2-Way Tables These are tables that use both the rows and columns to display information. It lets us look for comparative trends and calculate conditional probability. Category Data CategoryData

The first two things we will calculate are the Joint Relative Frequency and the Marginal Relative Frequency. Joint Relative Frequencies = To find the Marginal Relative Frequencies, add the Joint Relative Frequencies in each row and category (add them and write them in the margins)

20 children and adults were asked if they liked broccoli. The following table gives the results: Now we’ll calculate the Joint and Marginal Relative Frequencies. Joint always goes first. YesNo Children38 Adults72

YesNo Children Adults YesNo Children Adults Do the division and you get:

Now we use this to calculate the Marginal Relative Frequencies: YesNoTotal Children Adults Total0.5 1

100 high school students were asked if they preferred Math or English. Calculate the J.R.F. and M.R.F. for the data. 9 th 10 th 11 th 12th Math English

9 th 10 th 11 th 12 th Total Math English Total

Challenge round: 80 high school students were asked if they preferred burgers or pizza. Calculate the J.R.F. and M.R.F. for the data. Don’t round the answers. 9 th 10 th 11 th 12th Burgers Pizza121188

9 th 10 th 11 th 12 th Total Burgers Pizza Total Rounding would keep us from getting the 1 in the bottom-right corner. Does it change the basic process? No, it just means more to write down. If directions tell you to round, go ahead and do it. Otherwise, don’t.

Used to find conditional probability Calculated by dividing the JRF by the MRF Conditional Relative Frequency

100 households were asked if they owned a cat and/or a dog: What is the Conditional Relative Frequency that a dog owner also owns a cat? CatNo Cat Dog1524 No Dog1843

First we calculate the JRF and MRF: Then we can calculate the CRF: CatNo CatTotal Dog No Dog Total

Given that they own a cat, what is the probability that they own a dog? CatNo CatTotal Dog No Dog Total

You try: Given a selection of 200 dancers asked if they’d taken tap, ballet, or both, find the JRF, the MRF, and the probability that a ballet dancer also takes tap. BalletNo Ballet Tap3852 No Tap8624

BalletNo BalletTotal Tap No Tap Total