Question

The final position of twelve clubs in a football league and the average attendance at their home matches were as follows. Calculate a coefficient of correlation by ranks.

Club	A	B	C	D	E	F	G	H	I	J	K	L
Position	1	2	3	4	5	6	7	8	9	10	11	12
Attendance (thousands)	27	30	18	25	32	12	19	11	32	12	12	15

• A. 0.34
• B. 0.56
• C. 0.32
• D. 0.48

Answer 1

The correct option is D 0.48

Club	Attendance	Rank	Position	$|d|$	$d^2$
A B C D E F G H I J K L	27 30 18 25 32 12 19 11 32 12 12 15	4 3 7 5 1 9 6 12 1 9 9 8	1 2 3 4 5 6 7 8 9 10 11 12	3 1 4 1 4 3 1 4 8 1 2 4	9 1 16 1 16 9 1 16 64 1 4 16

$n=12,\sum d^2=154$

$r=1-\frac{6\sum d^2}{n(n^2-1)}=1-\frac{6\times 154}{12({12}^2-1)}=1-\frac{924}{1716}=0.48$