Question

Find the rank correlation coefficient between the heights of fathers and sons from the following data:

Heights of fathers in inches	65	66	67	67	68	69	70	72
Height of sons in inches	67	68	65	68	72	72	69	71

• A. $0.67$
• B. $0.58$
• C. $0.42$
• D. $0.92$

Answer 1

The correct option is B $0.58$

Height(Father)	Rank	Height(Son)	Rank	$|d|$	$d^2$
65 66 67 67 68 69 70 72	8 7 5 5 4 3 2 1	67 68 65 68 72 72 69 71	7 5 8 5 1 1 4 3	1 2 3 0 3 2 2 2	1 4 9 0 9 4 4 4

$n=08,\sum d^2=35$

$r=1-\frac{6\sum d^2}{n(n^2-1)}=1-\frac{6\times 35}{8(8^2-1)}=1-\frac{210}{504}=0.58$