AP Statistics – Ch 1.1 Notes Name: _________________ Analyzing Categorical Data

What is Statistics? • Statistics is the science of learning from Data

o Data are numbers with a context. • Statistics helps answer many of life’s questions:

o Does listening to music help or hinder studying? o Which of two diets will help obese children lose more weight and keep it off? o How strong is the evidence for global warming? o Do cell phones cause brain cancer?

1. Identify the individuals and variables in a set of data Individuals are objects described by a set of data (Who is being described?). Variables are any characteristics of an individual (What do we know about them/it?)

2. Classify variables as categorical or quantitative Categorical variables place an individual into one of several groups or categories Quantitative variables take numerical values for which it makes sense to take an average (ordinal/measurements)

Distribution tells us a) What values a variable takes and b) How often it takes those values

(Independent Practice)

Key

AP Statistics – Ch 1.1 Notes Name: _________________ Analyzing Categorical Data

3. Display categorical data with a bar graph. Decide whether it would be appropriate to make a pie chart Using the class data table, complete the Frequency Table to show the distribution of the variable “Most Used App” and create a graphical display of the data.

App Frequency Relative

Frequency

4. Identify what makes some graphs of categorical data deceptive.

There are two important lessons to keep in mind:

(1) beware the pictograph, and (2) watch those scales.

0Scalestartingat 10 is misleading

AP Statistics – Ch 1.1 Notes Name: _________________ Analyzing Categorical Data

Two-Way Tables: A two-way table describes two categorical variables, organizing counts according to a row variable and a column variable

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.

A conditional distribution of a variable describes the values of that variable among individuals who have a specific value of another variable.

We say there is an association between two variables if knowing the value of one variable helps predict the value of the other. 5. Calculate and display the marginal distribution of a categorical variable from a two-way table.

Below is a two-way table displaying the student data collected from Mr. McGee’s entire AP Statistics class for the 2019/20 school year.

a) The marginal distribution of “Predicted Income Status” can be displayed in a bar graph or a table.

OR b) What proportion of AP Statistics students predict they will be in the upper income status?

c) What percent of students were female and predicted they will be in the lower income status?

d) What proportion of students who predicted they will be in the middle income bracket were male?

Gender

Predicted Income bracket

Female Male Total

Lower 7 7 14

Middle 21 20 41

Upper 3 9 12

Total 31 36 67

Predicted Income Frequency

Lower 14

Middle 41

Upper 12

key

Allstudentsfromtable

f 0.1791 117.912f 0.1044 10.4402 0.4878 48.780

AP Statistics – Ch 1.1 Notes Name: _________________ Analyzing Categorical Data

6. Calculate and display the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table. Conditional distributions can be displayed by either a side-by-side bar graph or a segmented bar graph.

7. Describe the association between two categorical variables by comparing appropriate conditional

distributions. Can we say there is an association between gender and predicted income? There appears to be a small association between the variables gender and predicted income. Although the proportion of males and females in the lower and middle income is similar, there is a much larger proportion of males who believe they will be in the upper income bracket. Therefore, knowing the student is a male helps us estimate his predicted income bracket. He is more likely to believe he will be in the upper income bracket.

Independence = Not Associated In a two-way table, when the distribution of one variable is the same for all categories of another variable, we say that the variables are independent. That tells us there’s no association between these variables.

AP Statistics – Ch 1.1 Notes Name: _________________ Analyzing Categorical Data

Example Problem: In 1912 the luxury liner Titanic, on its first voyage across the Atlantic, struck an iceberg and sank. Some passengers made it off the ship in lifeboats, but many died. The two-way table gives information about adult passengers who survived and who died, by class of travel.

Survival Status

Class of Travel First Second Third Total

Survived 197 94 151 442 Died 122 167 476 765 Total 319 261 627 1207

1. What proportion of survivors were third-class passengers?

2. What percent of first-class passengers survived?

3. Find the distribution of survival status for each class of travel. Make a segmented bar graph to compare these distributions.

4. Describe what the graph in Question 4 reveals about the association between class of travel and survival status for adult passengers on the Titanic.

151442 34.16

19737g 61.75

orconditional Distribution sidebysidesurvived Died

1223190.382

Ingi Diedsurvived

15162 0.2414766270.759 yo

I

20

1st 2nd 3rd

class

Thereseemstobean association becauseknowingtheclass of thePassenger helps us topredict his or her survival statusfirstclasshadthehighestpercentage of survival 61.8 followedbysecondclass 36 and thirdclass 24.1