Question

Question 8 of 10

The following data values represent a sample. What is the variance of the
sample?x= 9. Use the information in the table to help you.


A. 5.3
B. 22.4
C. 28
D. 4.7

Answer 1

Explanation:

To calculate the variance of a sample, you need to follow these steps:

Find the mean (µ) of the sample.

Subtract the mean from each data value (x - µ).

Square each difference [(x - µ)²].

Calculate the sum of the squared differences.

Divide the sum by the sample size minus 1 (n - 1).

Let's apply these steps to the given sample:

x = 9

µ (mean) = (7 + 15 + 11 + 1 + 11) / 5 = 45 / 5 = 9

(x - µ)² : (7 - 9)² = 4, (15 - 9)² = 36, (11 - 9)² = 4, (1 - 9)² = 64, (11 - 9)² = 4

Sum of squared differences: 4 + 36 + 4 + 64 + 4 = 112

Sample size: n = 5

Variance = Sum of squared differences / (n - 1) = 112 / (5 - 1) = 112 / 4 = 28

Therefore, the variance of the sample is 28. Option C is the correct answer.