To determine the variance of this population, let's follow a step-by-step method using the provided data.
1. Given Values: The data values ([tex]\( x \)[/tex]) are 8, 10, 14, and 4. The population mean ([tex]\( \mu \)[/tex]) is 9. The squared deviations from the mean are 1, 1, 25, and 25.
2. Variance Calculation:
- Step 1: Sum the squared deviations.
[tex]\[
\text{Sum of squared deviations} = 1 + 1 + 25 + 25 = 52
\][/tex]
- Step 2: Count the number of data values (N). In this case, there are 4 data values (8, 10, 14, and 4).
[tex]\[
N = 4
\][/tex]
- Step 3: Compute the variance by dividing the sum of squared deviations by the number of data values.
[tex]\[
\text{Variance} = \frac{\text{Sum of squared deviations}}{N} = \frac{52}{4} = 13
\][/tex]
Hence, the variance for this population is 13.
3. Conclusion: Comparing with the options provided:
- A. 14
- B. 10
- C. 9
- D. 13
The correct answer is:
[tex]\[ \boxed{13} \][/tex]
