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### Course: Statistics and probability > Unit 1

Lesson 2: Two-way tables- Two-way frequency tables
- Read two-way frequency tables
- Create two-way frequency tables
- Create two-way relative frequency tables
- Analyze two-way frequency tables
- Interpret two-way tables
- Trends in categorical data
- Two-way relative frequency tables and associations
- Two-way tables review

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# Two-way tables review

Two-way tables organize data based on two categorical variables.

## Two way frequency tables

Two-way frequency tables show how many data points fit in each category.

Here's an example:

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.

Each cell tells us the number (or frequency) of students. For example, the $36$ is in the $36$ males who preferred dogs in this dataset.

**male column**and the**prefers dogs row.**This tells us that there areNotice that there are

**two variables**—gender and preference—this is where the**two**in**two**-way frequency table comes from.*Want a review of making two-way frequency tables? Check out this video.*

*Want to practice making frequency tables? Check out this exercise.*

*Want to practice reading frequency tables? Check out this exercise*

## Two way relative frequency tables

Two-way relative frequency tables show what percent of data points fit in each category. We can use row relative frequencies or column relative frequencies, it just depends on the context of the problem.

For example, here's how we would make column relative frequencies:

**Step 1: Find the totals for each column.**

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

Prefers dogs | ||

Prefers cats | ||

No preference | ||

Total |

**Step 2: Divide each cell count by its column total and convert to a percentage.**

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

Prefers dogs | ||

Prefers cats | ||

No preference | ||

Total |

Notice that sometimes your percentages won't add up to $100\mathrm{\%}$ even though we rounded properly. This is called round-off error, and we don't worry about it too much.

Two-way relative frequency tables are useful when there are different sample sizes in a dataset. In this example, more females were surveyed than males, so using percentages makes it easier to compare the preferences of males and females. From the relative frequencies, we can see that a large majority of males preferred dogs $(78\mathrm{\%})$ compared to a minority of females $(41\mathrm{\%})$ .

*Want a review of making two-way relative frequency tables? Check out this video.*

*Want to practice making relative frequency tables? Check out this exercise.*

*Want to practice reading relative frequency tables? Check out this exercise*

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