Problem 5BSC

In Exercises, find the range, variance, and standard deviation for the given samph data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-2 where we found measures of center. Here we find measures of variation.) Then answer the given questions.

Top 10 Celebrity Incomes Listed below are the earnings (in millions of dollars) of the celebrities with the 10 highest incomes in a recent year. The celebrities in order are Steven Spielberg, Howard Stern, George Lucas, Oprah Winfrey, Jerry Seinfeld, Tiger Woods, Dan Brown, Jerry Bruckheimer, J. K. Rowling, and Tom Cruise. Can this “Top 10” list be used to learn anything about the standard deviation of the annual earnings of all celebrities?

Solution 5BSC

From the given information, the earnings (in millions of dollars) of the celebrities with the 10 highest incomes in a recent year are.

From the given information, maximum data value is $332 million and minimum value is $67 million. We know that range of the given set of sample values found as follows:

Therefore, the range of the given set of observations is $265 million.

From the given information,. We know that variance of given set of sample value found as follows:

Therefore, the variance of the given sample is .

We know that standard deviation be the positive square root of the variance, that is

Therefore, the standard deviation of the given sample is $102.70 million.

Nothing can learn from the sample standard deviation, because the given sample is not a random sample and it is for the Top 10.