CHAPTER 1 Exploring Data

1. CHAPTER 1Exploring Data Introduction Data Analysis: Making Sense of Data

2. Data Analysis: Making Sense of Data • IDENTIFY the individuals and variables in a set of data • CLASSIFY variables as categorical or quantitative DEFINE “Distribution” DESCRIBE the idea behind “Inference”

3. Data Analysis Statisticsis the science of data. Data Analysis is the process of organizing, displaying, summarizing, and asking questions about data. • Individuals • objects 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.

4. Example: Quantitative or Categorical? Class (fr, soph, jun, sen) Grade point averageEmail addressNameBus routePhone numberDays absent

5. Example: Quantitative or Categorical? Address Number of Credits earned Allergies Exterior color Mileage Total car length Number of cylinders

6. Example: Quantitative or Categorical? Cost Model VIN Type of sound system Size of fuel tank Zip code Shoe Size

7. Data Analysis A variablegenerally takes on many different values. • We are interested in how often a variable takes on each value. • Distribution • tells us what values a variable takes and how often it takes those values. Dotplot of MPG Distribution Variable of Interest: MPG

8. Example

9. How to Explore Data Examine each variable by itself. Then study relationships among the variables. Start with a graph or graphs Add numerical summaries

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

11. Data Analysis: Making Sense of Data • 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.

12. CHAPTER 1Exploring Data 1.1Analyzing Categorical Data

13. Analyzing Categorical Data • DISPLAY categorical data with a bar graph • IDENTIFY what makes some graphs of categorical data deceptive • CALCULATE and DISPLAY the marginal distribution of a categorical variable from a two-way table • CALCULATE and DISPLAY the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table • DESCRIBE the association between two categorical variables

14. Categorical Variables Categorical variables place individuals into one of several groups or categories. Variable Values Count Percent

15. Displaying Categorical Data Frequency tables can be difficult to read. Sometimes it is easier to analyze a distribution by displaying it with a bar graph or pie chart.

16. Bar Graphs and Pie Charts Bar Graphs • Each bar must be same width. • Can display as count or percentage • Scale should start at 0 Pie Charts • Need to know the percentages to create. • Must add up to 100% (must be parts of a whole) • Can add another category when appropriate so that percentages total 100%. • Use when you want to emphasize each category’s relation to the whole.

17. Graphs: Good and Bad Bar graphs compare several quantities by comparing the heights of bars that represent those quantities. Our eyes, however, react to the area of the bars as well as to their height. • When you draw a bar graph, make the bars equally wide. It is tempting to replace the bars with pictures for greater eye appeal. • Don’t do it! • There are two important lessons to keep in mind: • beware the pictograph, and • watch those scales.

18. Graphs: Good and Bad

19. Graphs: Good and Bad This ad for DIRECTV has multiple problems. How many can you point out?

20. Graphs: Good and Bad

22. Careful with Scales!

23. These graphs show the same information: Google: 30% Yahoo: 35% MSN: 35%

25. Most Deceptive Graph Award

26. Homework pg. 6-7 # 1, 3, 5, 7, 8 pg. 20-22 #11, 13, 15, 17

27. Chapter 1: Exploring Data Section 1.1: Analyzing Categorical Data

28. Recap

29. Two-Way Tables and Marginal Distributions When a dataset involves two categorical variables, we begin by examining the counts or percents in various categories for one of the variables. A two-way table describes two categorical variables, organizing counts according to a row variable and a column variable. What are the variables described by this two-way table? How many young adults were surveyed?

30. Two-Way Tables and Marginal Distributions The marginal distribution of one of the categorical variables in a two-way table of counts is the distribution of values of that variable among all individuals described by the table. Note: Percents are often more informative than counts, especially when comparing groups of different sizes. • How to examine a marginal distribution: • Use the data in the table to calculate the marginal distribution (in percents) of the row or column totals. • Make a graph to display the marginal distribution.

31. Two-Way Tables and Marginal Distributions Examine the marginal distribution of chance of getting rich.

32. Homework Pg. 22 #19, 20

33. Relationships Between Categorical Variables A conditional distribution of a variable describes the values of that variable among individuals who have a specific value of another variable. • How to examine or compare conditional distributions: • Select the row(s) or column(s) of interest. • Use the data in the table to calculate the conditional distribution (in percents) of the row(s) or column(s). • Make a graph to display the conditional distribution. • Use a side-by-side bar graph or segmented bar graph to compare distributions.

34. Relationships Between Categorical Variables Calculate the conditional distribution of opinion among males and then females. Examine the relationship between gender and opinion.

35. Conclusion What does this tell us about the relationship between gender and opinion about future wealth for this sample of young adults? -There does seem to be an association between the two variables for this sample. -Men more often rated their chances in the two highest categories, while women said “some chance” much more frequently than men.

36. Relationships Between Categorical Variables Can we say there is an association between gender and opinion in the population of young adults? Making this determination requires formal inference, which will have to wait a few chapters. Caution! Even a strong association between two categorical variables can be influenced by other variables lurking in the background.

37. Superpowers A sample of 200 children from the United Kingdom aged 9-17 was selected from the CensusAtSchool Web site. The gender of each student was recorded along with which superpower they would most like to have: invisibility, superstrength, telepathy, ability to fly, ability to freeze time. Here are the results:

38. Superpowers 1. Use the data in the two-way table to calculate the marginal distribution (in percents) of superpower preferences. 2. Make a graph to display the marginal distribution. Describe what you see. 3. Do these data suggest that there is an association between gender and superpower preference? Give appropriate evidence to support your answer.

39. Data Analysis: Making Sense of Data • DISPLAY categorical data with a bar graph • IDENTIFY what makes some graphs of categorical data deceptive • CALCULATE and DISPLAY the marginal distribution of a categorical variable from a two-way table • CALCULATE and DISPLAY the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table • DESCRIBE the association between two categorical variables

40. Homework pg. 22-24 #21, 23, 26, 27-34