To determine the variance of the sample, we can follow these steps:
1. Determine the number of data points [tex]\( n \)[/tex]:
- The sample data values are [tex]\( 9, 5, 3, 7, 11 \)[/tex].
- The number of data points [tex]\( n \)[/tex] is 5.
2. Calculate the mean (sample mean) [tex]\( \bar{x} \)[/tex]:
- We are given that [tex]\( \bar{x} = 7 \)[/tex].
3. Compute the squared differences [tex]\((x_j - \bar{x})^2\)[/tex] for each data point:
- These values are provided in the table:
- For [tex]\( x = 9 \)[/tex], [tex]\((9 - 7)^2 = 4\)[/tex]
- For [tex]\( x = 5 \)[/tex], [tex]\((5 - 7)^2 = 4\)[/tex]
- For [tex]\( x = 3 \)[/tex], [tex]\((3 - 7)^2 = 16\)[/tex]
- For [tex]\( x = 7 \)[/tex], [tex]\((7 - 7)^2 = 0\)[/tex]
- For [tex]\( x = 11 \)[/tex], [tex]\((11 - 7)^2 = 16\)[/tex]
4. Sum the squared differences:
- Sum of squared differences = [tex]\( 4 + 4 + 16 + 0 + 16 \)[/tex].
- This sum = 40.
5. Calculate the sample variance [tex]\( s^2 \)[/tex]:
- The formula for the sample variance is:
[tex]\[
s^2 = \frac{\sum (x_j - \bar{x})^2}{n - 1}
\][/tex]
- Plugging in the values we have:
[tex]\[
s^2 = \frac{40}{5 - 1} = \frac{40}{4} = 10
\][/tex]
Therefore, the variance of the sample is [tex]\( 10 \)[/tex]. The correct answer is:
A. 10
