Q. The correlation coefficient between $x$ and $y$ from the following data $\sum_{}^{}x = 40,\$ $\sum_{}^{}y = 50,\ \sum_{}^{}{xy} = 220,\ \sum_{}^{}x^{2} = 200,\ \sum_{}^{}y^{2} = 262,\ n = 10$ is
A) 0.89
B) 0.76
C) 0.91
D) 0.98
Explanation
(c)
Correlation coefficient,
$r = \frac{n\sum_{}^{}{xy} - \sum_{}^{}x\sum_{}^{}y}{\sqrt{\{ n\sum_{}^{}x^{2} - \left( \sum_{}^{}x \right)^{2}\}}\sqrt{\left\{ n\sum_{}^{}y^{2} - \left( \sum_{}^{}y \right)^{2} \right\}}}$
$= \frac{10(220) - 40 \times 50}{\sqrt{10(200) - (40)^{2}}\sqrt{10(262) - (50)^{2}}}$
$= \frac{200}{20 \times 10.954} = \frac{200}{219.08} = 0.91$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.