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

3.1 Looking At DataFrequency and Relative Frequency Tables  The distribution of a categorical variable is a list of values with its associated count frequency  A frequency table summar

Describing Categorical

Data

Chapter 3

3.1 Looking At Data

Which hosts send the most visitors to

Amazon’s Web site?

 Data set consists of 188,996 visits

 To answer this question we must describe the

variation in Host

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

3.1 Looking At Data

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

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

3.2 Charts of Categorical Data

Bar Chart (Horizontal) of Top 10 Hosts

3.2 Charts of Categorical Data

Bar Chart (Vertical) of Top 10 Hosts

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)

3.2 Charts of Categorical Data

Pie Chart of Top 10 Hosts

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

3.3 The Area Principle

An Example Violating the Area Principle

3.3 The Area Principle

The Same Example Respecting the Area Principle

4M Example 3.1: ROLLING OVER

Motivation

Are certain types of vehicles more prone to

roll-over accidents than others?

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

4M Example 3.1: ROLLING OVER

Mechanics

4M Example 3.1: ROLLING OVER

Mechanics

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

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?

4M Example 3.2: CHIP SALES

Method

4M Example 3.2: CHIP SALES

Mechanics

4M Example 3.2: CHIP SALES

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)

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

Best Practices (Continued)

 Respect the area principle

 Show the best plots to answer the motivating

question

 Label your chart to show the categories and

indicate whether some have been combined or

omitted

 Avoid elaborate plots that may be deceptive

 Do not show too many categories

 Do not put ordinal data in a pie chart

 Do not carelessly round data