Question

find the standard deviation, $sigma$, of
the data.
16, 13, 20, 16, 12, 17, 18
$overline{x} = 16$
variance($sigma^2$) = 6.6
$sigma = ?$
round to the nearest tenth

Explanation:

Step1: Recall the relationship between standard deviation and variance

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

Step2: Substitute the given variance into the formula

We know that $\sigma^2 = 6.6$, so we calculate $\sigma = \sqrt{6.6}$.

Step3: Calculate the square root and round to the nearest tenth

$\sqrt{6.6} \approx 2.57$, and rounding to the nearest tenth gives $2.6$.

Answer:

$2.6$