$\text{ If mean and standard deviation of }8\text{ observation }{\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_8\text{ are }10\text{ and }3$

$\text{ respectively, then variance of }10\text{ observations }{\mathrm{x}}_1,{\mathrm{x}}_2,\dots .,{\mathrm{x}}_8,10,-10\text{ is equal to }$

$Mean =\overline{x}=\frac{\sum _{i=1}^8{x}_i}{8}=10,Variance ={\sigma }^2= \frac{\sum _{i=1}^8{x}_i^2}{8}-(\overline{x}{)}^2=3^2$

$\Rightarrow \sum _{i=1}^8{x}_i=80,\sum _{i=1}^8{x}_i^2=872$

For the required data

$\overline{x}=\frac{\sum _{i=1}^8{x}_i +10-10}{10}=8$

${\sigma }^2=\frac{\sum _{i=1}^8{x_i}^2 +100+100}{10}-{\overline{x}}^2= \frac{872 +100+100}{10}-64 =43.2$