Find the sample variance for the following data set:
$\begin{array} { l l l l l }
22 & 12 & 23 & 17 & 21
\end{array}$
A)4.5
B)20.5
C)11
D)16.4

Question

Find the sample variance for the following data set: 
$\begin{array} { l l l l l } 
22 & 12 & 23 & 17 & 21
\end{array}$
A)4.5
B)20.5
C)11
D)16.4

Quizplus · Accepted Answer

The sample variance $s^2$ is calculated using the formula $s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$, 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: $\bar{x} = \frac{22 + 12 + 23 + 17 + 21}{5} = 19$. Then, calculate the sum of squared deviations: $\sum (x_i - \bar{x})^2 = (22-19)^2 + (12-19)^2 + (23-19)^2 + (17-19)^2 + (21-19)^2 = 9 + 49 + 16 + 4 + 4 = 82$. Finally, divide by $n-1 = 5-1 = 4$: $s^2 = \frac{82}{4} = 20.5$.

Find the Sample Variance for the Following Data Set 2212231721\begin{array} { l l l l l } 22 & 12 & 23 & 17 & 21\end{array}22​12​23​17​21​

Find the Sample Variance for the Following Data Set $\begin{array} { l l l l l } 22 & 12 & 23 & 17 & 21\end{array}$