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?

42 40 39 31 22 18 15 12 11.7 10.5
The Range of the sample data is $[ ] million.
The variance of the sample data is [ ].
The standard deviation of the sample data is $[ ] million.
Is the the standard deviation of the sample a good estimate of the variation of the salaries of the TV personalities in general ?
A. Yes, because the standard deviation is an unbiased estimator
B. No, because the sample is not representative of the whole population.
C. No, because there is an outlier in the sample data.
D. Yes, because the sample is random.

Answer 1

Explanation:

The given data is

42 40 39 31 22 18 15 12 11.7 10.5

Range = 42 - 10.5 = 31.5

Mean = (42 + 40 + 39 + 31 + 22 + 18 + 15 + 12 + 11.7 + 10.5)/10 = 24.12

n = 10

Variance = Summation(x - mean)²/n

Summation(x - mean)² = (42 - 24.12)^2 + (40 - 24.12)^2 + (39 - 24.12)^2 + (31 - 24.12)^2 + (22 - 24.12)^2 + (18 - 24.12)^2 + (15 - 24.12)^2 + (12 - 24.12)^2 + (11.7 - 24.12)^2 + (10.5 - 24.12)^2 = 1452.396

Variance = 1452.396/10 = 145.2396

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

Standard deviation = √(145.2396

Standard deviation = 12.1

The standard deviation of the sample is not a good estimate of the variation of the salaries of the TV personalities in general because

B. No, because the sample is not representative of the whole population.