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

[tex]\[
\begin{array}{c}
147, 141, 120, 124, 128 \\
\bar{x} = 132 \\
\text{Variance } \left(\sigma^2\right) = 106 \\
\sigma = ?
\end{array}
\][/tex]

Round to the nearest tenth.

Sagot :

GinnyAnswer
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.
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