To calculate the variance \( s^2 \), we need to use the formula for variance of a sample:
\[ s^2 = \frac{\sum x_{i}^{2} - \frac{(\sum x_{i})^{2}}{n}}{n-1} \]
Given:
- \(\sum x_{i}^{2} = 23.1547\)
- \((\sum x_{i})^{2} = (10.59)^{2}\)
- \(n = 5\)
We will substitute these values into the formula to compute the variance.
We are given the following values:
- \(\sum x_{i}^{2} = 23.1547\)
- \((\sum x_{i})^{2} = (10.59)^{2}\)
- \(n = 5\)
The formula for the variance of a sample is:
\[
s^2 = \frac{\sum x_{i}^{2} - \frac{(\sum x_{i})^{2}}{n}}{n-1}
\]
Substitute the given values into the formula:
\[
s^2 = \frac{23.1547 - \frac{(10.59)^2}{5}}{5-1}
\]
Calculate the squared sum of \(x_i\):
\[
(10.59)^2 = 112.1481
\]
Substitute back into the formula:
\[
s^2 = \frac{23.1547 - \frac{112.1481}{5}}{4}
\]
Calculate the expression:
\[
s^2 = \frac{23.1547 - 22.42962}{4} = \frac{0.72508}{4} = 0.18127
\]