WAEC 2019 · Paper 2 · Q13

Statistics & correlation

In a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the results of ten randomly selected students were obtained as follows:

Student	A	B	C	D	E	F	G	H	I	J
Entrance examination	11	12	8	13	6	15	10	14	17	16
School performance	5	10	9	7	4	8	6	14	11	12

(a)
Calculate the Spearman's rank correlation coefficient (3 d.p.).
(b)
What would be the researcher's conclusion from the result in (a)?
Show the answer
There is a (fairly strong) positive correlation between entrance examination and school performance.

Worked solution (try it first)

(a)

Rank the entrance marks (1 for the highest): A 7, B 6, C 9, D 5, E 10, F 3, G 8, H 4, I 1, J 2.
Rank the school marks: A 9, B 4, C 5, D 7, E 10, F 6, G 8, H 1, I 3, J 2.
$d$ : $-2, 2, 4, -2, 0, -3, 0, 3, -2, 0$ , so $\sum d^2 = 50$ .
$\rho = 1 - \dfrac{6 \times 50}{10 \times 99}$
$= 1 - 0.3030$
$\approx 0.697$ .

(b)

There is a fairly strong positive correlation: students who do well in the entrance examination tend to do well in school.

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