Calculate the standard deviation of the following 38, 40, 34, 31, 28, 26, 34

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Solution

Arrange in ascending order
26, 28, 31, 34, 34, 38, 40
Mean, $¯ x = \frac{\sum x}{n} = \frac{231}{7} = 33$
$\begin{matrix} x & 26 & 28 & 31 & 34 & 34 & 38 & 40 x - ¯ x & - 7 & - 5 & - 2 & 1 & 1 & 5 & 7 x - {¯ x}^{2} & 49 & 25 & 4 & 1 & 1 & 25 & 49 \end{matrix}$
$δ^{2} = \frac{\sum (x - ¯ x) x}{=} \frac{154}{7} .22 δ = \sqrt{22} = 4.690$

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