Make a picture! First, create a frequency table



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AP Statistics: Chapter 3 Categorical Data

MAKE A PICTURE!


First, create a frequency table

Example: number of students at CB South in each grade:




Proportion = decimal: .30, .05 Percent = %: 30%, 5%
Frequency = # of things (count) Relative frequency = % of things
Distribution (of a variable)- shows the values of the variable ad how often the sample takes each value

Examples: bar chart, pie chart, histogram, stemplot, etc.



Categorical Distributions:

  1. Bar Chart


Notice the spaces

In between bars



Relative frequency

%

#

grade

grade



  1. Pie Chart


Be sure to use labels and percents!



grade
Contingency tables (aka 2-Way tables)
Frosh

Soph

Junior

Senior

Total


Male

 


cells
 

 

 



 

Female

 


margins
 

 

 



 

Total


 

 

 



 

 


gender

Identify:



  • Row variable  gender

  • Column variable  grade

  • Values of the variable  the different rows/columns

  • Total (n)  bottom right of chart

  • # of Cells  8 (don’t count totals)

  • Totals  margins


Example: Hospitals
Hospital A

Hospital B

Died

63


2821

79
16

Survived

2037



2900
784

2100 800


  • What percent of people died?



Notation:

Probability: P(event) Given/Of: And: (overlap) Or:



Probability of A given B


  • Of those people that went to Hospital A, what percent died?



  • Given that someone went to Hospital B, what is the chance that they died?





  • What percent of people died and went to Hospital B?



  • What percent of people survived or went to Hospital A?



2 types of Distributions for Categorical Variables

  1. MARGINAL DISTRIBUTIONS

  • How to make: Convert totals into percentages




  • Example: Hair color vs. Gender




Brown

Blonde

Black

Red

Total

MALE

26

24

10

3

63

FEMALE

20

35

12

6

73

TOTALs

46

59

22

9

136


margins
Find the marginal distribution for the HAIR COLOR variable

Brown:

Blonde:

Black:

Red:



  • Find the marginal distribution for the GENDER variable

Male:

Female:







  1. CONDITIONAL DISTRIBUTIONS

  • Look at … one variable




  • Then look at … each value of the variable individually




Brown

Blonde

Black

Red

Total

MALE

26

24

10

3

63

FEMALE

20

35

12

6

73

TOTALs

46

59

22

9

136







  • ALWAYS … in %

  • Example: Hair Color vs. Gender




  • Find the conditional Distribution for the HAIR COLOR variable

Brown: Blonde: Black: Red:




  • Find the conditional Distribution for the GENDER variable

Male: Female:




  • Represented visually: SEGMENTED (or STACKED) BAR GRAPH



Independence: When one variable does not affect the other variable


How do we tell independence? Independence exists when the conditional distributions looks the same throughout all values of the variable (when the sections look approximately the same). There is generally less than a 5 % difference between percentages. When categorical variables are dependent, they are said to be associated.
Independent: Dependent:



AP Stat- worksheet 3A- Categorical Variables practice

In a survey of adult Americans, people were asked to indicate their age and to categorize their political preference (liberal, moderate, conservative). The results are as follows:







Liberal

Moderate

Conservative

Total

under 30

83

140

73

296

30 - 50

119

280

161

560

over 50

88

284

214

586

total

290

704

448

1442




  1. What are the row and column variables?

  2. What percent of Liberals are under 30?

  3. Of those over 50, what percent are Liberals?

  4. Of those that are moderates, what percent are 30-50?

  5. What percent of respondents are moderate and under 30?

  6. Calculate the marginal distribution for the AGE variable. Write these down. Then make a bar graph of the marginal distribution for age.




  1. Calculate the marginal distribution for the PREFERENCE variable. Write these down. Then make a bar graph of this marginal distribution.




  1. Calculate the conditional distribution of the AGE variable. Write these down. Then make a segmented bar graph of this marginal distribution.




  1. Calculate the conditional distribution of the PREFERENCE variable. Write these down. Then make a segmented bar graph of this marginal distribution.




  1. Are the two variables independent?


AP Stat- worksheet 3B- Categorical Variable practice

A 4-year study reported in The New York Times, on men more than 70 years old analyzed blood cholesterol and noted how many men with different cholesterol levels suffered nonfatal or fatal heart attacks.






Low cholesterol

Medium cholesterol

High cholesterol

Nonfatal heart attacks

29

17

18

Fatal heart attacks

19

20

9




  1. Calculate the marginal distribution for cholesterol level and make a bar graph.

  2. Calculate the marginal distribution for severity of heart attack and make a bar graph.

  3. Calculate three conditional distributions for the three levels of cholesterol and make a stacked bar graph.

  4. Calculate the conditional distributions for the type of heart attack and make a stacked bar graph.

  5. Are the two variables independent?


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