Problem

Here are 6 celebrities with some of the highest net worths (in millions of dollars) in a recent year: Steven Spielberg (3700), Oprah Winfrey (3200), Paul McCartney (1200), J. K. Rowling (1000), David Copperfield (1000), and Jerry Seinfeld (950) ㅁ . Find the range, variance, and standard deviation for the sample data. What do the results tell us about the population of all celebrities? Based on the nature of the amounts, what can be inferred about their precision? The range is $\$ 2750$ million. (Round to the nearest integer as needed.) The variance is million dollars squared. (Round to the neanst integer as needed.)

Solution

Step 1 :Given the net worths of six celebrities: Steven Spielberg (3700), Oprah Winfrey (3200), Paul McCartney (1200), J. K. Rowling (1000), David Copperfield (1000), and Jerry Seinfeld (950) in millions of dollars.

Step 2 :The range is calculated as the difference between the highest and lowest values. In this case, the range is \(3700 - 950 = 2750\) million dollars.

Step 3 :The variance is the average of the squared differences from the mean. The variance for this data set is approximately \(1320347\) million dollars squared.

Step 4 :The standard deviation is the square root of the variance. For this data set, the standard deviation is approximately \(1149\) million dollars.

Step 5 :These results indicate a significant disparity in the net worths of these celebrities. The high range, variance, and standard deviation suggest that the net worths are spread out over a large range and are not clustered around the mean.

Step 6 :Based on the precision of the amounts, it can be inferred that the net worths are estimated with a high degree of accuracy.

Step 7 :Final Answer: The range of the net worths is \(\boxed{2750}\) million dollars. The variance is approximately \(\boxed{1320347}\) million dollars squared. The standard deviation is approximately \(\boxed{1149}\) million dollars.

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Source: https://solvelyapp.com/problems/16869/

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