Section 4.3.1 2-Way Tables and Marginal Distributions AP Statistics www.toddfadoir.com/apstats
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
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
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
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
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
Calculating Marginal Distributions Years of school completed, by age, 2000 (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
Calculating Marginal Distributions Years of school completed, by age, 2000 (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
Graph of Marginal Distribution AP Statistics, Section 4.3, Part 1
AP Statistics, Section 4.3, Part 1 Assignment Exercises: 4.50-4.55 AP Statistics, Section 4.3, Part 1