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? 39     37     35     28     20     19     17     16     15.5    14.9

The range of the sample data is $ 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 $ 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?

A. Yes, because the standard deviation is an unbiased estimator.

B. Yes, because the sample is random.

C. No, because there is an outlier in the sample data.

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

Answer 1

The range of the sample data is as below:

To find variance we will first find mean

Create the following table.

data	data-mean	(data - mean)2
39	14.86	220.8196
37	12.86	165.3796
35	10.86	117.9396
28	3.86	14.8996
20	-4.14	17.1396
19	-5.14	26.4196
17	-7.14	50.9796
16	-8.14	66.2596
15.5	-8.64	74.6496
14.9	-9.24	85.3776

Find the sum of numbers in the last column to get.

Standard deviation is

We know that standard deviation if unbiased estimator of population standard deviation

Hence answer is

A. ​Yes, because the standard deviation is an unbiased estimator.