Find the sample variance for the following data set: $\begin{array} { l l l l l }
23 & 14 & 32 & 29 & 17
\end{array}$
A) 7.6
B) 18
C) 58.5
D) 46.8

Question

Find the sample variance for the following data set: $\begin{array} { l l l l l } 
23 & 14 & 32 & 29 & 17
\end{array}$
A) 7.6
B) 18
C) 58.5
D) 46.8

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: $\bar{x} = \frac{23 + 14 + 32 + 29 + 17}{5} = 23$. Then, calculate the sum of squared deviations: $\sum (x_i - \bar{x})^2 = (23-23)^2 + (14-23)^2 + (32-23)^2 + (29-23)^2 + (17-23)^2 = 0 + 81 + 81 + 36 + 36 = 234$. Finally, divide by $n-1 = 5-1 = 4$: $s^2 = \frac{234}{4} = 58.5$.

Find the Sample Variance for the Following Data Set 2314322917\begin{array} { l l l l l } 23 & 14 & 32 & 29 & 17\end{array}23​14​32​29​17​

Find the Sample Variance for the Following Data Set $\begin{array} { l l l l l } 23 & 14 & 32 & 29 & 17\end{array}$