WAEC 2009 · Paper 2 · Q8✱

Statistics: data & averages

The marks scored by 50 students in a Geography examination are as follows:


60	54	40	67	53	73	37	55	62	43
44	69	39	32	45	58	48	67	39	51
46	59	40	52	61	48	23	60	59	47
65	58	74	47	40	59	68	51	50	50
71	51	26	36	38	70	46	40	51	42

(a)
Using class intervals 21 – 30, 31 – 40, …, prepare a frequency distribution table.
Model answer

Marks 21–30 31–40 41–50 51–60 61–70 71–80

Class mark $x$ 25.5 35.5 45.5 55.5 65.5 75.5

Frequency $f$ 2 10 12 15 8 3

$fx$ 51 355 546 832.5 524 226.5

The frequencies add up to 50 and $\sum fx = 2535$ .
(b)
Calculate the mean mark of the distribution.
(c)
What percentage of the students scored more than 60 marks?

Worked solution (try it first)

(a)

Tally each mark into its class.
The frequencies are 2, 10, 12, 15, 8 and 3.
Check they add up to 50.

(b)

Class marks are the midpoints: $25.5, 35.5, \dots, 75.5$ .
Multiply each by its frequency: $51, 355, 546, 832.5, 524, 226.5$ .
Add them: $\sum fx = 2535$ .
Mean $= \frac{\sum fx}{\sum f}$
$= \frac{2535}{50}$
$= 50.7$ .

(c)

More than 60 marks means the classes 61–70 and 71–80: $8 + 3 = 11$ students.
Percentage $= \frac{11}{50} \times 100 = 22\%$ .

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