If the variance of $6, 7, 8, 9, 10, 11$ is $\sigma^2$,then the variance of $12, 14, 16, 18, 20, 22$ is

  • A
    $2 \sigma^2$
  • B
    $4 \sigma^2$
  • C
    $100 + 2 \sigma^2$
  • D
    $100 + 4 \sigma^2$

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$\text{Assertion (A):}$ Variance of $4x_1, 4x_2, \ldots, 4x_n$ is $16$ times the variance of $x_1, x_2, \ldots, x_n$. $\text{Reason (R):}$ If $y = ax + b$,then variance of $y$ is $a(\text{variance of } x) + b$. The correct option among the following is

Find the variance of $2, 4, 6, 8, 10$.

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