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?

41  40  38  32  22  18  16  12  11.6 10.7

The range of the sample data is ​$ nothing million. ​ (Type an integer or a​ decimal.) T

he 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 there is an outlier in the sample data.

B. Yes, because the sample is random.

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

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

Answer 1

Range :

The lowest value is 10.7.

The highest value is 41.

The range = 41 - 10.7 = 30.3.

• Answer : Range = 30.3

Variance :

Solution:

x	x2
41	1681
40	1600
38	1444
32	1024
22	484
18	324
16	256
12	144
11.6	134.56
10.7	114.49
---	---
∑x=241.3	∑x2=7206.05

• Answer : Variance = 153.72

Standard deviation :

S = sqrt ( var )

    = sqrt ( 153.72 )

    = 12.40

• Answer : Standard deviation = 12.40
• Answer : ​No, because the sample is not representative of the whole population.