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### Course: 8th grade (Eureka Math/EngageNY) > Unit 6

Lesson 4: Topic D: Bivariate categorical data- Two-way frequency tables and Venn diagrams
- Two-way frequency tables
- Read two-way frequency tables
- Create two-way frequency tables
- Two-way relative frequency tables
- Create two-way relative frequency tables
- Analyze two-way frequency tables
- Interpreting two-way tables
- Interpret two-way tables

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# Two-way frequency tables

Learn how to read and use two-way frequency tables.

Let's jump right in and look at a two-way frequency table that came from asking $100$ students whether they prefer cats or dogs.

Preference | Male | Female |
---|---|---|

Prefers dogs | ||

Prefers cats | ||

No preference |

The columns of the table tell us whether the student is a male or a female. The rows of the table tell us whether the student prefers dogs, cats, or doesn't have a preference.

Notice that there are

**two variables**-- gender and preference-- this is where the**two**in**two**-way frequency table comes from.The cells tell us the number (or frequency) of students. For example, the $36$ is in the $36$ male students who prefer dogs.

**male column**and the**prefers dogs row.**This tells us that there are## Row and column totals

To find the number of students that prefer cats, we just add up the number of students in the

**prefers cats row**:Preference | Male | Female |
---|---|---|

Prefers dogs | ||

Prefers cats | ||

No preference |

## Let's practice!

### Problem 1

### Problem 2

### Problem 3

## Challenge problem

## Want to join the conversation?

- the question about help Elena organized in the following two way frequency table? How can you resolve it?(20 votes)
- First, the question tells us that Lena has 10 candies that have caramel AND chocolate so thus the first column and first row's value would be 10. Then we are told that there are 3 candies that do NOT contain chocolate OR caramel. This means that the value at column 2, row 2 would be 3. Then we are told that there are 12 candies that contain chocolate. So adding up both values in row 1 should be equal to 12 (10+X=12) which would give us 2 for Column 2, Row 1. We are also told that she has a total of 18 candies so adding up all values should give us 18 (10+2+3+X=18). Thus the value for Column 1, Row 2 would be 3. The complete answer would be:

C D

C 10 2

D 3 3(36 votes)

- How did Lena get 3 candies under the label of do not contain chocolate and also contains caramel? Please help me, I am having trouble understanding.(9 votes)
- We know that there are 18 candies in total, and 12 of them contain chocolate.

This means that 18 − 12 = 6 candies do*not*contain chocolate.

We also know that 3 candies contain neither chocolate nor caramel, and thereby there are 6 − 3 = 3 candies that don't contain chocolate but do contain caramel.(26 votes)

- I can do the ones with the numbers in the box but when the question doesn't have a box in it then I struggle with the question, how do you do the last question?(9 votes)
- First this is actually a analytic problem. You need to see the items,then to find the boxes that have the same information,and copy the number down.Sometimes it is hard to distinguish the information,you need to compare the items and the information in the boxes.(25 votes)

- whats the point of this bro(16 votes)
- Everything in learning has a purpose but not all of them are used for regular everyday tasks. This type of math is specifically used for people who need a different perspective of data in a table.(1 vote)

- Ya, The last one is confusing can someone help please?(9 votes)
- The first helpful clue is the second statement: 10 candies contain both chocolate and caramel. Because it contains both flavors, it should be placed between the 'contain chocolate' row and the 'contain caramel' column.

The next clue: 3 candies contain neither chocolate nor caramel, has the same pattern. It should go in the 'do not contain caramel' column, and the 'do not contain chocolate' row. The fourth statement states that there are 12 candies in total that contain chocolate, meaning that the sum of the'contain chocolate' row should equal 12. 12-10 = 2, so there must be 2 chocolate candies that don't have caramel.

Finally, we know that there are a total of 18 candies. 18-(10+2+3) = 3. So, there are 3 candies that contain caramel but do not contain chocolate.

Hope this helps! :)(13 votes)

- waffles are the answer to all of life's problems(12 votes)
- Bro, I want waffles now and am still in the third hour.(2 votes)

- Is relative frequency supposed to be written as a decimal or fraction?(4 votes)
- Relative frequency can be either a fraction or a decimal.

Have a blessed, wonderful day!(10 votes)

- how did u get two for containing no chocolate nor caramel(4 votes)
- It says 3 contain neither

Since 12 contain chocolate and 10 contain both, that means the remaining 2 ONLY contains chocolate. Since there are 12 total and 10 contain both.

Thensince there are 18 total and 10 contain both that leaves 8, 2 only contain chocolate which leaves 6 and 3 contain neither that leaves 4 that only contain caramel.

I hope that makes sense.(10 votes)

- how do I know that the 12 candies that contain chocolate don't contain caramel(7 votes)
- you don´t, it says 10 both though so now you know(2 votes)

- How did you find out there were 10 people that like chocolate but hates caramel(6 votes)