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## Measurement & Data - Statistics & Probability 229+

### Unit 3: Lesson 1

Two-way frequency tables# Two-way frequency tables

CCSS.Math:

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 | 36 | 22 |

Prefers cats | 8 | 26 |

No preference | 2 | 6 |

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

**male column**and the**prefers dogs row.**This tells us that there are 36 male students who prefer dogs.## 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 | 36 | 22 |

Prefers cats | start color #11accd, 8, end color #11accd | start color #11accd, 26, end color #11accd |

No preference | 2 | 6 |

## 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?(13 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(18 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?(7 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.(21 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.(5 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.(15 votes)

- whats the point of this bro(8 votes)
- Is relative frequency supposed to be written as a decimal or fraction?(3 votes)
- Relative frequency can be either a fraction or a decimal.

Have a blessed, wonderful day!(9 votes)

- how do I know that the 12 candies that contain chocolate don't contain caramel(7 votes)
- How did you find out there were 10 people that like chocolate but hates caramel(5 votes)
- The candies one was difficult and I'm sure I can speak for my class when I say this. I hope that our teacher doesn't end up putting a problem like this on our test. Yikes! That'll be scary/tuff if she do! Hahaha(4 votes)
- Honestly it was not that hard for me, rather a fun, quick, logic challenge.🙂(3 votes)

- how did u get two for containing no chocolate nor caramel(3 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.(2 votes)

- how did you get two when it says that 12 candies in total contain chocolate but i would assuming that it would be 12 because it do-sent say anything about containing caramel(3 votes)