1. Unit 1: Analyzing Data – Describing Distributions
Analyzing Categorical Data:
Describing the Modal Category and Patterns from Sets and Displays

2. Analyzing Categorical Data
Categorical Variables place individuals into one of several groups or categories
The values of a categorical variable are labels for the different categories
The distribution of a categorical variable lists the count or percent of individuals who fall into each category.
Analyzing Categorical Data
Frequency Table
Format
Count of Stations
Adult Contemporary
1556
Adult Standards
1196
Contemporary Hit
569
Country
2066
News/Talk
2179
Oldies
1060
Religious
2014
Rock
869
Spanish Language
750
Other Formats
1579
Total
13838
Relative Frequency Table
Format
Percent of Stations
Adult Contemporary
11.2
Adult Standards
8.6
Contemporary Hit
4.1
Country
14.9
News/Talk
15.7
Oldies
7.7
Religious
14.6
Rock
6.3
Spanish Language
5.4
Other Formats
11.4
Total
99.9
Variable
Count
Percent
Values

3. Analyzing Categorical Data
Displaying categorical data
Frequency tables can be difficult to read. Sometimes is is easier to analyze a distribution by displaying it with a bar graph or pie chart.
Analyzing Categorical Data
Frequency Table
Format
Count of Stations
Adult Contemporary
1556
Adult Standards
1196
Contemporary Hit
569
Country
2066
News/Talk
2179
Oldies
1060
Religious
2014
Rock
869
Spanish Language
750
Other Formats
1579
Total
13838
Relative Frequency Table
Format
Percent of Stations
Adult Contemporary
11.2
Adult Standards
8.6
Contemporary Hit
4.1
Country
14.9
News/Talk
15.7
Oldies
7.7
Religious
14.6
Rock
6.3
Spanish Language
5.4
Other Formats
11.4
Total
99.9

6. The frequency table below shows the responses to a survey that asked participants if they believed they had a change of being wealthy by the age of 30

8. Pie & Bar Summary
A pie chart should be used when displaying what part each category is of the whole
Must display ALL categories that make up the whole
Must total to 100%
A bar graph can be used when showing category percentages OR COUNTS
Also, use a bar graph if pie pieces become difficult to estimate and when comparing groups (we’ll see this tomorrow)

9. Classwork: Analyze our Statistical Reasoning Categorical Data
Analyze the data displayed on each of the following slides
On a sheet of paper (each student should have their own), provide:
Number your paper as you go by the slide number (top left corner of each slide)
Report the “modal category” (the mode) in a complete sentence and in context
Two OTHER observations in complete sentences (what can be said from the information displayed? Any patterns?)
Let’s do the first one together