If the mean and variance of the data 65, 68, 58, 44 , 48, 45, 60,...

Given: $\overset{¯}{x} = 56$ and ${\sigma}^{2} = 66 . 2$

We know that, ${\sigma}^{2} = \dfrac{\mathop{∑}_{}^{}{\left({x}_{i}\right)}^{2}}{n} - {\left(x\right)}^{2}$

$⇒ \dfrac{{65}^{2} + {68}^{2} + {58}^{2} + {44}^{2} + {48}^{2} + {45}^{2} + {60}^{2} + {\alpha}^{2} + {\beta}^{2} + {60}^{2}}{10} - {\left(56\right)}^{2} = 66 . 2$

$⇒ \dfrac{{\alpha}^{2} + {\beta}^{2} + 25678}{10} - ( 56{)}^{2} = 66 . 2$

$⇒ \dfrac{{\alpha}^{2} + {\beta}^{2} + 25678}{10} = \left(3136 + 66 . 2\right)$

$⇒ {\alpha}^{2} + {\beta}^{2} = 32022 - 25678$

$⇒ {\alpha}^{2} + {\beta}^{2} = 6344$