Question

Karl Pearson's coefficient of correlation between the heights (in inches) of teachers and students corresponding to the given data is

Height of teachers x :	66	67	68	69	70
Height of students y :	68	66	69	72	70

• A. $\frac { 1 } { \sqrt { 2 } }$
• B. $\sqrt { 2 }$
• C. $- \frac { 1 } { \sqrt { 2 } }$
• D. 0

Answer 1

Answer: (A)

$\frac { 1 } { \sqrt { 2 } }$

Answer 2

Here $\Sigma ( x - \bar { x } ) ( y - \bar { y } ) = 10 , \Sigma ( x - \bar { x } ) ^ { 2 } = 10$

and $\Sigma ( y - \bar { y } ) ^ { 2 } = 20$

Hence the coefficient of correlation is given by

$r = \frac { \Sigma ( x - \bar { x } ) ( y - \bar { y } ) } { \sqrt { \Sigma ( x - \bar { x } ) ^ { 2 } \Sigma ( y - \bar { y } ) ^ { 2 } } } = \frac { 10 } { \sqrt { 10 \times 20 } } = \frac { 10 } { 10 \sqrt { 2 } } = \frac { 1 } { \sqrt { 2 } }$ .