# Common Core Algebra 1: Everything You Need to Know About Two Way Frequency Tables

## Two Way Frequency Tables Common Core Algebra 1 Homework

If you are studying common core algebra 1, you may encounter a type of data analysis called two way frequency tables. In this article, we will explain what two way frequency tables are, how to create them from categorical data, how to calculate relative frequencies, and how to interpret and analyze them. By the end of this article, you will be able to answer your homework questions on two way frequency tables with confidence.

## Two Way Frequency Tables Common Core Algebra 1 Homework

## What are two way frequency tables?

Two way frequency tables are a way of organizing and displaying categorical data in a table. Categorical data are data that can be grouped into categories, such as gender, eye color, favorite sport, etc. Two way frequency tables show the frequencies (counts) of data for two categories at the same time.

### Definition and examples of two way frequency tables

A two way frequency table has rows and columns that represent the categories of each variable. The cells of the table show the frequencies of each combination of categories. For example, suppose we have data on the gender and eye color of 50 students in a class. We can create a two way frequency table as follows:

Gender

Blue

Brown

Green

Total

Male

8

12

5

25

Female

7

10

8

25

Total

15

22

13

50

This table shows that there are 8 males with blue eyes, 12 males with brown eyes, 5 males with green eyes, and so on. The totals in the last row and column show the frequencies of each category for one variable. For example, there are 15 students with blue eyes, 25 males, etc.

### How to create two way frequency tables from categorical data

To create a two way frequency table from categorical data, we need to follow these steps:

Identify the two variables (categories) that we want to analyze.

Create a table with rows and columns that correspond to the categories of each variable.

Count the number of data points that fall into each combination of categories and fill in the cells of the table.

Add up the frequencies in each row and column and write them in the last row and column.

Add up all the frequencies and write it in the bottom right corner of the table.

For example, suppose we have data on the favorite sport and grade level of 100 students in a school. We can create a two way frequency table as follows:

Sport

9th Grade

10th Grade

11th Grade

12th Grade

Total

Basketball

12

8

10

5

35

Soccer

6

9

7

4

26

Tennis

4

6

5

8

23

Volleyball

3

4

6

3

16

Total

25

27

28

20

100

This table shows that there are 12 9th graders who like basketball, 9 10th graders who like soccer, 8 12th graders who like tennis, and so on. The totals in the last row and column show the frequencies of each category for one variable. For example, there are 35 students who like basketball, 27 10th graders, etc.

## What are relative frequencies and how to calculate them?

Relative frequencies are the ratios or percentages of frequencies to the total number of data points. Relative frequencies show how often a category or a combination of categories occurs relative to the whole data set. Relative frequencies can help us compare and analyze data more easily.

### Definition and examples of relative frequencies

A relative frequency is calculated by dividing a frequency by the total number of data points. For example, if we have 50 students in a class and 15 of them have blue eyes, the relative frequency of blue eyes is 15/50 = 0.3 or 30%. This means that 30% of the students in the class have blue eyes.

We can also calculate relative frequencies for two way frequency tables. There are three types of relative frequencies that we can calculate: joint, marginal and conditional.

A joint relative frequency is the ratio or percentage of a frequency in a cell to the total number of data points. For example, in the table above, the joint relative frequency of males with blue eyes is 8/50 = 0.16 or 16%. This means that 16% of the students in the class are males with blue eyes.

A marginal relative frequency is the ratio or percentage of a frequency in the last row or column to the total number of data points. For example, in the table above, the marginal relative frequency of blue eyes is 15/50 = 0.3 or 30%. This means that 30% of the students in the class have blue eyes.

A conditional relative frequency is the ratio or percentage of a frequency in a cell to the total frequency in its row or column. For example, in the table above, the conditional relative frequency of males with blue eyes is 8/25 = 0.32 or 32%. This means that 32% of the males in the class have blue eyes.

### How to calculate joint, marginal and conditional relative frequencies?

To calculate joint, marginal and conditional relative frequencies for a two way frequency table, we need to follow these steps:

Create a new table with the same rows and columns as the original table.

To calculate joint relative frequencies, divide each frequency in a cell by the total number of data points and write it in the corresponding cell of the new table.

To calculate marginal relative frequencies, divide each frequency in the last row or column by the total number of data points and write it in the corresponding cell of the new table.

To calculate conditional relative frequencies, divide each frequency in a cell by the total frequency in its row or column and write it in the corresponding cell of the new table.

If needed, convert fractions to decimals or percentages.

If needed, round decimals to a certain number of decimal places.

If needed, add labels to indicate what type of relative frequencies are shown in each row or column.

For example, suppose we want to calculate joint, marginal and conditional relative frequencies for the table below:

Sport

9th Grade

10th Grade

Total (Marginal)

Conditional)

Basketball

12

8

20

0.2

Soccer

6

9

15

0.15

Tennis

4

6

10

0.1

Total (Marginal)

22

23

45

0.45

Total (Joint)

0.22

0.23

0.45

Total (Conditional)

0.49

0.51

This table shows the joint, marginal and conditional relative frequencies for the data on sport and grade level. For example, the joint relative frequency of 9th graders who like basketball is 12/45 = 0.27 or 27%. This means that 27% of the students who participated in the survey are 9th graders who like basketball. The marginal relative frequency of 9th grade is 22/45 = 0.49 or 49%. This means that 49% of the students who participated in the survey are 9th graders. The conditional relative frequency of basketball given 9th grade is 12/22 = 0.55 or 55%. This means that 55% of the 9th graders who participated in the survey like basketball.

