1. 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

2. 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)

3. 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

4. YesNo Children Adults YesNo Children0.150.4 Adults0.350.1 Do the division and you get:

5. Now we use this to calculate the Marginal Relative Frequencies: YesNoTotal Children0.150.40.55 Adults0.350.10.45 Total0.5 1

6. 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 Math1418168 English1211813

7. 9 th 10 th 11 th 12 th Total Math0.140.180.160.080.56 English0.120.110.080.130.44 Total0.260.290.240.211

8. 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 Burgers1012118 Pizza121188

9. 9 th 10 th 11 th 12 th Total Burgers0.1250.150.13750.10.5125 Pizza0.150.13750.1 0.4875 Total0.2750.28750.23750.21 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.

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

11. 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

12. First we calculate the JRF and MRF: Then we can calculate the CRF: CatNo CatTotal Dog0.150.240.39 No Dog0.180.430.61 Total0.330.671

13. Given that they own a cat, what is the probability that they own a dog? CatNo CatTotal Dog0.150.240.39 No Dog0.180.430.61 Total0.330.671

14. 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

15. BalletNo BalletTotal Tap0.190.260.45 No Tap0.430.120.55 Total0.620.381