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? 40     38     37     30     19     15     12     9     8.9     8.0

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

Answer 1

The range of the data is:

Range = Maximum - Minimum

= 38-8

=30

The sample size is n=9. The provided sample data along with the data required to compute the sample mean \bar X and sample variance and standard deviation are shown in the table below:

	X	X2
	38	1444
	37	1369
	30	900
	19	361
	15	225
	12	144
	9	81
	8.9	79.21
	8	64
Sum =	176.9	4667.21

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

No, since we are given only the top 10 salaries, therefore we have a very extreme dataset and we cannot infer anything about the variation of salaries of TV personalities in general.

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