Here are 6 celebrities with some of the highest net worths (in millions of dollars) in a recent year: George Lucas (5500), Oprah Winfrey (3200), Michael Jordan (1700), J. K. Rowling (1000), David Copperfield (1000), and Jerry Seinfeld (950) 미 . 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 $\$ \square$ million. (Round to the nearest integer as needed.) The variance is $\square$ million dollars squared. (Round to the nearest integer as needed.) The standard deviation is $\$ \square$ million. (Round to the nearest integer as needed.) What do the results tell us about the population of all celebrities? A. Because the statistics are calculated from the data, the measures of variation are typical for all celebrities. B. Because the statistics are calculated from the data, the measures of variation cannot tell us about other celebrities. C. Because the data are from celebrities with the highest net worths, the measures of variation are typical for all celebrities. D. Because the data are from celebrities with the highest net worths, the measures of variation are not at all typical for all celebrities. Based on the nature of the amounts, what can be inferred about their precision? Because all of the amounts end with $\nabla$ it appears that they are rounded to the nearest so it would make sense to rolfnd the results to the nearest
Solution
Step 1 ：First, we need to calculate the range, variance, and standard deviation for the given data. The range is the difference between the highest and lowest values. The variance is the average of the squared differences from the mean. The standard deviation is the square root of the variance.
Step 2 ：Given the net worths of the celebrities are [5500, 3200, 1700, 1000, 1000, 950] in millions of dollars.
Step 3 ：The range is calculated as the difference between the highest and lowest values, which is 5500 - 950 = \(\boxed{4550}\) million dollars.
Step 4 ：The variance is calculated as the average of the squared differences from the mean, which is \(\boxed{2763125}\) million dollars squared.
Step 5 ：The standard deviation is the square root of the variance, which is \(\boxed{1662}\) million dollars.
Step 6 ：The results tell us that the population of all celebrities has a wide range of net worths, with a large variance and standard deviation, indicating a high level of disparity in their net worths. This suggests that the measures of variation are not at all typical for all celebrities.
Step 7 ：Based on the nature of the amounts, it appears that they are rounded to the nearest million, so it would make sense to round the results to the nearest million as well.
