$\begin{array}{1 1}(A)\; 6.5 \\(B)\;2.87 \\(C)\;3.87 \\(D)\;8.25 \end{array} $

The formula to calculate variance $\sigma^2 = \large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2$

Adding a constant to each numbers, does not affect the value of the variance.

It remain the same.

As calculated SD in the previous problem for 1st 10 natural numbers

Variance $=(SD)^2$

$\qquad= (2.87)^2=8.25$

and adding 1 to each numbers will not change the value of the variance.

Hence D is the correct answer.

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