Answer :
Answer:
B. 29.143
Explanation:
Given the set of data: 23, 9, 8, 12, 21, 18, 14
To find the variance, we follow the steps below:
Step 1: Find their mean.
[tex]\begin{gathered} \text{Mean}=\frac{23+9+8+12+21+18+14}{7} \\ =\frac{105}{7} \\ =15 \end{gathered}[/tex]Step 2: We subtract the mean from each of the values and square it.
[tex]\begin{gathered} (23-15)^2=8^2=64 \\ (9-15)^2=6^2=36 \\ (8-15)^2=7^2=49 \\ (12-15)^2=3^2=9 \\ (21-15)^2=6^2=36 \\ (18-15)^2=3^2=9 \\ (14-15)^2=1^2=1 \end{gathered}[/tex]Step 3: We find the average of our results from step 2.
[tex]\begin{gathered} \text{Variance}=\frac{64+36+49+9+36+9+1}{7} \\ =\frac{204}{7} \\ =29.143 \end{gathered}[/tex]The variance is 29.143.