The mean and standard deviation of a distribution of weights of a group of 20 boys are 40 kgs and 5 kgs respectively. If two boys of weights 43 kg and 37kg are excluded from this group, then the variance of the distribution of weights  of the remaining group of boys is

Mean of 20 boys   $=40\Rightarrow \sum _{i=1}^{20}{x}_i=20\times 40=800\Rightarrow$ sum of weights of 20 boys  $=800.$
Sum of weights of 18 boys  $=800-43-47=720.$
Mean of 18 boys  $=\frac{720}{18}=40.$
Variance of 20 boys  $=25\Rightarrow \sum _{i=1}^{20}{(x_i-\overline{x})}^2=20\times 25=500$
 $\Rightarrow \sum _{i=1}^{18}{(x_i-\overline{x})}^2=500-{(43-40)}^2-{(37-40)}^2=482$
Variance of 18 boys  $\frac{482}{18}=\frac{241}{9}=26.78$