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.
Find the conditional Distribution for the HAIR COLOR variable
Brown: Blonde: Black: Red:
Find the conditional Distribution for the GENDER variable
Represented visually: SEGMENTED (or STACKED) BAR GRAPH
Each bar = 100%
Values of variable on the x-axis
Bars are segmented into parts of each value
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:
30 - 50
What are the row and column variables?
What percent of Liberals are under 30?
Of those over 50, what percent are Liberals?
Of those that are moderates, what percent are 30-50?
What percent of respondents are moderate and under 30?
Calculate the marginal distribution for the AGE variable. Write these down. Then make a bar graph of the marginal distribution for age.
Calculate the marginal distribution for the PREFERENCE variable. Write these down. Then make a bar graph of this marginal distribution.
Calculate the conditional distribution of the AGE variable. Write these down. Then make a segmented bar graph of this marginal distribution.
Calculate the conditional distribution of the PREFERENCE variable. Write these down. Then make a segmented bar graph of this marginal distribution.
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.
Nonfatal heart attacks
Fatal heart attacks
Calculate the marginal distribution for cholesterol level and make a bar graph.
Calculate the marginal distribution for severity of heart attack and make a bar graph.
Calculate three conditional distributions for the three levels of cholesterol and make a stacked bar graph.
Calculate the conditional distributions for the type of heart attack and make a stacked bar graph.