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.
