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 A: Mean is $37.60 The mean is an excellent representation of the data, because the variability is so small. Both stores have medians close to the means, but the IQR is much less for the first store.
19
2189
30448
413
50037
For B: Mean is $48.53. Here, there is a lot of spread, and the mean is not as good a representation of the data.
0 7
158
277
33
405
51
6059
75
86
9
10
112