Question

Find the standard deviation of X series, if coefficient of correlation between two series X and Y is 0.35 and their covariance in 10.5 and variance of Y series is 56.25.

Answer 1

Given, r = 0.35
Cov (x,y) = 10.5
$$\begin{gathered} {\sigma }_y^2=56.25 \\ \Rightarrow {\sigma }_y^{}=7.5 \end{gathered}$$
Substituting the given values in the formula we get,

$$\begin{gathered} r=\frac{\mathrm{Cov}\left(x,y\right)}{{\sigma }_x{\sigma }_y} \\ or,0.35=\frac{10.5}{7.5{\sigma }_x} \\ {\sigma }_x=\frac{10.5}{7.5\times 0.35} \\ \Rightarrow {\sigma }_x=4 \end{gathered}$$

Hence, standard deviation of X series is 4.