To find the standard deviation [tex]\(\sigma\)[/tex] of the data given the variance [tex]\(\sigma^2\)[/tex]:
1. Understand the relationship between standard deviation and variance:
[tex]\[
\sigma = \sqrt{\sigma^2}
\][/tex]
The standard deviation is the square root of the variance.
2. We are provided with the variance:
[tex]\[
\text{Variance} (\sigma^2) = 106
\][/tex]
3. Calculate the standard deviation:
[tex]\[
\sigma = \sqrt{106}
\][/tex]
4. Compute the square root of 106:
The square root of 106 is approximately 10.29563014.
5. Round the result to the nearest tenth:
[tex]\[
10.29563014 \approx 10.3
\][/tex]
Therefore, the standard deviation, [tex]\(\sigma\)[/tex], of the data is approximately 10.3 when rounded to the nearest tenth.
