## Two Way Tables

#### Aligned To Common Core Standard:

**High School Statistics** - HSS-ID.B.5

What are Two Way Data Tables? You must know how to pick data from the graph and place it in the table form. Generally, we do this with only one categorical variable.
In the two way data table, as the name implies, we are working with two categorical variables. The data provided for the two way table is referred to as bivariate data. Two way tables are employed to establish the relationship between the two categorical variables. These tables are specifically important for analyzing surveys ad reports, where two variables are examined.
**BASICS OF A TWO WAY DATA TABLE** - Two way data tables visually represent the relationship between the two variables. The categorical variables are labeled at the top while their counts are written within the tables. The total of each categorical variable is given at the bottom of each column, and the total of each row is written at the right. It is crucial to note that in two way data tables, the row totals are equal to the column totals.
Let us consider an example of a two way data table, a survey of college students asking about their pet preferences is represented in the two way data table as follows:

**Preference Male Female**

Prefer dogs 45 20

Prefer cats 9 32

No preference 12 10

The columns tell us whether the student is a male or a female. The rows represent whether the student prefers a cat or dog as a pet or has no pet preference
The cells of the table show the number of students with their preference. For example, 45 male students like dogs as their pets.
This selection of worksheets and lessons help students learn how to read and use two way table (contingency tables) to examine relationships that exist between mixed variables.

### Printable Worksheets And Lessons

- Car Accidents and Age Step-by-step Lesson- Use the data to find a solution to the problem.
- Guided Lesson - Boys and girls are taking summer cooking, dancing, or painting classes.
- Guided Lesson Explanation - Navigate the table to answer the questions. You will need to do a few computations.
- Practice Worksheet - Drinking water or soda and a look at sports matches.
- Matching Worksheet - Swimming, Racing, and Cycling participation is tracked in this one.

#### Homework Sheets

We try to pull statistics into the children's every day world.

- Homework 1 - A car company selected drivers in a particular city to find a relationship between the age of the driver and the number of car accidents.
- Homework 2 - What percentage of the group are boys that are painting?
- Homework 3 - In the 40 to 80 age group, what is the percentage of people who like Pepsi?

#### Practice Worksheets

We start to use our data observation skills to help us along with these.

- Practice 1 - What percentage of the girls voted for Germany?
- Practice 2 - People that were leaving the zoo were surveyed and asked if which of the following animals were their favorite: tiger, bear, wolf, or lion.
- Practice 3 - What is the percentage of the girls are in the 6-10 age group?

#### Math Skill Quizzes

Some interesting uses of data can be found here.

### What Are the Common Uses of Two Way Tables?

You can learn a great deal from the way in which you look at data. The charting tool we have discussed here is very similar to the popular tool the standard Venn diagram. They both display statistics that are separated into two categories, but they also display the overlap of that same figures. The Venn diagram does not have a technique for displaying any outlier values that may not pertain to either of the categories, but that is where the two way table chart shines. It allows you to display this inconsistent information as well. When that data is important to communicate, we would encourage you to stay away from using Venn diagrams. Both of these organizing structures are used heavily when displaying and analyzing the results from opinionated or preference surveys. This allows you to instantly spot trends in differing opinions, based on your figures. In addition to displaying outliers, if you need to understand the frequency of your inputs, we would also tell you to stick to using tables such as these.