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

For the manager's store

 Population size: 15
 Arithmetic mean (μ): 37.6
 Standard deviation (σ): 11,056

 For the competitor's store
 
 Population size: 15
 Arithmetic mean (μ): 48,533
 Standard deviation (σ): 28,356

 For the manager's store the average is a better representation of the data since it does not have Outlier points in the box diagram. Also the median is close to the average.

 For the competition store the average of the data collected is not as good representation of the data since they are dispersed from the mean with a standard deviation of 28.35. It also presents Outliers points in the box diagram, such as 112 which is very far from the average