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
20
17
15
14
13.6
12.3

The range of the sample data is

​$nothing

million. ​(Type an integer or a​ decimal.)

The variance of the sample data is

nothing.

​(Round to two decimal places as​ needed.)

The standard deviation of the sample data is

​$nothing

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

Solution: Given that 38,37,36,29,20,17,15,14,13.6,12.3

=> The range of the sample data is 25.7

Explanation

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

12.3 13.6 14 15 17 20 29 36 37 38   

The lowest value is 12.3.

The highest value is 38.

The range = 38 - 12.3 = 25.7.

=> The variance of the sample data is 113.17

=> The standard deviation of the sample data is 10.64

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