What is the Population Variance for the following numbers: 88, 93, 37, 32, 41, 31, 85, 19, 68 Level of difficulty = 2 of 2 Please format to 2 decimal place

1. Calculate the mean (average) of the numbers:

\text{Mean} \ (\mu) = \frac{88 + 93 + 37 + 32 + 41 + 31 + 85 + 19 + 68}{9} = \frac{494}{9} = 54.89

2. Calculate the squared differences from the mean for each number and find the sum of these squared differences:

\text{Squared Differences} = (88 - 54.89)^2 + (93 - 54.89)^2 + (37 - 54.89)^2 + (32 - 54.89)^2 + (41 - 54.89)^2 + (31 - 54.89)^2 + (85 - 54.89)^2 + (19 - 54.89)^2 + (68 - 54.89)^2

\text{Squared Differences} = 1080.97 + 1450.49 + 324.36 + 533.65 + 191.68 + 565.29 + 904.51 + 1292.25 + 171.37

\sum = 6514.57

3. Divide the sum of squared differences by the number of values to find the population variance:

\sigma^2=\frac{6514.57}{9}=724.765

Answer rounded to 2 decimal place:

\sigma^2=724.77