Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.



This objective is about the construction and use of two-way frequency tables to store data effectively and help us to easily classify the events as independent or not.





(1) The student will be able to construct a two-way frequency table.

(2) The student will be able to complete a two-way table given partial information.

(3) The student will be able to determine from a two-way frequency table basic probabilities, intersections, unions and conditional probabilities.

(4) The student will be able to determine independence of events using the data found in a two-way frequency table.


(5) The student will be able to determine convert a two-way frequency table to a two-way relative frequency table.




A quick and powerful way to display and interpret data is to put it into a two-way frequency table. Learning how to gather data, construct a two-way frequency table and then determine whether pieces of the data are independent or not is a very important skill to have.






Probably the biggest issue with using two-way frequency tables is the miscalculation of the union. Students add a row and a column together and don't realize that they are double counting the intersection. Be careful of this. I have found shading or circling the row or column help to show that the intersection got circled twice and needs to be subtracted out or not counted double in the first place




The two-way frequency table acts as a nice place where all of the previous objectives in this unit get practiced again. Sample spaces, intersections, unions, complements, conditional probabilities and independence all surface in two-way tables.



Two-way frequency tables are probably the most common way to represent data of this type. Students will see this format many times in the future when working with probability.



MY REFLECTIONS (over line l)

Truthfully I didn't do much with two-way tables my first time around... mostly be I had had very little experience with them. The more I work with them the more I like them. They are a powerful way to gather and organize data and things like the intersection are very easy to find and visually see. This objective discusses have students gather data and then create tables. I have not done that yet but that will be something to do and improve on in the future.