Question

find the standard deviation, \\( \sigma \\), of the data.
16, 13, 20, 16, 12, 17, 18
\\( \overline { x } = 16 \\)
\\( \text { variance } \left( \sigma ^ { 2 } \
ight) = 6.6 \\)
\\( \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 $\sigma^{2} = 6.6$, then $\sigma=\sqrt{6.6}$.

Step3: Calculate the square - root

Using a calculator, $\sqrt{6.6}\approx2.569$.

Answer:

$2.6$