Introduction to statistics

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Question

$If \sum_{i = 1}^{5} (x_{i} - 10) = 5 and \sum_{i = 1}^{5} {(x_{i} - 10)}^{2} = 25, then standard deviation of observations$ $2 x_{1} + 7, 2 x_{2} + 7, 2 x_{3} + 7, 2 x_{4} + 7 and 2 x_{5} + 7 is equal to.$

Moderate

Solution

$\begin{aligned} σ (x_{i}) = \sqrt{\frac{25}{5} - {(\frac{5}{5})}^{2}} = 2 \\ \Rightarrow σ (2 x_{i} + 7) = 2 σ (x_{i}) = 4 \end{aligned}$

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