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Are you a. CrimiNole. OR. Gatorbait. ?. Two rivalries in one table! !. Garnet and Gold or Orange and Blue ? You decide!. A survey was conducted and the results are shown in the table below. Try to answer the following questions. How many males like orange and blue?

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Are you a

CrimiNole

OR

Gatorbait

?

Two rivalries in one table!!


Garnet and gold or orange and blue you decide
Garnet and Gold or Orange and Blue? You decide!

A survey was conducted and the results are shown in the table below. Try to answer the following questions.

  • How many males like orange and blue?

  • What does the number 16 represent?

  • How many people were surveyed?

  • How would you determine if there was a possible association between favorite team colors and gender?



Florida standard
Florida Standard

MAFS.912.S-ID.2.5 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 data.


Objectives
Objectives

  • Create and interpret a two-way frequency table from two categorical variables.

  • Read and interpret data displayed in a two-way table and calculate the relative frequencies.

  • Describe patterns and trends observed in the data.


What is a two-way frequency table?

Two-Way Table

LOOKS LIKE

CATEGORY A

A table used to study the relationship between two categorical variables.

CATEGORY B


Joint and Marginal Frequency

Joint Frequency

Marginal Frequency

CATEGORY A

The values that make up the BODY of the table.

The ROW and COLUMNtotals for each category.

8

13

21

CATEGORY B

11

21

32

34

53

19


Ex. 1 Construct a Two-Way Table

25 seniors were surveyed and asked which college football team they liked best. Out of the 17 that liked Florida State, 6 were females. There was a total of 13 females surveyed. Summarize the data in a two-way table.

TIPS FOR COMPLETING THE TABLE

  • Fill in the values you already know.

  • Determine if each value represents a JOINT or MARGINAL frequency.

  • Recall that JOINT frequency goes in the body (yellow area) of the table, and MARGINAL frequency goes in the row and column total (green area) of the table.

  • Use reasoning to find the remaining values.


Guided Practice

Construct a Two-Way Table

There were 45 students in gym class that were asked if they like football or basketball and if they liked Nike or Adidas. Out of the 19 students that liked basketball, 7 liked Adidas. There were 23 students that liked Adidas. Use reasoning to find the missing values.


Calculate Row Relative Frequencies

  • Relative frequency is the ratio of the subtotal to the total

For each row, find the ratio of each joint frequency to the marginal frequency for that row.

The relative frequencies in the body of the table are called conditional relative frequencies.


Calculate Column Relative Frequencies

  • Relative frequency is the ratio of the subtotal to the total

For each column, find the ratio of each joint frequency to the marginal frequency for that column.


Guided Practice

Calculate Relative Frequencies

Round to the nearest hundredth. Show all work.

Calculate the missing row relative frequencies for the table.

Calculate the missing column relative frequencies for the table.


Association between two categorical variables occur when the conditional relative frequencies for the rows or columns differ significantly.

There is little to no association between two categorical variables when the conditional relative frequencies for the rows or columns are equal or evenly distributed.


Read, Interpret, and Draw Conclusions conditional relative frequencies for the rows or columns differ significantly.

Use the tables to answer the following questions.

Which table can we use to determine the percentage of males that like Florida? What is the percentage?

Based on the row conditional frequencies, is there evidence of an association between gender and favorite college football team?

Which table can we use to determine the percentage of females that took the survey? What is the percentage?

What do the numbers 7, 11, and 12 represent? Are they JOINT or MARGINAL frequencies?


Guided Practice conditional relative frequencies for the rows or columns differ significantly.

Read, Interpret, and Draw Conclusions

Refer back to the tables in problem 1 & 2 to answer the following questions.

5. Is there evidence of an association between the sport a student likes and the brand of sneakers they like? Explain.

1. What is the joint frequency of students who like Nike?

2. What is the marginal frequency of students who like basketball?

3. Of the students who like Nike, what percentage like football as well?

4. What percentage of the students like basketball and Adidas?


What have you learned? conditional relative frequencies for the rows or columns differ significantly.

Refer back to the opening problem. Answer the questions again. How do your “post lesson” answers compare to your “pre-lesson” answers? Are they the same or different?

A survey was conducted and the results are shown in the table below. Answer the following questions.

  • How many males like orange and blue?

  • What does the number 16 represent?

  • How many people were surveyed?

  • How would you determine if there was a possible association between favorite team colors and gender?


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