Step 1 :We are given the top 10 annual salaries (in millions of dollars) of TV personalities as follows: \(41, 40, 38, 32, 24, 21, 18, 17, 16.9, 15.7\)
Step 2 :To find the variance of the sample data, we first need to calculate the mean of the data.
Step 3 :The mean of the data is calculated as \(\frac{41 + 40 + 38 + 32 + 24 + 21 + 18 + 17 + 16.9 + 15.7}{10} = 26.36\)
Step 4 :Next, for each number in the data, we subtract the mean and square the result. The variance is the average of these squared differences.
Step 5 :The variance of the sample data is calculated as \(\frac{(41-26.36)^2 + (40-26.36)^2 + (38-26.36)^2 + (32-26.36)^2 + (24-26.36)^2 + (21-26.36)^2 + (18-26.36)^2 + (17-26.36)^2 + (16.9-26.36)^2 + (15.7-26.36)^2}{10} = 106.956\)
Step 6 :Rounding to two decimal places, the variance of the sample data is \(\boxed{106.96}\)