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Boxplots

Boxplots

Author: Al Greene
Description:

Demonstrate how to create a boxplot from the 5-number summary
Discuss how a boxplot can show either symmetry or skew of a distribution
Present how to algebraically determine if there is an outlier [Q1 – 1.5(IQR) and Q3 + 1.5(IQR)]
Show how to represent outliers on a boxplot

This packet covers all facets of boxplots, from 5 number summaries to IQR tests to boxplots with outliers.
There is a powerpoint of definitions, videos of an example, and a data set for you to create your own boxplot for.

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Tutorial

Overview

This packet introduces you to the idea of a boxplot. Some terms that should already be familiar to you are:

- 5 number summary

- outlier

- range

Source: Greene

Definitions

This powerpoint gives definitions of terms used in the packet. Please refer to the videos below for more details and an example.

Source: Greene

Box and Whisker Plot

Here is a good example on creating a 5 number summary. The data is not sorted originally for this problem, so it is helpful to see it being sorted.

Example

Consider the following data set: 13,14, 16, 18, 21, 22, 22, 25, 29, 40

Create a 5 number summary, perform an IQR test to see if there are any outliers, and create a boxplot, making sure to include any outliers.

Source: Greene

Example solutions

13,14, 16, 18, 21, 22, 22, 25, 29, 40

 

Numbers for 5 number summary:

Min - 13     Q1 - 16        Median - 21.5        Q3 - 25         Max - 40

 

IQR test: 

1. Q3-Q1=IQR       25-16 = 9

2. IQR*1.5 = NUMBER       9*1.5 = 13.5

3. Q3 + NUMBER = upper limit          25+13.5 = 38.5

    Q1 - NUMBER = lower limit             16 - 13.5 = 2.5

4. Nothing is less than 2.5, but 40 is greater than the upper limit of 38.5. Therefore, 40 is an outlier.

 

For the boxplot, you should have an asterisk at 40 to indicate it is an outlier.

Source: Greene