Problem 5BSC

In Exercises, find the (a)mean, (b) median, (c) mode, and (d) midrange for the given sample data. Express answers with the appropriate units of measurement. 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 mean annual earnings of all celebrities?

Answer:

Step 1 of 1

(a) The "Mean" is computed by adding all of the numbers in the data together and dividing by the number elements contained in the data set.

Mean = = 159.8 or $159,800,000

(b) The "Median" of a data set is dependant on whether the number of elements in the data set is odd or even. First reorder the data set from the smallest to the largest then if the number of elements are odd, then the Median is the element in the middle of the data set. If the number of elements are even, then the Median is the average of the two middle terms.

67 |
75 |
84 |
88 |
90 |
100 |
225 |
235 |
302 |
332 |

Median = = 95 or $95,000,000

(c) The "Mode" for a data set is the element that occurs the most often. It is not uncommon for a data set to have more than one mode. This happens when two or more elements occur with equal frequency in the data set. A data set with two modes is called bimodal. A data set with three modes is called trimodal.

Since there is no repeated terms in the data. Hence there is no mode.

(d) In statistics, the mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set, defined as

Mid range = 199.5 or $199,500,000