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 $x_i$ are the data points, $\bar{x}$ is the mean of the data, and $n$ is the number of data points. First, calculate the mean: $\bar{x} = \frac{7 + 7 + 2 + 5 + 1}{5} = \frac{22}{5} = 4.4$. Then, calculate the sum of the squared differences from the mean: $\sum (x_i - \bar{x})^2 = (7-4.4)^2 + (7-4.4)^2 + (2-4.4)^2 + (5-4.4)^2 + (1-4.4)^2 = 6.76 + 6.76 + 5.76 + 0.36 + 11.56 = 31.2$. Finally, divide by $n - 1 = 5 - 1 = 4$: $\sigma^2 = \frac{31.2}{4} = 7.8$.

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 $\begin{array} { l l l l l } 7 & 7 & 2 & 5 & 1\end{array}$