Stand Quietly

Lesson 9.3_Two-Way Tables

Standards: Common Core State Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Attend to precision.   MCC9-12.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.

Homework 5/24/17 Worksheet: Scatter plot, Correlation, and Line of Best Fit Worksheet: Lesson 9.3 A Notes_Two- Way Table

YOU HAVE A QUIZ TOMORROW! * Study line of best fit, lesson 9.2 worksheet

Two-Way Frequency Table Watch this: http://www.youtube.com/watch?v=aUwpxoaCV-w

Two-way table: categorical data organized in 2 dimensions 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.

Creating a Relative Frequency Table: Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables 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 Dog Cat Other Total Frequency 18 12 10 40 Relative Frequency Decimals Relative Frequency Percents 18 40 12 40 10 40 40 40 = .45 = .30 = .25 = 1.00 45% 30% 25% 100%

Creating a Two-Way Frequency Table: Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables 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 Totals 18 12 10 40 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

Creating a Two-Way Relative Frequency Table: Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables 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 40 Preferred Pet Dog Cat Other Total Boys Girls Totals 10 40 5 40 9 40 24 40 = .25 = .125 = .225 = .60 8 40 7 40 1 40 16 40 = .20 = .175 = .025 = .40 18 40 12 40 10 40 40 40 = .45 = .30 = .25 = 1.00

Creating a Two-Way Relative Frequency Table: Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables Creating a Two-Way Relative Frequency Table: Preferred Pet Dog Cat Other Total Boys Girls Totals 10 40 5 40 9 40 24 40 = .25 = .125 = .225 = .60 8 40 7 40 1 40 16 40 = .20 = .175 = .025 = .40 18 40 12 40 10 40 40 40 = .45 = .30 = .25 = 1.00 State the percents for the table above. Preferred Pet Dog Cat Other Total Boys Girls Totals 25% 12.5% 22.5% 60% 20% 17.5% 2.5% 40% 45% 30% 25% 100%

Creating a Two-Way Relative Frequency Table: Old Holt 4-5/4-6; New Holt 10-1/10-2/10-3 On-Core: 9-5 Two Way Frequency Tables Creating a Two-Way Relative Frequency Table: Preferred Pet Dog Cat Other Total Boys 25% 12.5% 22.5% 60% Girls 20% 17.5% 2.5% 40% Totals 45% 30% 100% 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%

Make sure you try the 10 practice problems. Relative Frequency Go here: http://www.mathsisfun.com/data/relative- frequency.html Make sure you try the 10 practice problems.

Android vs. iPhone -On ONE post-it, please write your name (first and last). -Stick it to the appropriate quadrant on the whiteboard. Discuss graphical representations. Histogram? No (this is categorical data only) Box plot? (no, we need 2x2 format)

Android vs. iPhone Android iPhone Total Female Male On the board: Post-it with: Male/Female, Date/No Date

Do you see any trends (patterns in the data)? Discuss with your partner. Any patterns in the data? Can you find certain statistics, such as the mean? Re-iterate that this is categorical data, so you cannot find statistics such as the mean or median.

Remember: We summarize categorical data for two categories in a two-way frequency table In our data, we might say there appears to be an association (a relationship between two measured quantities). Answer the following questions with your partner. Be prepared to share with the class.

Using the class data, answer & discuss: How many students total from this class prefer the Android? How many students prefer the iPhone? How many students are females? How many students are males? How many students are females AND prefer the Android? How many students are males AND prefer the iPhone? What ratio (think fraction) are males AND prefer iPhones? What ratio of students are males AND prefer Androids? What ratio of students prefer the iPhone? What percent is this? If we only look at the female students, what ratio prefers the iPhone? 11. If we only look at students who prefer Android, what proportion are male? These are frequency questions. Questions #1-6 are frequency questions about data.

Questions #7-8 These questions are questions of joint relative frequency (the ratio of the value in the body of the table, to the total).

Question #9 This question is a question of marginal relative frequency (the ratio of the value of a subtotal, to the total)

Questions #10-11 These questions are questions of conditional relative frequency (the ratio of the value in the body of a table, to a subtotal)

Create a two-way table to display the data, and answer the following question(s). Example 2. It was found that 70 students own headphones and 22 students own LED TVs. There were 63 students that do not own LED TVs. 11 students own both. 1. Of the students who own headphones, what is the ratio of those who own LED TVs?

As a class, we will… 1. Select a topic to create a two-way table. Complete the two-way table. Come up with 3 questions on the given two-way table. Answer the questions.

Class Data