Calculate the coefficient of correlation for the ages of husbands and wives(up to three decimals):

Age of husband	$23$	$27$	$28$	$28$	$29$	$30$	$31$	$33$	$35$	$36$
Age of wife	$18$	$20$	$22$	$27$	$21$	$22$	$27$	$29$	$28$	$29$

Prove that though covariance is independent of the choice of origin it depends upon the scale. If $u=ax+b, v=cy+d,$ show that $\mathrm{cov} \left(u\mathit{,}\mathit{ }v\right)=a\mathit{.}c.\mathrm{cov} \left(x\mathit{,}\mathit{ }\mathrm{y}\right)$.

The coefficient of correlation between two variables $X$ and $Y$ is $0.64$. Their covariance is $16$. The variance of $X$ is $9$. Find the standard deviation of $Y-$series.

Coefficient of correlation between $\mathrm{X}$ and $\mathrm{Y}$ for $50$ observations is $0.3$, mean of $\mathrm{X}$ is $10$ and that of $\mathrm{Y} 6$, $\mathrm{SD}$. of $\mathrm{X}$ is $3$ and that of $\mathrm{Y}$ is $2$ Later it was discovered that one pair of values $(10, 6)$ was inaccurate and hence weeded out. Calculate the correlation between remaining $9$ pairs of values.

The ranking of the $10$ individuals at the start and on the finish of a course of training are as follows: 

Calculate spearman's coefficient of correlation(three digits after decimal place).

Find the spearman's rank correlation(three digits after decimal place) between marks in mathematics and statistics obtained by $10$ students: