Question

find the standard deviation, \\( \sigma \\), of the data. 16, 31, 38, 24, 36 \\( \overline { x } = 29 \\) variance \\( ( \sigma ^ { 2 } ) = 65.6 \\) \\( \sigma = ? \\)

Explanation:

Step1: Recall the formula for standard deviation

The standard deviation $\sigma$ is the square root of the variance $\sigma^{2}$. So, $\sigma=\sqrt{\sigma^{2}}$.

Step2: Substitute the value of variance

Given $\sigma^{2} = 65.6$, then $\sigma=\sqrt{65.6}$.
Using a calculator, $\sqrt{65.6}\approx 8.1$.

Answer:

$8.1$