Question

Calculate coefficient of correlation from the following data:
(i) Sum of deviation of X values = −6
(ii) Sum of deviation of Y values = 1
(iii) Sum of squares of deviations of X values = 196
(iv) Sum of squares of deviation of Y values = 87
(v) Sum of the product of deviations of X and Y values =124
(vi) No of pairs of observations = 6

Answer 1

Given:
$$\begin{gathered} \sum _{}^{}{d}_x=-6 \\ \sum _{}^{}{d}_y=1 \\ {\sum }_{}^{}{d}_x^2=196 \\ {\sum }_{}^{}{d}_y^2=87 \\ {\sum }_{}^{}{d}_x{d}_y=124 \\ N=6 \\ r=\frac{{\displaystyle \sum _{}^{}}{d}_x{\displaystyle \sum _{}^{}}{d}_y-{\displaystyle \frac{\left({\sum }_{}^{}{d}_x\right)\times \left({\sum }_{}^{}{d}_y\right)}{N}}}{\sqrt{{\sum }_{}^{}{d}_x^2-\frac{({\sum }_{}^{}{d}_x{)}^2}{N}}\times \sqrt{{\sum }_{}^{}{d}_y^2-\frac{({\sum }_{}^{}{d}_y{)}^2}{N}}} \\ \mathrm{or},r=\frac{124-{\displaystyle \frac{(-6\times 1)}{6}}}{\sqrt{196-\frac{(-6{)}^2}{6}}\times \sqrt{87-\frac{(1{)}^2}{6}}} \\ \mathrm{or},r=\frac{124+1}{13.78\times 9.31} \\ \mathrm{or},r=\frac{125}{13.78\times 9.31} \\ \mathrm{or},r=\frac{125}{128.29} \\ \Rightarrow r=0.974 \end{gathered}$$

Hence, coefficient of correlation=0.974