Warm Up Write down objective and homework in agenda Lay out homework (Exponents review) Homework (Two way table wkst)

Warm Up Benchmark

Warm-Up Using the Venn Diagram you have been given, place each statement in the appropriate place. Average blood pressure Who received high school diplomas Right-handed or left-handed Favorite TV show Hours spent outdoors each day Time of day you go to bed Age group Whether or not people smoke Favorite food Common majors in college Average calories consumed in a day Gender Population Number of brothers and sisters Height Shoe size Hours spent doing HW each night Miles from home to school

Average blood pressure Favorite TV Show Categorical Quantitative Average blood pressure Favorite TV Show Age group Population Shoe size Common majors in college Hours spent outdoors each day Average calories consumed in a day Who received high school diplomas Number of brothers and sisters Whether or not people smoke Hours spent doing HW each night Right-handed or left-handed Time of day you go to bed Favorite food Gender Height Miles from home to school

Two Way Table Notes

Investigation: Two-Way Tables The data from a survey of 50 students is shown in the Venn diagram below. The students were asked whether or not they were taking a foreign language and whether or not they played a sport.

Two Way tables 1. How many students are taking a foreign language? 37 2. How many students play a sport? 24 3. How many students do both? 14 4. How many students do not play a sport and do not take a foreign language? 3 5. How many students play a sport but do not take a foreign language? 10

Two Way Tables A two-way table is similar to a Venn diagram. A two-way table shows data that pertain to two different categories, which requires us to only use categorical variables. The data from one sample group is shown as it relates to two different categories. One variable is represented by rows, and the other is represented by columns.

Two Way Tables Felipe surveyed students at his school. He found that 78 students own a cell phone and 57 of those students own an MP3 player. There are 13 students that do not own a cell phone, but own an MP3 player. Nine students do not own either device.

Analyzing Two way Tables Marginal distributions are the totals of each individual category. These are located in the margins of the table. Use your table above to fill in the following: Marginal distribution = 1 event happened total Marginal frequency = percent of marginal distribution What are the marginal distributions for the previous table?

Analyzing Two Way Tables Joint distributions are the values that “join” the two variables together. Use your table to fill in the following: Joint distribution = 2 events happened total Joint frequency = percent of joint distribution What are the joint distributions for the previous table?

Two Way Tables The tables you have created so far use frequencies. Some people better understand data if displayed as a percent. We can do this by creating a two-way relative frequency table. Remember from Unit 1 that relative frequency is found by dividing the frequency and the overall total. Because we are working with percents, what should your overall total be? Why?

Two Way Table Use the table to answer the following:  What percent of students have a cell phone, but not an MP3 player? What percent of students have neither a cell phone nor an MP3 player? What percent of students have an MP3 player, but not cell phone? What percent of students have a cell phone and an MP3 player? By converting the table to percents, we have also given ourselves probabilities! Another way to state your answer to the first is “The probability a person will have a cell phone and not have an MP3 player is…..”

Conditional Probability How likely is one event to happen, given that another event has happened? percentages/probability based on the row or column total of the given event Conditional Probability = one event total of occurred event joint frequency divided by marginal frequency of the “given”. List and describe a few conditional probabilities of the previous table

Categorical Data: Two Way Tables People leaving a soccer match were asked if they supported Manchester United or Newcastle United. They were also asked if they were happy. The table below gives the results.   Manchester United Newcastle United Happy 40 8 Not Happy 2 20 vs.

Categorical Data: Two-Way Tables Marginal Distribution How many Manchester fans were surveyed? What is the probability that a randomly selected person is a fan of Newcastle? What is the probability that a randomly selected person left the game happy? Manchester United Newcastle United Total Happy 40 8 48 Not Happy 2 20 22 42 28 70

Categorical Data: Two Way Tables Joint Probability How many of those surveyed are happy Manchester United fans? What percentage of those surveyed are Newcastle fans and not happy? How likely is a person to be a Newcastle fan or Not Happy? usually one cell based on the table total - Ex. Probability (Newcastle and Happy) = ? Manchester United Newcastle United Total Happy 40 8 48 Not Happy 2 20 22 42 28 70

Categorical Data: Two Way Tables Conditional Probability How likely is a person to be happy, given that they were a Newcastle fan? If a person left the game happy, how likely is it that he/she is a Manchester fan? usually one cell based on the table total - Ex. Probability (Newcastle and Happy) = ? Manchester United Newcastle United Total Happy 40 8 48 Not Happy 2 20 22 42 28 70

Extra Resources http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i1/bk7_1i2.htm http://www.glencoe.com/sites/pdfs/impact_math/ls3_c3_two_way_tables.pdf http://stattrek.com/statistics/two-way-table.aspx http://learni.st/users/S33572/boards/1638-creating-and-interpreting-two-way-tables-common-core-standard-8-sp-4#/users/S33572/boards/1638-creating-and-interpreting-two-way-tables-common-core-standard-8-sp-4 http://learnzillion.com/lessonsets/295 http://www.stat.ufl.edu/~ssaha/3024/CHAPTER9.pdf