Find the variance for the given sample data. Round your answer to one more decimal place_ than the original data. $$\begin{array} { l l l l l }
7 & 7 & 2 & 5 & 1
\end{array}$$
A)7.7
B)11.8
C)7.8
D)6.2

Question

Find the variance for the given sample data. Round your answer to one more decimal place_ than the original data. $$\begin{array} { l l l l l } 
7 & 7 & 2 & 5 & 1
\end{array}$$
A)7.7
B)11.8
C)7.8
D)6.2

Quizplus · Accepted Answer

The variance of a sample is calculated using the formula $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$, where $\bar{x}$ is the sample mean, $x_i$ are the individual sample values, and $n$ is the sample size. For the given data (7, 7, 2, 5, 1), the mean $\bar{x} = \frac{7+7+2+5+1}{5} = \frac{22}{5} = 4.4$. The sum of squared deviations from the mean is $\sum (x_i - \bar{x})^2 = (7-4.4)^2 + (7-4.4)^2 + (2-4.4)^2 + (5-4.4)^2 + (1-4.4)^2 = 6.76 + 6.76 + 5.76 + 0.36 + 11.56 = 31.2$. The variance is $\sigma^2 = \frac{31.2}{5-1} = \frac{31.2}{4} = 7.8$.

Find the Variance for the Given Sample Data 77251\begin{array} { l l l l l } 7 & 7 & 2 & 5 & 1\end{array}7​7​2​5​1​

Find the Variance for the Given Sample Data $\begin{array} { l l l l l } 7 & 7 & 2 & 5 & 1\end{array}$