Question

Calculate the variance of: 2, 4, 5, 6, 8, 17.

• A. 20
• B. 21
• C. 22
• D. 23

Hint:

To calculate variance, find the mean first, then compute the squared differences from the mean, and divide by the number of elements.

Answer 1

The Correct Option is C

The formula for variance is: \[ \text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n} \] where \( \bar{x} \) is the mean of the numbers and \( x_i \) are the individual numbers. First, calculate the mean of the numbers: \[ \bar{x} = \frac{2 + 4 + 5 + 6 + 8 + 17}{6} = 7 \] Then, calculate the squared differences from the mean for each number, sum them up, and divide by \( n \). \[ \text{Variance} = \frac{(2-7)^2 + (4-7)^2 + (5-7)^2 + (6-7)^2 + (8-7)^2 + (17-7)^2}{6} = 22 \]