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Does This Predict That?

Associations in Categorical Data

This week your student will work with scatter plots. Scatter plots show us how two different variables are related. In the example below, each plotted point corresponds to a dog, and its coordinates tell us the height and weight of that dog. The point on the lower left of the graph, for example, might represent a dog that is 8 inches tall and weighs about 5 pounds. The plot shows that, generally speaking, taller dogs weigh more than shorter dogs. Since a larger value for one characteristic (height) generally means a larger value for the other characteristic (weight), we say that there is a positive association between dog height and dog weight.

In the next example, each point corresponds to a car, and its coordinates tell us the weight and fuel efficiency of the car. This time, we see that larger values for one characteristic (car weight) generally have lower values for the other characteristic (fuel efficiency), and so we say that there is a negative association between car weight and fuel efficiency.

Here is a task to try with your student:

The following scatter plot shows the relationship between average temperature and gas usage in a buildings.

Solution:

This week your student will use two-way tables. Two-way tables are a way of comparing two variables. For example, this table shows the results of a study of the relation between meditation and state of mind of athletes before a track meet.

23 of the people who meditated were agitated, while 21 of the people who did not meditate were agitated. Does this mean that meditation has no impact or even a slight negative association with mood? Probably not. When we look for associations between variables it can be more informative to know the percentages in each category, like this:

Of the people who meditated, 66% were calm, and 34% were agitated. When we compare that to the percentages for people who did not meditate, we can now see more easily that the group of people who meditated has a lower percentage of athletes who are agitated. The percentages in this table are called relative frequencies.

The following table contains data about whether people in various age groups use their cell phone as their main alarm clock.

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.