Answered

From beginner to expert, IDNLearn.com has answers for everyone. Get accurate and detailed answers to your questions from our knowledgeable and dedicated community members.

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.
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thanks for visiting IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more helpful information.