1. Section 4.3.1 2-Way Tables and Marginal Distributions
AP Statistics

2. What about Categorical Data?
Whenever we have looked at data so far, it has quantitative vs. quantitative
What tools do we use if we are faced with categorical data?
AP Statistics, Section 4.3, Part 1

3. AP Statistics, Section 4.3, Part 1
2-Way Tables
First, think of data where each member of the distribution belongs to only one category.
Education Level:
Did not complete high school
Completed high school
1 to 3 years of college
4 or more years of college
AP Statistics, Section 4.3, Part 1

4. AP Statistics, Section 4.3, Part 1
2-Way Tables
First, think of data where the member of the distribution belong to only category.
Age:
25 to 34 years
35 to 54 years
55+ years
AP Statistics, Section 4.3, Part 1

5. Sample 2-Way Table Education is considered Age is considered
Each number represents a “count”, or the number of data points that meet the criteria
Sample 2-Way Table
Education is considered
“row variables”
Age is considered
“column variables”
25 to 34
35 to 54
55+
Total
Did not complete HS
4,474
9,155
14,224
27,853
Completed HS
11,546
26,481
20,060
58,087
1 to 3 years of college
10,700
22,618
11,127
44,445
4+ years of college
11,066
23,183
10,596
44,845
37,786
81,435
56,008
175,230
AP Statistics, Section 4.3, Part 1

6. Calculating Marginal Distributions
When we do a marginal distribution, we only look at totals (the values found on the right margin or bottom margin)
In marginal distributions, we divide by “Grand Total”
25 to 34
35 to 54
55+
Total
Did not complete HS
4,474
9,155
14,224
27,853
Completed HS
11,546
26,481
20,060
58,087
1 to 3 years of college
10,700
22,618
11,127
44,445
4+ years of college
11,066
23,183
10,596
44,845
37,786
81,435
56,008
175,230
AP Statistics, Section 4.3, Part 1

7. Calculating Marginal Distributions
Years of school completed, by age, (thousand of persons)
25 to 34
35 to 54
55+
Total
Did not complete HS
4,474
9,155
14,224
27,853
Completed HS
11,546
26,481
20,060
58,087
1 to 3 years of college
10,700
22,618
11,127
44,445
4+ years of college
11,066
23,183
10,596
44,845
37,786
81,435
56,008
175,230
AP Statistics, Section 4.3, Part 1

8. Calculating Marginal Distributions
Years of school completed, by age, (thousand of persons)
25 to 34
35 to 54
55+
Total
Did not complete HS
4,474
9,155
14,224
27,853
Completed HS
11,546
26,481
20,060
58,087
1 to 3 years of college
10,700
22,618
11,127
44,445
4+ years of college
11,066
23,183
10,596
44,845
37,786
81,435
56,008
175,230
AP Statistics, Section 4.3, Part 1

9. Graph of Marginal Distribution
AP Statistics, Section 4.3, Part 1

10. AP Statistics, Section 4.3, Part 1
Assignment
Exercises:
AP Statistics, Section 4.3, Part 1