+ The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE Chapter 1: Exploring Data Introduction – D ata Analysis: Making Sense of Data Section 1.1 – Analyzing Categorical Data

+ Data Analysis Statistics is the science of data. Data Analysis is the process of organizing, displaying, summarizing, and asking questions about data. Definitions: Individuals – objects (people, animals, things) described by a set of data Variable - any characteristic of an individual Categorical Variable – places an individual into one of several groups or categories. Quantitative Variable – takes numerical values for which it makes sense to find an average.

+ Why the distinction is important You will receive NO credit (really!) on the AP exam if you construct a graph that isn’t appropriate for that type of data Type of VariableAppropriate Graph CategoricalPie Chart, Bar Graph QuantitativeDotplot, Stemplot, Histogram

+ What type of variable? Yesterday, I collected two data sets from you. I asked you the fastest speed you’ve ever driven and your favorite subject. Speed – quantitative or categorical? Subject – quantitative or categorical?

+ Data Analysis A variable generally takes on many different values.In data analysis, we are interested in how often avariable takes on each value. Definition: Distribution – tells us what values a variable takes and how often it takes those values Variable of Interest: MPG Dotplot of MPG Distribution Example

+ Data Analysis From Data Analysis to Inference Population Sample Collect data from a representative Sample... Perform Data Analysis, keeping probability in mind… Make an Inference about the Population.

+ Analyzing Categorical Data Categorical Variables place individuals into one of several groups or categories The values of a categorical variable are labels for thedifferent categories The distribution of a categorical variable lists the count orpercent of individuals who fall into each category. Frequency Table FormatCount of Stations Adult Contemporary1556 Adult Standards1196 Contemporary Hit569 Country2066 News/Talk2179 Oldies1060 Religious2014 Rock869 Spanish Language750 Other Formats1579 Total13838 Relative Frequency Table FormatPercent of Stations Adult Contemporary11.2 Adult Standards8.6 Contemporary Hit4.1 Country14.9 News/Talk15.7 Oldies7.7 Religious14.6 Rock6.3 Spanish Language5.4 Other Formats11.4 Total99.9 Example, page 8 Count Percent Variable Values

+ Analyzing Categorical Data Displaying categorical data Frequency tables can be difficult to read. Sometimes is is easier to analyze a distribution by displaying itwith a bar graph or pie chart. Frequency Table FormatCount of Stations Adult Contemporary1556 Adult Standards1196 Contemporary Hit569 Country2066 News/Talk2179 Oldies1060 Religious2014 Rock869 Spanish Language750 Other Formats1579 Total13838 Relative Frequency Table FormatPercent of Stations Adult Contemporary11.2 Adult Standards8.6 Contemporary Hit4.1 Country14.9 News/Talk15.7 Oldies7.7 Religious14.6 Rock6.3 Spanish Language5.4 Other Formats11.4 Total99.9

+ Analyzing Categorical Data Bar graphs compare several quantities by comparing the heights of bars that represent those quantities. Our eyes react to the area of the bars as well as height. Be sure to make your bars equally wide. Avoid the temptation to replace the bars with pictures for greater appeal…this can be misleading! Graphs: Good and Bad This ad for DIRECTV has multiple problems. How many can you point out?

+ Introduction Data Analysis: Making Sense of Data In this section, we learned that… A dataset contains information on individuals. For each individual, data give values for one or more variables. Variables can be categorical or quantitative. The distribution of a variable describes what values it takes and how often it takes them. Inference is the process of making a conclusion about a population based on a sample set of data. Identify good and bad graphs – and label correctly! Summary