Listed below are the top 10 annual salaries (in millions of dollars) of TV perso

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? 40383628 20 16 15 12 11.8 11.0 The range ofthe sam ple data is SO million. (Type an integer or a decimal.) The variance of the sample data is(Round to two decimal places as needed.) The standard deviation of the sample data is S million. (Round to two decimal places as needed.) Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in general? O A. Yes, because the sample is random. O B. Yes, because the standard deviation is an unbiased estimator. O C. No, because there is an outlier in the sample data. D. No, because the sample is not representative of the whole population.

Explanation / Answer

a) range = maximum - minimum = 40 - 11 = 29

b) Mean = (40 + 38 + 36 + 28 + 20 + 16 + 15 + 12 + 11.8 + 11) / 10 = 22.78

Variance = [(40 - 22.78)2 + (38 - 22.78)2 + (36 - 22.78)2 + (28 - 22.78)2 + (20 - 22.78)2 + (16 - 22.78)2 + (15 - 22.78)2 + (12 - 22.78)2 + (11.8 - 22.78)2 + (11 - 22.78)2 ] / 9 = 135.55

c) sample standard deviation = sqrt(135.55) = 11.64

d) Option-B) Yes, because the standard deviation is an unbiased estimator

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