1. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) NC Common Core Standards S.ID.5 – Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Objectives Create: relative frequency, two-way frequency, and two-way relative frequency tables, in addition to recognizing associations and trends Calculate and interpret a conditional relative frequency data, to include joint and marginal Using the appropriate graph, to graph the data and analyze the results Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables

2. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Glossary Terms: Joint relative frequency: is found by dividing a frequency that is not in the Total row or the Total column by the grand total. Two-way Frequency table: a table listing two categorical variables who values have been paired. 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 column total. Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables

3. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) 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 PetDogCatOtherTotal Frequency18121040 Relative Frequency Decimals Relative Frequency Percents 18 40 =.45 45% 12 40 =.30 30% 10 40 =.25 25% 40 = 1.00 100% Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables

4. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) 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 PetDogCatOtherTotal Boys105924 Girls87116 Totals 18 12 10 40 1) How many total students took the survey? 2) How many total boys took the survey? 3) How many students said they like dogs as pets? 4) How many boys said they like dogs as pets? 40 24 18 10 Warm-up 1/17/2013

5. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Creating a Two-Way Relative Frequency Table: Jenna also recorded the gender of each student surveyed, complete the two-way frequency table below. Preferred PetDogCatOtherTotal Boys Girls Totals 10 40 =.25 5 40 =.125 9 40 =.225 24 40 =.60 8 40 =.20 7 40 =.175 1 40 =.025 16 40 =.40 18 40 =.45 12 40 =.30 10 40 =.25 40 = 1.00 Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables Preferred PetDogCatOtherTotal Boys105924 Girls87116 Totals 18 12 10 40

6. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Creating a Two-Way Relative Frequency Table: Preferred PetDogCatOtherTotal Boys Girls Totals 10 40 =.25 5 40 =.125 9 40 =.225 24 40 =.60 8 40 =.20 7 40 =.175 1 40 =.025 16 40 =.40 18 40 =.45 12 40 =.30 10 40 =.25 40 = 1.00 Preferred PetDogCatOtherTotal Boys Girls Totals State the percents for the table above. 25% 12.5% 22.5% 60% 20% 17.5% 2.5% 40% 45% 30% 25% 100% Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables

7. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Creating a Two-Way Relative Frequency Table: 1) Find the joint relative frequency of students surveyed who are girls and prefer dogs as pets. 3) Find the marginal RF of students surveyed who prefer dogs as pets and then prefer cats as pets. dogs - 45% 12.5% 2) Find the joint relative frequency of students surveyed who are boys and prefer cats as pets. 20% cats - 30% Preferred PetDogCatOtherTotal Boys25%12.5%22.5%60% Girls20%17.5%2.5%40% Totals45%30%25%100% Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables

8. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Calculating a Conditional Relative Frequency: 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% Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables Preferred PetDogCatOtherTotal Boys105924 Girls87116 Totals 18 12 10 40

9. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Calculating a Conditional Relative Frequency: Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables Preferred PetDogCatOtherTotal Boys105924 Girls87116 Totals 18 12 10 40 Find the conditional relative frequency that a student surveyed is a girl, given that the student prefers cats as pets. Number of students who prefer cats: Number of girls who prefer cats: 7 12 =.583 = 58.3%

10. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Calculating a Conditional Relative Frequency: 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% Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables Preferred PetDogCatOtherTotal Boys105924 Girls87116 Totals 18 12 10 40

11. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Calculating a Conditional Relative Frequency: Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables Preferred PetDogCatOtherTotal Boys105924 Girls87116 Totals 18 12 10 40 Find the conditional relative frequency that a student surveyed is a boy, given that the student prefers dogs as pets. Number of students who prefer dogs: Number of boys who prefer dogs: 10 18 =.556 = 55.6%

12. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Graph the Two-Way Relative Frequency Table: Preferred PetDogCatOtherTotal Boys25%12.5%22.5%60% Girls20%17.5%2.5%40% Totals45%30%25%100% What benefit can these graphs provide in analyzing the data? Visual analysis; quicker/faster comparison of the data; scales; colors Boys Girls Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables

13. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Graph the Two-Way Relative Frequency Table: Preferred PetDogCatOtherTotal Boys25%12.5%22.5%60% Girls20%17.5%2.5%40% Totals45%30%25%100% What benefit can these graphs provide in analyzing the data? Visual analysis, quicker/faster comparison of the data, scales, colors Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables

14. Copyright © by Holt, Rinehart and Winston (2004); Holt McDougal (2012); On-Core Mathematics by HMH (2012) All Rights Reserved. (Alg 1 Power Point Slides edited by Mr. G. Weidinger, EWHS Goldsboro, NC) Finding Possible Associations and Trends Jenna survey results (numbers vs percents). DogCatOtherTotal Boys10/25%5/12.5%9/22.5%24/60% Girls8/20%7/17.5%1/2.5%16/40% Totals18/45%12/30%10/25%40/100% 1) Does the table reflect gender bias towards pets? 2) If so, which gender, likes which pets the best? 3) What are some examples of “other” pets? NO N/A Hamsters, gerbils, mice, rats, snakes, rabbits, pigs, etc., 4) Girls tend not to like which types of pets? “other” types But, it does imply, boys like “other” pets more than girls: 22.5% to 2.5%, Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables