## What is a Two Way Table?

A two way table is a way to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a second category is represented by columns.

### Example

Sixty people (30 men and 30 women) were asked what type of movie they would prefer to watch and the following responses were recorded:

- 6 men preferred rom-coms.
- 16 men preferred action movies.
- 8 men preferred horror movies.
- 12 women preferred rom-coms.
- 14 women preferred action movies.
- 4 women preferred horror movies.

The information collected was used to build the following two way table:

The entries in the table are **counts**; this type of table is called a **two way frequency table.** The table has several features:

**Categories**are labeled in the left column and top row.- The
**counts**are placed in the center of the table. **Totals**appear at the end of each row and column.- A sum of all counts (a
**grand total**) is placed at the bottom right. - The totals in the right column and bottom row are called marginal distributions (excluding the grand total).
- The entries in the center of the table (everything except the marginal distributions) are called joint frequencies.

## Two Way Relative Frequency Table

Instead of displaying counts in the table, you could show *relative frequencies*. This is the same two way relative frequency table (decimals, percents, or ratios) displayed instead of counts:

To convert counts into relative frequencies, divide the count by the total number of items. In the above table, the first count is for men / Rom-com (count=6), so 6/60 = 0.1.

The totals in the right column and bottom row are, like the two way frequency table, called marginal distributions. However, the entries in the center of the table are called **conditional frequencies** or conditional distributions.

Two way frequency tables are sometimes called contingency tables, but that term is usually only used once you get into more advanced statistics that involves research and hypothesis testing.

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A group of students were surveyed to find out if they like building snowmen or skiing as a winter activity. The results of the survey are shown below:

60 students like building snowmen

10 students like building snowmen but do not like skiing

80 students like skiing

50 students do not like building snowmen

Make a two-way table to represent the data and use the table to answer the following questions.

What percentage of the total students surveyed like both building snowmen and skiing? Show your work.

What is the probability that a student who does not like building snowmen also does not like skiing? Explain your answer.

Please answer these questions, I am a teacher and I had a kid ask me these questions, but I am a history teacher, math is not my thing.

Mrs. Kary, I’m curious why a kid would ask a history teacher these questions. Can you give me an idea of what you do know? If you don’t have any basic statistics background, like basic probability, then any explanation I would give would go over your head. Do you have any probability background at all? For example, do you know how to calculate the probability of an event happening? What about percentages?

Yes I do but I don’t feel like having to anwer these questions……

Please just answer the questions….

Nevermind, I got the answer. Thanks for all your help….