To calculate the standard deviation, [tex]\(\sigma\)[/tex], of the given data, we need to follow these steps:
1. Understand the given values:
- The mean of the data, [tex]\(\bar{x}\)[/tex], is 205.
- The variance, [tex]\(\sigma^2\)[/tex], is 366.3.
2. Recall the relationship between variance and standard deviation:
Variance ([tex]\(\sigma^2\)[/tex]) is the square of the standard deviation ([tex]\(\sigma\)[/tex]). Therefore, to find the standard deviation, we need to take the square root of the variance.
3. Compute the standard deviation:
Given the variance ([tex]\(\sigma^2\)[/tex]) is 366.3, the standard deviation ([tex]\(\sigma\)[/tex]) is given by the square root of the variance.
[tex]\[
\sigma = \sqrt{\sigma^2} = \sqrt{366.3}
\][/tex]
4. Find the numerical value:
Taking the square root of 366.3, we get:
[tex]\[
\sigma \approx 19.138965489283898
\][/tex]
Hence, the standard deviation, [tex]\(\sigma\)[/tex], of the data is approximately [tex]\(19.139\)[/tex] (rounding to three decimal places).
