A busy grocery store in San Antonio captures the time per item it takes to check out customers during their peak time. (The total time for the customer was divided by the number of items for that customer. If a customer took 8 minutes, or 480 seconds, to check out and purchased 24 items, the time would be 20). A sample of times is calculated for each cashier. They want to compare 2 cashiers. The following are the average time per item scanned in seconds for each cashier: Cashier 1 Cashier 2 Time per Item Scanned Time per Item Scanned 20 24 10 16 52 19 60 55 65 45 58 36 40 5 38 29 40 52 25 45 35 15 40 19 35 28 27 28 15 30 16 28 18 19 Compare the following (a through k) for these two cashiers and then help the store determine which of the two cashiers has better metrics (explain why): Cashier 1 Cashier 2 a. Means b. Q1 (or 25thpercentile) c. Median d. Q3 (or 75thPercentile e. Standard Deviations f. Ranges g. Interquartile Ranges

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A busy grocery store in San Antonio captures the time per item it takes to check out customers during their peak time. (The total time for the customer was divided by the number of items for that customer. If a customer took 8 minutes, or 480 seconds, to check out and purchased 24 items, the time would be 20). A sample of times is calculated for each cashier. They want to compare 2 cashiers. The following are the average time per item scanned in seconds for each cashier:

Cashier 1	Cashier 2
Time per Item Scanned	Time per Item Scanned
20	24
10	16
52	19
60	55
65	45
58	36
40	5
38	29
40	52
25	45
35	15
40	19
35	28
27	28
15	30
16	28
	18
	19

Compare the following (a through k) for these two cashiers and then help the store determine which of the two cashiers has better metrics (explain why):

	Cashier 1	Cashier 2
a. Means
b. Q1 (or 25^thpercentile)
c. Median
d. Q3 (or 75^thPercentile
e. Standard Deviations
f. Ranges
g. Interquartile Ranges

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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