Question

The variance of 15 observations is 8. If each observation is multiplied by 4, then the
variance of new observations is ........​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Variance of 15 observations is 8}$

$\underline{\textsf{To find:}}$

$\textsf{Variance when each observation is multiplied by 4}$

$\underline{\textsf{Solution:}}$

$\textsf{Concept:}$

$\boxed{\begin{minipage}{9cm} \\\textsf{If each observation is multiplied by a constant k, the new}\\\\\textsf{variance is}\;\mathsf{k^2}\;\textsf{times the old variance} \end{minipage}}$

$\textsf{When each observation is multiplied by 4}$

$\textsf{New Variance}$

$\mathsf{=4^2{\times}}\textsf{old variance}$

$\mathsf{=16{\times}8}$

$\mathsf{=128}$

$\underline{\textsf{Answer:}}$

$\mathsf{New\;variance=128}$

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