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?

38     37     36     29     19     15     13     9     8.9     7.4

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

B. ​Yes, because the sample is random.

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

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

Answer 1

First we arrange the observation in incresing order

7.4,8.9,9,13,15,19,29,36,37,38

Range = L -S

Where L=largest value and S=smallest value

	x		(x-)	(x-)^2
	7.4	21.23	-13.83	191.2689
	8.9	21.23	-12.33	152.0289
	9	21.23	-12.23	149.5729
	13	21.23	-8.23	67.7329
	15	21.23	-6.23	38.8129
	19	21.23	-2.23	4.9729
	29	21.23	7.77	60.3729
	36	21.23	14.77	218.1529
	37	21.23	15.77	248.6929
	38	21.23	16.77	281.2329
Total	212.3			1412.841

variance =

standard deviation =

The range of the sample data is ​$ 30.6 million.

The variance of the sample data is 156.98

The standard deviation of the sample data is ​$ 12.53 million.

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