Joint Marginal and Conditional Frequencies TWOWAY FREQUENCY TABLES

Joint, Marginal, and Conditional Frequencies TWO-WAY FREQUENCY TABLES

STANDARDS: MGSE 9 -12. S. CP. 4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, use collected data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

BY THE END OF THIS LESSON, YOU SHOULD BE ABLE TO: 1. Interpret data from a two-way frequency table 2. Identify and interpret joint, marginal, and conditional relative frequencies 3. Create a conditional distribution table 4. Create a relative frequency chart

TWO-WAY FREQUENCY TABLE Watch this: http: //www. youtube. com/watch? v=a. Uwpxoa. CV-w

CONDITIONAL DISTRIBUTIONS Watch: http: //www. youtube. com/watch? v=- v. LW 7 Ss 7 M 94

TERMS • Two-way Frequency table: a table listing two categorical variables who values have been paired • Joint relative frequency: is found by dividing a frequency that is not in the Total row or the Total column by the grand total. • Marginal relative frequency: is found by dividing a row total or a column total by the grand total. • Two-Way relative frequency table: displays both the joint relative and marginal relative frequencies. • Conditional relative frequency: is found by dividing a frequency that is not in the Total row or Total column by the frequency’s row total or

Creating a Relative Frequency Table: Jenna asked 40 randomly selected students whether they preferred dogs, cats or other pets. Complete the table for both decimals and percents Preferred Pet Frequency Relative Frequency Decimals Relative Frequency Percents Dog Cat Other Total 18 12 10 40 18 =. 45 40 12 =. 30 40 10 =. 25 40 40 = 1. 00 40 45% 30% 25% 100%

Creating a Two-Way Frequency Table: Jenna also recorded the gender of each student. The results are shown in the two-way frequency table. Find the totals and answer the questions. Preferred Pet Dog Cat Other Total Boys 10 5 9 24 Girls 8 7 1 16 18 12 10 Totals 1) How many total students took the survey? 40 2) How many total boys took the survey? 24 3) How many students said they like dogs as pets? 18 4) How many boys said they like dogs as pets? 10 40

Creating a Two-Way Relative Frequency Table: Jenna also recorded the gender of each student surveyed, complete the two-way frequency table below. Preferred Pet Dog Cat Other Total Boys 10 5 9 24 Girls 8 7 1 16 Totals 18 12 10 Preferred Pet Dog Cat Boys Girls Totals 10 =. 25 40 8 40 =. 20 18 =. 45 40 Other 40 Total 5 =. 125 9 =. 225 24 =. 60 40 40 40 1 7 16 40 =. 175 40 =. 025 40 =. 40 12 40 10 = 1. 00 =. 25 =. 30 40 40 40

Creating a Two-Way Relative Frequency Table: Preferred Pet Boys Girls Totals Dog 10 =. 25 40 8 40 =. 20 18 =. 45 40 Cat Other Total 5 =. 125 9 =. 225 24 =. 60 40 40 40 1 7 16 40 =. 175 40 =. 025 40 =. 40 12 40 10 = 1. 00 =. 25 40 =. 30 40 40 State the percents for the table above. Preferred Pet Boys Girls Totals Dog Cat Other Total 25% 20% 45% 12. 5% 17. 5% 22. 5% 30% 25% 60% 40% 100%

Creating a Two-Way Relative Frequency Table: Preferred Pet Dog Boys Girls Totals Cat Other Total 25% 12. 5% 22. 5% 60% 20% 45% 17. 5% 30% 40% 100% 2. 5% 25% 1) Find the joint relative frequency of students surveyed who are girls and prefer dogs as pets. 20% 2) Find the joint relative frequency of students surveyed who are boys and prefer cats as pets. 12. 5% 3) Find the marginal RF of students surveyed who prefer dogs as pets and then prefer cats as pets. dogs - 45% cats - 30%

Calculating a Conditional Relative Frequency: Preferred Pet Dog Cat Other Total Boys 10 5 9 24 Girls 8 7 1 16 18 12 10 Totals 40 Find the conditional relative frequency that a student surveyed prefers cats as pets, given the student is a girl. Number of girls who prefer cats: Number of girls: 7 16 =. 4375 = 43. 75%

Calculating a Conditional Relative Frequency: Preferred Pet Dog Cat Other Total Boys 10 5 9 24 Girls 8 7 1 16 18 12 10 Totals 40 Find the conditional relative frequency that a student surveyed is a girl, given that the student prefers cats as pets. Number of girls who prefer cats: Number of students who prefer cats: 7 =. 583 = 58. 3% 12

Calculating a Conditional Relative Frequency: Preferred Pet Dog Cat Other Total Boys 10 5 9 24 Girls 8 7 1 16 18 12 10 Totals 40 Find the conditional relative frequency that a student surveyed prefers cats as pets, given the student is a boy. Number of boys who prefer cats: Number of boys: 5 24 =. 208 = 20. 8%

Calculating a Conditional Relative Frequency: Preferred Pet Dog Cat Other Total Boys 10 5 9 24 Girls 8 7 1 16 18 12 10 Totals 40 Find the conditional relative frequency that a student surveyed is a boy, given that the student prefers dogs as pets. 10 Number of boys who prefer dogs: =. 556 = 55. 6% Number of students who prefer dogs: 18

Finding Possible Associations and Trends Jenna survey results (numbers vs percents). Dog Cat Other Total Boys 10/25% 5/12. 5% 9/22. 5% 24/60% Girls 8/20% 7/17. 5% 1/2. 5% 16/40% Totals 18/45% 12/30% 10/25% 40/100% 1) Does the table reflect gender bias towards pets? NO But, it does imply, boys like “other” pets more than girls: 22. 5% to 2. 5%, 2) If so, which gender, likes which pets the best? N/A 3) What are some examples of “other” pets? Hamsters, gerbils, mice, rats, snakes, rabbits, pigs, etc. , 4) Girls tend not to like which types of pets? “other” types

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