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

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

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

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

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)

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