ .
Median $= 39.5 + \dfrac{40 - 31}{18} \times 10$
$= 39.5 + 5$
$= 44.5$ .

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