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? 4242 4040 3838 3131 2222 1919 1717 1616 15.915.9 15.015.0

Answer 1

Explanation:

The data is written wrongly. The correct data is:

42, 40, 38, 31, 22, 19, 17, 16, 15.9, 15.0

Range = largest value - smallest value

Range = 42 - 15 = 27

n = 10

The mean of the set of data given is

Mean = (42 + 40 + 38 + 31 + 22 + 19 + 17 + 16 + 15.9 + 15.0)/10 = 25.59

Standard deviation = √(summation(x - mean)²/n

Variance = Summation(x - mean)²/n =

Summation(x - mean)² = (42 - 25.59)^2 + (40 - 25.59)^2 + (38 - 25.59)^2 + (31 - 25.59)^2 + (22 - 25.59)^2 + (19 - 25.59)^2 + (17 - 25.59)^2 + (16 - 25.59)^2 + (15.9 - 25.59)^2 + (15.0 - 25.59)^2 = 1088.329

Variance = 1088.329/10 = 108.8329

Standard deviation = √variance = √(108.8329 = 10.43