## How to interpret and analyze two way frequency tables?

Two way frequency tables can help us understand and compare data more easily. We can use relative frequencies to answer questions about the data, such as:

What is the most or least common category or combination of categories?

How do the categories or combinations of categories vary across rows or columns?

Is there an association or a trend between the two variables?

If there is an association or a trend, how strong or weak is it?

If there is an association or a trend, what are some possible explanations or implications for it?

### How to read and compare values in two way frequency tables?

To read and compare values in two way frequency tables, we need to pay attention to the type of relative frequency that we are using and the context of the data. For example:

To compare the frequencies of different categories for one variable, we can use marginal relative frequencies. For example, in the table above, we can see that basketball is the most common sport among the students who participated in the survey, with a marginal relative frequency of 0.2 or 20%. We can also see that tennis is the least common sport, with a marginal relative frequency of 0.1 or 10%.

To compare the frequencies of different combinations of categories for two variables, we can use joint relative frequencies. For example, in the table above, we can see that soccer is more popular among 10th graders than among 9th graders, with a joint relative frequency of 0.23 or 23% for soccer and 10th grade, compared to a joint relative frequency of 0.22 or 22% for soccer and 9th grade.

To compare the frequencies of one category for one variable given another category for another variable, we can use conditional relative frequencies. For example, in the table above, we can see that tennis is more popular among 12th graders than among other grade levels, with a conditional relative frequency of 0.4 or 40% for tennis given 12th grade, compared to a conditional relative frequency of 0.18 or 18% for tennis given any other grade level.

### How to recognize possible associations and trends in the data?

An association between two variables means that there is some relationship between them, such that knowing the value of one variable gives us some information about the value of another variable. A trend between two variables means that there is some pattern or direction in the data, such that the values of one variable change in a consistent way with the values of another variable.

To recognize possible associations and trends in the data, we can look for differences or similarities in the conditional relative frequencies across rows or columns. For example:

If the conditional relative frequencies are different across rows or columns, it means that there is an association between the two variables. For example, in the table above, we can see that there is an association between sport and grade level, because the conditional relative frequencies of each sport vary across different grade levels. For instance, basketball is more popular among 9th graders than among other grade levels, while tennis is more popular among 12th graders than among other grade levels.

If the conditional relative frequencies are similar across rows or columns, it means that there is no association between the two variables. For example, suppose we have a table that shows the favorite color and gender of 100 students in a school. If the conditional relative frequencies of each color are similar across different genders, it means that there is no association between color and gender, because knowing the gender of a student does not give us any information about their favorite color.

If the conditional relative frequencies show a pattern or direction across rows or columns, it means that there is a trend between the two variables. For example, suppose we have a table that shows the number of hours spent studying and the test score of 50 students in a class. If the conditional relative frequencies of each test score increase as the number of hours spent studying increase, it means that there is a positive trend between studying and test score, because the more hours a student spends studying, the higher their test score tends to be.

## Conclusion

In this article, we have learned what two way frequency tables are, how to create them from categorical data, how to calculate relative frequencies, and how to interpret and analyze them. We have seen that two way frequency tables can help us organize and display data in a clear and concise way, and that relative frequencies can help us compare and understand data more easily. We have also learned how to recognize possible associations and trends in the data using conditional relative frequencies.

Two way frequency tables are a useful tool for data analysis in common core algebra 1. They can help us answer questions about the data, such as what is the most or least common category or combination of categories, how do the categories or combinations of categories vary across rows or columns, is there an association or a trend between the two variables, and if so, how strong or weak is it and what are some possible explanations or implications for it.

By mastering two way frequency tables, we can improve our skills in statistics and data science. We hope this article has helped you with your homework on two way frequency tables common core algebra 1.

## FAQs

### What is the difference between a frequency table and a two way frequency table?

A frequency table is a table that shows the frequencies (counts) of data for one category at a time. A two way frequency table is a table that shows the frequencies (counts) of data for two categories at the same time.

### What is the difference between a frequency and a relative frequency?

A frequency is the number of times a category or a combination of categories occurs in a data set. A relative frequency is the ratio or percentage of a frequency to the total number of data points.

### What are some examples of categorical data?

Categorical data are data that can be grouped into categories, such as gender, eye color, favorite sport, etc. Some examples of categorical data are:

The names of different types of animals

The colors of different types of flowers

The genres of different types of books

The brands of different types of cars

The languages spoken by different people

### How do I know if there is an association or a trend between two variables?

You can use conditional relative frequencies to check if there is an association or a trend between two variables. If the conditional relative frequencies are different across rows or columns, it means that there is an association between the two variables. If the conditional relative frequencies show a pattern or direction across rows or columns, it means that there is a trend between the two variables.

### How do I create a two way frequency table in Excel?

You can create a two way frequency table in Excel by using the PivotTable feature. Here are the steps:

Enter your data in a worksheet with column labels for each variable.

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