High School

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------------------------------------------------ Find the standard deviation, [tex]\sigma[/tex], of the data set:

[tex]\begin{array}{c} 198, 190, 245, 211, 193, 193 \\ \bar{x}=205 \end{array}[/tex]

Variance [tex]\left(\sigma^2\right) = 366.3[/tex]

[tex]\sigma = \, ?[/tex]

Answer :

To find the standard deviation, [tex]\(\sigma\)[/tex], from the given data, we start with the provided variance. The formula to calculate the standard deviation from the variance is:

[tex]\[
\sigma = \sqrt{\sigma^2}
\][/tex]

where [tex]\(\sigma^2\)[/tex] is the variance.

In this problem, the variance ([tex]\(\sigma^2\)[/tex]) is given as 366.3. So, to find the standard deviation, we simply take the square root of the variance:

[tex]\[
\sigma = \sqrt{366.3}
\][/tex]

After calculating the square root, we find that:

[tex]\[
\sigma \approx 19.14
\][/tex]

Therefore, the standard deviation of the data is approximately 19.14.

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