WAEC 2025 · Paper 2 · Q5✱✱

Statistics: data & averages

The table shows the marks scored by 32 students.

Mark	1	2	3	4	5	6	7	8	9	10
Frequency	2	3	4	4	4	4	5	3	2	1

(a)
Find the (i) mean, correct to two decimal places; (ii) median; (iii) mode.
Separate values with commas, e.g. 3, −2
(b)
Find the percentage of students who scored at least 8 marks.

Worked solution (try it first)

(a)(i)

$\sum fx = 1(2) + 2(3) + 3(4) + 4(4) + 5(4) + 6(4) + 7(5) + 8(3) + 9(2) + 10(1)$
$= 2 + 6 + 12 + 16 + 20 + 24 + 35 + 24 + 18 + 10$
$= 167$ , and $\sum f = 32$ .
Mean $= \frac{167}{32} \approx 5.22$ .

(ii)

With 32 marks, the median is halfway between the 16th and 17th.
Running totals: $2, 5, 9, 13, 17, \ldots$ .
The 14th to 17th marks are all 5, so the median is 5.

(iii)

The highest frequency is 5, for the mark 7, so the mode is 7.

(b)

"At least 8" means 8, 9 or 10: $3 + 2 + 1 = 6$ students.
As a percentage: $\frac{6}{32} \times 100 = 18.75\%$ .

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