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     39     37     29     17     16     13     10     9.8     9.0 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?

Answer 1

Let's use excel to find descriptive statistics

Step 1) Enter the given data in excel

Step 2) Click on Data >>>Data Analysis>>>Descriptive Statistics>>>OK

Step 3) Input Range: Select the range of the column A

Then select Labels in first row

Click on output range : select any empty cell and then click on OK

Look the following box

so we get the following output

From the above output  

Range = 32 ( 41 - 9)

Variance = 169.75

Standard deviation = 13.03

Yes, the standard deviation of the sample is a good estimate of the variation of salaries of TV personalities in​ general

Because it is less affected to the extreme observations than the range.

Also it depend on all the observations in the data set.

Note that range depend on only two values as maximum observation and minimum observation.