Question

here are 6 celebrities with some of the highest net worths (in millions of dollars) in a recent year: oprah winfrey (3200), michael jordan (1700), paul mccartney (1200), j. k. rowling (1000), david copperfield (1000), and jerry seinfeld (950) ㊀. 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 $ 2250 million. (round to the nearest integer as needed.)

the variance is 764.417 million dollars squared. (round to the nearest integer as needed.)

the standard deviation is $ 87.4 million. (round to the nearest integer as needed.)

what do the results tell us about the population of all celebrities?

a. because the data are from celebrities with the highest net worths, 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 not at all typical for all celebrities.

d. because the statistics are calculated from the data, the measures of variation are typical for all celebrities.

Explanation:

The data is from a sample of 6 celebrities with the highest net worths. These are not representative of all celebrities (most celebrities likely have much lower net worths). So measures of variation from this sample (which includes extreme high values) aren't typical for the entire population of celebrities. Option C states this: "Because the data are from celebrities with the highest net worths, the measures of variation are not at all typical for all celebrities." Option A is wrong as the sample isn't typical. Option B is wrong as we know the sample is of highest net worths, so we can infer it's not typical. Option D is wrong as the sample has extreme values, so statistics aren't typical for all.

Answer:

C. Because the data are from celebrities with the highest net worths, the measures of variation are not at all typical for all celebrities.