Two-Way Tables

Two Way FRequency Tables

We can represent categorical and quantitative data in different way.

In the image, you can see the difference between the two types of data.

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Categorical vs. Quantitative Data

Multiple Select

Select the two answers below that represent categorial data:

• Weight

• Favorite Pizza Type

• Class Size

• Breed of Dog

• Shoe Size

Multiple Choice

How many more people prefer to visit Louisiana or New Mexico than Arkansas or Oklahoma?

• 39

• 145

• 167

• 184

Multiple Choice

If 100 students were surveyed, which of the following survey questions would produce categorical data?

• What is your favorite sports team?

• How many hours did you sleep last night?

• How much money do you spend in a week?

Two-way tables are a concise way of representing categorial data and they are generally used to show survey results.

• This table shows the results of a survey conducted of students on what type of animal they prefer.

Two-Way Frequency Tables

Two-way tables get their name from the fact that they can be read in TWO DIRECTIONS, ROWS AND COLUMNS:

1. The ROWS of the table go left and right (boys/girls).

2. The COLUMNS of the table go up and down (dog/cat/other).

Two-Way Frequency Tables

​Watch if you need a recap

Multiple Choice

Which age group liked Action movies the least?

• 18-25

• 25-49

• 50+

• 238

Multiple Choice

How many females were surveyed?

• 10

• 16

• 26

• 14

Multiple Choice

What was the most popular party type?

• Bowling

• Skating

• Dancing

• Total

Multiple Choice

How many males were surveyed?

• 10

• 16

• 26

• 14

Multiple Choice

A survey was given to decide what sport males & females prefer to watch on TV. What is the GRAND TOTAL of people that were surveyed?

• 48

• 52

• 100

• 36

Multiple Choice

How many males prefer basketball?

• 13

• 15

• 20

• 48

Multiple Choice

How many chemical engineers chose Science as their favorite subject?

• 80

• 91

• 171

• 262

Multiple Choice

How many students in the 8th grade were surveyed?

• 182

• 116

• 81

• 298

In order to find missing values in a two-way table, we must utilize the row and column totals.

• Notice the table in the picture is missing several values. We must use the totals to find those missing values.

​

Using the totals to find missing values

​For example:

If we wanted to find the number of students that have chores but no curfew, we would subtract 20 and 16, which would give us 4.

We could continue filling in pieces until the table is complete.

Multiple Choice

What number should go in the blue box?

• 21

• 135

• 19

• 22

Multiple Choice

How many students were in the survey all together?

• 30

• 42

• 62

• 72

Multiple Choice

How many adults took this survey?

• 52

• 41

• 93

• 131

Multiple Choice

How many total small sized items were ordered?

• 2

• 200

• 76

• 66

Multiple Choice

How many large coats were ordered?

• 51

• 73

• 44

• 15

Joint Frequencies:

• The values in the table that represent the overlap of two different categories.

Joint and Marginal Frequencies

Marginal Frequencies:

• The values in the table that represent the row or column totals.

Multiple Select

Using the table in the picture, identify the values below the represent joint frequencies:

• 50

• 9

• 25

• 12

• 16

Multiple Select

Using the table in the picture, identify the values below the represent marginal frequencies:

• 50

• 22

• 25

• 12

• 13

Multiple Choice

Two Way table shows the results of a survey where high school students were asked if they have a curfew. Use the table to answer the following questions

How many more freshmen students have a curfew than senior students?

• 39

• 25

• 60

• 53

Multiple Choice

Two Way table shows the results of a survey where high school students were asked if they have a curfew. Use the table to answer the following questions

How many more junior students were surveyed than sophomore students?

• 36

• 25

• 45

• 67

Multiple Choice

Participants were asked about their gender and their favorite season.

How many people like spring?

• 201

• 281

• 91

• 251

Multiple Choice

Participants were asked about their gender and their favorite season.

True or False:

The most popular season among the males surveyed was summer.

• True

• False

Dropdown

A two-way table is used to display and observe relationships between two sets of ​

Select answer

data.

Dropdown

Two Way tables show us ​

Select answer

, or number of times, that something occurs.

Math Response

How many people attended the basketball game but did not attend the school play?

Type answer here

Correct Answer: 63

Deg^°

Rad

Multiple Choice

What color car is the least popular at this car dealership?

• Red

• White

• Blue

• Green

Multiple Choice

How many females studied Spanish?

• 13

• 30

• 24

• 17

Multiple Choice

How many students were in the survey all together?

• 30

• 42

• 62

• 72