Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general?
$\begin{array}{lllllllllll}41 & 40 & 38 & 32 & 24 & 21 & 18 & 17 & 16.9 & 15.7\end{array}$
The variance of the sample data is (Round to two decima places as needed.)
Rounding to two decimal places, the variance of the sample data is \(\boxed{106.96}\)
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 \(\boxed{106.96}\)