1 4 2 1 Summarizing Data Using TwoWay

1 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables

Two-Way Frequency Tables Concept: Representing and Interpreting Data EQ: How do we represent and interpret data in two variables? (Standard S. ID. 5) Vocabulary: Two-Way Frequency Table, Bivariate, Joint Frequency, Marginal Frequency, Conditional Relative Frequency http: //www. youtube. com/watch? feature=player_embedded&v=Ss. Wr. Y 77 o 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables 2

Guided Practice - Example 1 Say you own your own nail salon and you are looking at some advertising options. You want to know which age group and which service is the most popular so you can target a particular audience. You look at your records from the last month and you find the following: 58 Adults – manicure 77 Adults – pedicure 31 Teenagers – manicure 27 Teenagers – pedicure How could you display this data? 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables 3

Introduction Information about people who are surveyed can be captured in two-way frequency tables. A two-way frequency table is a table of data that compares two variables (bivariate). It separates responses by a characteristic of the respondents. Nail Service Age Group Adults Teenagers Manicure 58 31 Pedicure 77 27 Total 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables Total 4

Vocabulary A joint frequency is the number of responses for a given characteristic. • The entries in the cells of a two-way frequency table are joint frequencies. • In our table, 58, 77, 31, and 27 are each joint frequencies. Nail Service Age Group Adults Teenagers Manicure 58 31 Pedicure 77 27 Total 5 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables

Vocabulary A joint frequency is the number of responses for a given characteristic. • The entries in the cells of a two-way frequency table are joint frequencies. • In our table, 58, 77, 31, and 27 are each joint frequencies. Nail Service Age Group Adults Teenagers Total Manicure 58 31 89 Pedicure 77 27 104 Total 135 58 193 6 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables

Vocabulary A marginal frequency is the total number of times a response was given, or the total number of respondents with a given characteristic. • This is the sum of either a row or a column in a twoway frequency table. • In our table, 89, 104, 135, and 58 are all marginal frequencies. Nail Service Age group Adults Teenagers Total Manicure 58 31 89 Pedicure 77 27 104 Total 135 58 193 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables 7

Nail Service Age Group Adults Teenagers Total Manicure 58 31 89 Pedicure 77 27 104 Total 135 58 193 • Looking at our table, who and what service would you target? • Your answer probably involved the highest total between the age groups and the highest total between the services, but is this really accurate? • The only way to know for sure is to calculate the conditional relative frequencies for each joint frequency. 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables 8

Vocabulary A conditional relative frequency expresses a number of responses as a percentage of the total number of responses. • It allows a comparison to be made for multiple responses in a single row, single column, or table. 9 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables

Vocabulary A conditional relative frequency They are found by dividing the number of responses by the total number of responses. • Three conditional relative frequencies can be found for each joint frequency (one for each characteristic and one for the total people surveyed). In our table, you can do it with respect to the age group, to the service, or to the total people surveyed. 10 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables

Conditional Relative Frequency Conditional relative frequency with respect to Age group. Conditional relative frequency with respect to nail service. Conditional relative frequency with respect to all people. Nail Service Age group Adults Teenagers Manicure Pedicure Nail Service Age Group Adults Teenagers Manicure Pedicure Nail Service Manicure Pedicure Age Group Adults Teenagers Would you change your mind about who and what service to target?

Mrs. Rojas class played a game of trashketball This is a survey of the results probability Trashketball Gender boys girls Totals Made 7 6 13 Missed 11 9 20 Totals 18 15 33 Trashketball Gender boys girls Totals Made . 21 . 18 . 39 Missed . 33 . 27 . 60 Totals . 54 . 45 100 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables 12

Mrs. Rojas class played a game of trashketball This is a survey of the results probability Trashketball Gender boys girls Totals Made . 21 . 18 . 39 Missed . 33 . 27 . 60 Totals . 54 . 45 100 Joint probability of boys who made a basket Joint probability 7/33 of boys who made the basket Probability is from 0 -1 Marginal is outside on the margins 13 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables

Conditional probability Trashketball Gender boys girls Totals Made 7 6 13 Missed 11 9 20 Totals 18 15 33 If you are given a girl she also missed a basket There are 15 girls total 9 girls missed 9/15 =. 53 is the probability 14 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables

Guided Practice - Example 2 Deshaun surveyed different age groups at a middle school and high school to find out who eats and doesn’t eat breakfast regularly. Their responses are in the table below. Breakfast habits Age 10 -13 Eats breakfast Gender Skips Breakfast 40 Age 14 -17 Totals 14 24 36 Totals 52 90 1) How many students ages 10 -13 “eat breakfast regularly”? _____ This is a ______ frequency 2) 52 is a _______ frequency. It represents _______________________. 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables 15

Guided Practice - Example 2 Deshaun surveyed different age groups at a middle school and high school to find out who eats and doesn’t eat breakfast regularly. Their responses are in the table below. Breakfast habits Eats breakfast Gender Skips Breakfast Totals Age 10 -13 40 14 54 Age 14 -17 12 24 36 Totals 52 90 38 1) How many students ages 10 -13 “eat breakfast regularly”? 40 This is a Joint frequency 2) 52 is a Marginal frequency. It represents _The total amount of people who eat breakfast_. 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables 16

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Your Turn YOU ARE AN ENTREPENUR AND YOU WOULD LIKE TO OPEN A NEW AMC MOVIE THEATHER. – 1. Survey 10 students in your class. On what movie genre they prefer – Fill out the frequency table within your groups on Poster paper – Answer the questions on the form – Present your data detail how this will help your business.

Closing – In your own words describe Marginal and relative frequency. – Why does probability (Conditional relative frequency) Important in describing data? – Describe a time when data was an important factor in your life. 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables

Guided Practice: Example 3, continued 5. Complete the marginal frequencies for each type of pet and for each grade level. Which one is the smallest? Grade Preferred pet Bird Cat Dog Fish 9 3 49 53 22 10 7 36 64 10 Total 6. How many students are represented in the survey? 7. What would the conditional relative frequency be for 9 th graders who preferred cats (with respect to 9 th graders)? 8. What would the conditional relative frequency be for fish 20 (with respect to everyone surveyed)? 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables

Guided Practice - Example 3 Abigail surveys students in different grades, and asks each student which pet they prefer. Their responses are in the table below. Grade Preferred pet Bird Cat Dog Fish 9 3 49 53 22 10 7 36 64 10 1. How many 9 th graders preferred fish? 2. What does the joint frequency 7 represent? 3. What is the joint frequency of 9 th graders who preferred cats? 4. Which pet was the most popular among all the students surveyed? 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables 21

1. Looking at just the marginal frequencies (row & column totals) what can we conclude about the 3 activities? A. Dance is way more interesting. B. They have roughly equal appeal. C. Sports is the least chosen activity. D. TV is the preferred activity. You Try!. 2. Looking at the joint frequencies we see that women show a strong preference for which activity? 3. What are the conditional relative frequencies (for both gender and hobby) for men who showed a preference for Sports? 4. 2. 1: Summarizing Data Using Two-Way Frequency Tables 22