Question

The manager of a grocery store wants to determine the average amount of money spent at his store as it compares to the average dollar amount spent at his competitor's store. At the end of the day, he reviews the amounts of the last 15 grocery orders. The amounts rounded to the nearest dollar are: 41, 38, 19, 30, 21, 53, 34, 34, 37, 29, 50, 43, 57, 28, 50 He then visits the store of his competitor and surveys the first 15 people leaving the store with groceries. The amounts he records, also rounded to the nearest dollar, are: 86, 15, 75, 40, 51, 60, 27, 45, 112, 7, 65, 31, 18, 27, 69 What is the average amount of money spent at each store to the nearest cent? For which store is the mean a better representation of the data? In two or more complete sentences, explain your answer.

Answer 1

Given

Expenditures at Manager's Store; expenditures at Competitor's Store.

Find

a) average spent at each store

b) which store is better represented by the mean value

c) an explanation for the answer in ≥ 2 sentences

Solution

a) The sum of expenditures divided by the number of expenditures (15) is ...

... average for Manager's Store: $37.60

... average for Competitor's Store: $48.53

b) The expenditures at Manager's Store are well-represented by the mean (average).

c) The range of expenditures at Competitor's Store is significantly higher than at Manager's store, so a single number such as mean or median does not represent the data well. The expenditures at Manager's store are more compactly grouped around the mean and median, which are closer together, so the mean is a good representation of Manager's Store expenditures overall.