College

Find the standard deviation, [tex]\sigma[/tex], of the data.

\[
\begin{array}{c}
198, 190, 245, 211, 193, 193 \\
\bar{x} = 205 \\
\text{Variance } (\sigma^2) = 366.3 \\
\sigma = [?]
\end{array}
\]

Answer :

We are given the variance of the data as

$$
\sigma^2 = 366.3.
$$

The standard deviation, $\sigma$, is defined as the square root of the variance. Therefore, we calculate

$$
\sigma = \sqrt{\sigma^2} = \sqrt{366.3}.
$$

Evaluating the square root gives

$$
\sigma \approx 19.138965489283898.
$$

Thus, the standard deviation of the data is approximately

$$
\boxed{19.14}.
$$