Statistics for business decision making and analysis robert stine and foster chapter 03

Chapter 3

Describing Categorical
Data

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3.1 Looking At Data
Which hosts send the most visitors to
Amazon’s Web site?


Data set consists of 188,996 visits



Host is a categorical variable



To answer this question we must describe the
variation in Host
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3.1 Looking At Data
Frequency and Relative Frequency Tables


The distribution of a categorical variable is a list
of values with its associated count (frequency)



A frequency table summarizes the distribution of
a categorical variable



A relative frequency table shows the proportion
(or percentage) in each category
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3.1 Looking At Data

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3.2 Charts of Categorical Data
Bar Charts and Pie Charts


Unless you need to know exact counts, charts are
better than tables for summarizing more than five
categories



The two most common displays of a categorical
variable are a bar chart and a pie chart

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3.2 Charts of Categorical Data
The Bar Chart


Uses horizontal or vertical bars to show the
distribution of a categorical variable



Is called a Pareto chart when the categories are
sorted by frequency (popular in quality control)



Becomes cluttered with too many categories



Is appropriate for ordinal categorical variables
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3.2 Charts of Categorical Data
Bar Chart (Horizontal) of Top 10 Hosts

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3.2 Charts of Categorical Data
Bar Chart (Vertical) of Top 10 Hosts

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3.2 Charts of Categorical Data
The Pie Chart


Uses wedges of a circle to show the distribution of
a categorical variable



Commonly chosen to illustrate market shares or
sources of revenue for a company



Less useful than bar charts if we want to compare
actual counts (easier to compare bars than angles
of wedges)
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3.2 Charts of Categorical Data
Pie Chart of Top 10 Hosts

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3.3 The Area Principle
The Fundamental Rule for Data Displays


The area occupied by a part of the graph/chart
that displays data should be proportional to the
amount of data it represents



Charts decorated to attract attention often violate
the area principle

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3.3 The Area Principle
An Example Violating the Area Principle

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3.3 The Area Principle
The Same Example Respecting the Area Principle

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4M Example 3.1: ROLLING OVER
Motivation
Are certain types of vehicles more prone to rollover accidents than others?

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4M Example 3.1: ROLLING OVER
Method
Data gathered from Fatality Analysis Reporting
System (FARS) for roll-over accidents on
interstate highways. Cases that make up the
rows are accidents resulting in roll-overs in 2000.

The column of interest is model of the car
involved.

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4M Example 3.1: ROLLING OVER
Mechanics

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4M Example 3.1: ROLLING OVER
Mechanics

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4M Example 3.1: ROLLING OVER
Message
Ford Broncos were involved in more than twice as
many roll-over accidents as the next-closest
model.

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4M Example 3.2: CHIP SALES
Motivation
Infineon pled guilty to price fixing for DRAM’s
in September 2004. Did Infineon gain a
larger share of the market for chips during
this period?

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4M Example 3.2: CHIP SALES
Method

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4M Example 3.2: CHIP SALES
Mechanics

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4M Example 3.2: CHIP SALES
Message
Infineon and Samsung increased their shares
from 1999 to 2002. It appears to have

been at the expense of smaller companies.

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3.4 Mode and Median
Mode


Category with the highest frequency



The longest bar in a bar chart



The widest slice in a pie chart



Two or more categories can tie with the highest
frequency (bimodal or multimodal)
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3.4 Mode and Median
Median



Not appropriate for nominal data



Data must be ordinal



It is the category label of the middle observation
in ordered data

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