Question

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? 18 39383022 13.5 12.4

Answer 1

Range Calculation

Range = Maximum Salary - Minimum Salary

Range = 40 -12.4

Range = 27.6

Variance Calculation

We will compute this formula in 4 steps. (x) Step 1: Find the mean.

Mean = (40 + 39 + 38 + 30 + 22 + 18 + 16 + 14 + 13.5 + 12.4)/10

Mean = 24.29

Step 2: Create the following table. (data -mean)2 data data-mean 40 15.71 246.8041 39 14.71 216.3841 38 13.71 187.9641 30 5.71 32.6041 -2.29 5.2441 22 18 -6.29 39.5641 -8.29 16 68.7241 14 -10.29 105.8841 13.5 -10.79 116.4241 141.3721 12.4 -11.89 Step 3: Find the sum of numbers in the last column to get Σ--1 = 1160.969 Step 4: Calculate variance using the above formula. 2 Σ(3 1160.969 128,9966 ar= 10 1

Variance = 129.00

Standard Deviation Calculation

Standard Deviation = SQRT(Variance) = SQRT(128.9966)

Standard Deviation = 11.36