High School

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

[tex]\begin{array}{c}
198, 190, 245, 211, 193, 193 \\
\overline{x}=205 \\
\text{Variance }\left(\sigma^2\right)=360.3 \\
\sigma=[?]
\end{array}[/tex]

Answer :

To find the standard deviation, [tex]\(\sigma\)[/tex], of the given data set, you can follow these steps:

1. Understand the Concepts:
- The variance ([tex]\(\sigma^2\)[/tex]) is a measure of how much the data values vary from the mean.
- The standard deviation ([tex]\(\sigma\)[/tex]) is the square root of the variance and represents the average distance of each data point from the mean.

2. Start with the Given Information:
- You have the variance of the data set already provided as 360.3.

3. Calculate the Standard Deviation:
- Since the variance is provided as [tex]\(\sigma^2 = 360.3\)[/tex], the standard deviation is the square root of the variance.
- [tex]\(\sigma = \sqrt{360.3}\)[/tex].

4. Compute the Square Root:
- When you calculate the square root of 360.3, you get approximately 18.98.

So, the standard deviation of the data set is approximately 18.98.