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? 42 40 39 32 21 18 16 14 13.7 12.6 The range of the sample data is ​$ 29.4 million. ​(Type an integer or a​ decimal.) The variance of the sample data is 145.24. ​(Round to two decimal places as​ needed.) The standard deviation of the sample data is ​$ 12.05 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. ​Yes, because the standard deviation is an unbiased estimator. D. ​No, because the sample is not representative of the whole populatio

Answer 1

Answer:

1. $29.4 million

2. 145.24

3. 145.24

4. 12.05

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

Step-by-step explanation:

1. The computation of range of the sample data is shown below:-

Range of the sample data = Maximum value - Minimum value

= 42 - 12.6

= $29.4 million

2. For the computation of variance of the sample data first, we need to find out the mean which is shown below:-

Mean = $\frac{(42 + 40 + 39 + 32 + 21 + 18 + 16 + 14 + 13.7 + 12.6) }{10}$

= 24.83

The Variance of the sample data

= $\frac{(42 - 24.83)^2 + ..... + (12.6 - 24.93)^2}{10 - 1}$

= $\frac{1307.161}{9}$

=  145.24

3. The computation of the standard deviation of the sample data is shown below:-

The Standard deviation of the sample

= $\sqrt{145.24}$

= $12.05155592

or

$12.05

4. No, as the sample does not represent the whole population.