Answer:
8
Explanation:
To find the value of the sample variance, we use the formula below:
[tex]\text{Var}=\frac{\sum ^{}_{}(x_i-\bar{x})^2}{n-1}[/tex]First, we determine the mean of the data: 3, 9, 4, 4, 4, 9, 9
[tex]\begin{gathered} \text{Mean}=\frac{3+9+4+4+4+9+9}{7} \\ =\frac{42}{7} \\ \bar{x}=6 \end{gathered}[/tex]Next, we find the sum of the squares of the mean deviation.
[tex]\begin{gathered} \sum ^{}_{}(x_i-\bar{x})^2=(3-6)^2+(9-6)^2+(4-6)^2+(4-6)^2+(4-6)^2+(9-6)^2+(9-6)^2 \\ =(-3)^2+(3)^2+(-2)^2+(-2)^2+(-2)^2+(3)^2+(3)^2 \\ =9+9+4+4+4+9+9 \\ \sum ^{}_{}(x_i-\bar{x})^2=48 \end{gathered}[/tex]Therefore, the sample variance is:
[tex]\begin{gathered} \text{Var}=\frac{\sum^{}_{}(x_i-\bar{x})^2}{n-1}=\frac{48}{7-1} \\ =\frac{48}{6} \\ =8 \end{gathered}[/tex]The sample variance is 8.
