Question

find the standard deviation, $\sigma$, of the data.
15, 21, 46, 49, 31, 24
$\overline{x} = 31$
variance($\sigma^2$) = 159
$\sigma = \boxed{?}$
round to the nearest tenth.

Explanation:

Step1: Recall the formula for standard deviation

The standard deviation \(\sigma\) is the square root of the variance \(\sigma^2\). So the formula is \(\sigma=\sqrt{\sigma^2}\).

Step2: Substitute the variance value

We know that the variance \(\sigma^2 = 159\). So we need to calculate \(\sqrt{159}\).
Calculating \(\sqrt{159}\approx12.6\) (rounded to the nearest tenth).

Answer:

\(12.6\)