Q. For the given data, the calculation corresponding to all values of variates $(x,y)$ is following$\ \sum_{}^{}\left( x - \overline{x} \right)^{2} = 36,\ \sum_{}^{}\left( y - \overline{y} \right)^{2} = 25,\ \sum_{}^{}{\left( x - \overline{x} \right)(y - \overline{y})} = 20$. The Karl Pearson’s correlation coefficient is
A) 0.2
B) 0.5
C) 0.66
D) 0.33
Explanation
(c)
$r_{xy} = \frac{\sum_{}^{}{\left( x - \overline{x} \right)(y - \overline{y})}}{\sqrt{\sum_{}^{}\left( x - \overline{x} \right)^{2}\sum_{}^{}\left( y - \overline{y} \right)^{2}}}$
$= \frac{20}{\sqrt{36 \times 25}} = \frac{2}{3} = 0.66$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.