Question

Calculate the value of the sample variance. Round your answer to one decimal place. 9_5,9_5,2,9_5

Answer 1

`s^2 = 0.01`

Explanation:

Given

Values: 9/5, 9/5, 2, 9/5

Required

Calculate the sample variance

Sample variance is calculated using:

`s^2 = (\sum (x_i - \overline x)^2)/(n - 1)`

First, we calculate the mean

`\overline x = (\sum x)/(n)`

`\overline x = (9/5 + 9/5 + 2 + 9/5)/(4)`

`\overline x = (7.4)/(4)`

`\overline x = 1.85`

`s^2 = (\sum (x_i - \overline x)^2)/(n - 1)` becomes

`s^2 = ((9/5 - 1.85)^2+(9/5 - 1.85)^2+(2 - 1.85)^2+(9/5 - 1.85)^2)/(4 - 1)`

`s^2 = ((-0.05)^2+(-0.05)^2+(0.15)^2+(-0.05)^2)/(4 - 1)`

`s^2 = (0.0025+0.0025+0.0225+0.0025)/(3)`

`s^2 = (0.03)/(3)`

`s^2 = 0.01`

Hence, the variance is 0.01