Find the sample variance for the following data set: 25 20 19 15 31
A) 16
B) 38
C) 6.2
D) 30.4

Question

Quizplus · Accepted Answer

The sample variance 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: $\bar{x} = \frac{25 + 20 + 19 + 15 + 31}{5} = 22$. Then, calculate the sum of the squared deviations: $\sum (x_i - \bar{x})^2 = (25-22)^2 + (20-22)^2 + (19-22)^2 + (15-22)^2 + (31-22)^2 = 9 + 4 + 9 + 49 + 81 = 152$. Finally, divide by $n-1 = 5-1 = 4$: $s^2 = \frac{152}{4} = 38$.

Find the Sample Variance for the Following Data Set: 25