Math 1001 Assignment 4 Question 1: Robbers

There have been a series of four robberies of jewellery stores recently in a police precinct. The detectives suspect the robberies may be the actions of two or more separate sets of thieves acting independently. Detective Eames thinks there are three groups, Detective Logan thinks there are two groups, and Detective Goran thinks there is only one group responsible.

Mud was found at the scene of each robbery, believed to come from the shoes of the thieves. In an effort to determine if two or more separate groups are responsible for the robberies, different samples of mud from each robbery is collected, and analyzed for chemical content. The results of this analysis are provided in the following table:

Crime Scene Data: Analysis of 10 Samples from each robbery

Store	% Aluminum Oxide	% Iron Oxide	% Magnesium Oxide
Maison Birks	14.2	5.5	3.5
	13.1	2.3	2.9
	14.5	2.6	2.6
	14.1	0.9	1.9
	13.9	4.8	3.8
	13.7	6.4	3.4
	14.3	2.1	2.7
	14.0	2.8	2.8
	13.7	1.9	2.3
	13.3	1.8	1.8
Ben Moss Jewelery	14.0	2.5	2.1
	13.4	2.5	2.1
	14.2	2.9	1.9
	14.0	1.9	2.2
	13.6	2.8	2.0
	13.2	6.3	1.3
	14.1	2.1	1.5
	14.5	2.8	1.3
	14.3	1.9	1.6
	13.5	1.8	1.4
Michael Hill	13.8	5.2	3.2
	13.2	4.3	3.3
	14.2	4.6	2.6
	14.6	4.9	1.9
	14.8	4.7	2.7
	14.1	5.9	3.9
	14.5	4.5	2.5
	14.0	3.9	2.9
	13.9	4.9	2.9
	13.2	3.8	1.8
Peoples Jewelers	13.8	2.2	2.2
	14.4	2.4	2.2
	14.3	2.8	2.2
	14.6	2.0	2.1
	13.8	2.7	2.0
	13.3	0.3	1.7
	14.2	2.5	1.3
	14.0	2.3	1.5
	13.6	1.6	1.6
	13.9	1.4	1.4

Question 1

1. Compute the 5-number summaries for the distributions, which are used to create the boxplots. (use Excel for this part)
2. By constructing appropriate groupings of boxplots from this data, determine if separate groups of thieves are responsible for the heists.

   Because you will be comparing boxplots, it is important that only the boxplots that you are comparing are plotted together.

   You can either create the box plots by hand, or use Excel. Excel 2016 does boxplots, Excel 2013 does not. If you do them by hand, make sure your plots are to scale, and drawn neatly.

3. If there are more than one group, which groups did which heists? Justify your conclusion using statistical properties of the boxplots. Which detective got it right?

This is a small data set, so you may be able to figure this out from staring at the data for awhile. Finding the solution this way would be more difficult for larger data sets. Regardless, the box plots will provide a good way to present your conclusions in a convincing way to others!