Introduction to Statistics

Question

Neikia wants to determine the average amount of money moviegoers typically spend on snacks at the theater. He surverys 150 people leaving the theater one evening, and finds that 79 did not spend any money on refreshments. The maximum amount spent was 22.50.

a. What is the largest possible value for the mean?

b. What is the median amount spent on refreshments?

Answer 1

If we are to assume that all the people who spent any money on snacks spent $22.50 each, we can calculate the total amount spent in the movie theater on snacks. There were 150 movie-goers, and 79 didn't buy any refreshments, so (150 - 79) will give us the number who spent money. 150 - 79 = 71.

To find the theater's total snack sales, we multiply $22.50 by 71, which gives us $1,597.5.

To find the average, or mean, amount spent per person, we divide this total by the number of people who visited that night, so $1,597.5 divided by 150 = $10.65.

Since the chances are that not everyone spent the same amount, and the most anyone spent was $22.50, the actual mean is probably lower, so $10.65 is the largest possible value for the mean.

To find the median, we line up all the night's customers in order from "spent the least" to "spent the most" and then pick the middle person. Doing this, we will have 79 people who didn't spend money and then 71 people who did. The middle person in a line of 150 people is the gap between the 75th person and the 76th person. Since both the 75th person and the 76th person spent nothing, the median amount spent is $0.00.