WAEC 2016 · Paper 2 · Q6

Statistics & correlation

The scores of 20 students are: 3, 2, 4, 2, 3, 2, 1, 2, 2, 4, 5, 2, 5, 3, 1, 2, 2, 6, 2, 3.

(a)
Draw a frequency distribution table for the scores.
Model answer

Score $x$ Frequency $f$

$1$ $2$

$2$ $9$

$3$ $4$

$4$ $2$

$5$ $2$

$6$ $1$

Total $20$

Count each score in the list (a tally helps); the frequencies must add up to 20.
(b)
Use the frequency distribution table to find the mean deviation.

Worked solution (try it first)

(a)

Frequencies: score 1: 2, score 2: 9, score 3: 4, score 4: 2, score 5: 2, score 6: 1 (total 20).

(b)

$\sum fx = 2 + 18 + 12 + 8 + 10 + 6 = 56$ , so the mean is $\dfrac{56}{20} = 2.8$ .
Distances from 2.8: $1.8, 0.8, 0.2, 1.2, 2.2, 3.2$ .
$\sum f|x - \bar x| = 3.6 + 7.2 + 0.8 + 2.4 + 4.4 + 3.2$
$= 21.6$ .
Mean deviation $= \dfrac{21.6}{20} = 1.08$ .

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