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

[tex]\[
\begin{array}{c}
147, 141, 120, 124, 128 \\
\bar{x} = 132
\end{array}
\][/tex]

[tex]\[
\begin{array}{c}
\text{Variance} \left(\sigma^2\right) = 106 \\
\sigma = \, ?
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To find the standard deviation, [tex]\(\sigma\)[/tex], given the variance, [tex]\(\sigma^2\)[/tex], follow the steps below:

1. Understand the relationship between variance and standard deviation:
The variance, denoted as [tex]\(\sigma^2\)[/tex], is a measure of how much the values in a dataset differ from the mean. The standard deviation, denoted as [tex]\(\sigma\)[/tex], is the square root of the variance.

2. Given data:
- Variance: [tex]\(\sigma^2 = 106\)[/tex]

3. Calculate the standard deviation:
To find the standard deviation, [tex]\(\sigma\)[/tex], take the square root of the variance.

[tex]\[ \sigma = \sqrt{\sigma^2} = \sqrt{106} \][/tex]

4. Compute the square root:

Using the given data, the square root of 106 is approximately 10.295630140987.

5. Conclusion:

Therefore, the standard deviation, [tex]\(\sigma\)[/tex], of the data is:

[tex]\[ \sigma = 10.295630140987 \][/tex]

This value represents how spread out the numbers in the dataset are around the mean.
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