If the standard deviation of n observations x _ 1 , x _ 2 ,..... ,...

${\left(S. D\right)}^{2} = {\sigma}_{x - y}^{2}$
$= \dfrac{1}{n}\mathop{∑}_{i = 1}^{n}{\left({x}_{i} - {y}_{i} - \overset{¯}{x} + \overset{¯}{y}\right)}^{2}$
$= \dfrac{1}{n}\mathop{∑}_{i = 1}^{n}{\left({x}_{i} - \overset{¯}{x}\right)}^{2} + \dfrac{1}{n}\mathop{∑}_{i = 1}^{n}{\left({y}_{i} - \overset{¯}{y}\right)}^{2} - \dfrac{2}{n}\mathop{∑}_{i = 1}^{n} \left({x}_{i} - \overset{¯}{x}\right)\left({y}_{i} - \overset{¯}{y}\right)<br />$= {σ}_x^{2} + {σ}_y^{2} - 2$\alpha\left\{where, \dfrac{1}{n}\mathop{∑}_{i = 1}^{n} \left({x}_{i} - \overset{¯}{x}\right)\left({y}_{i} - \overset{¯}{y}\right) = \alpha\right\}$
As $\alpha$ is not known, therefore we cannot find ${\sigma}_{x - y}^{2}$ or ${\sigma}_{x - y}.$

Hence, data is insufficient.&