Answer:
[tex]s^2 = 0.01[/tex]
Step-by-step explanation:
Given
Values: 9/5, 9/5, 2, 9/5
Required
Calculate the sample variance
Sample variance is calculated using:
[tex]s^2 = \frac{\sum (x_i - \overline x)^2}{n - 1}[/tex]
First, we calculate the mean
[tex]\overline x = \frac{\sum x}{n}[/tex]
[tex]\overline x = \frac{9/5 + 9/5 + 2 + 9/5}{4}[/tex]
[tex]\overline x = \frac{7.4}{4}[/tex]
[tex]\overline x = 1.85[/tex]
[tex]s^2 = \frac{\sum (x_i - \overline x)^2}{n - 1}[/tex] becomes
[tex]s^2 = \frac{(9/5 - 1.85)^2+(9/5 - 1.85)^2+(2 - 1.85)^2+(9/5 - 1.85)^2}{4 - 1}[/tex]
[tex]s^2 = \frac{(-0.05)^2+(-0.05)^2+(0.15)^2+(-0.05)^2}{4 - 1}[/tex]
[tex]s^2 = \frac{0.0025+0.0025+0.0225+0.0025}{3}[/tex]
[tex]s^2 = \frac{0.03}{3}[/tex]
[tex]s^2 = 0.01[/tex]
Hence, the variance is 0.01
