DETERMINING THE ASSOCIATION BETWEEN TWO VARIABLES

Association describes how sets of data are related. A positive association means that both data sets increase together. A negative association means that as one data set increases, the other decreases. No association means that there is no relationship between the two data sets.

Data that show a positive or negative association and lie basically along a line exhibit a linear association. Data that show a positive or negative association but do not lie basically along a line exhibit a nonlinear association.

Solved Examples

Example 1 :

David asked 20 people if they can buy a new product that he developed at each of several prices. The scatter plot shows how many of the 20 people said “yes” at a given price. Describe the association between price and the number of buyers.

Solution : 

When price gets increased, the number of buyers gets    decreased. So, there is a negative association. Because the data points do not lie along a line, the association is non-linear.

Example 2 :

A survey made among students in a district and the scatter plot shows the level of reading and height for 16 students in the district. Describe the association and give a possible reason for it.

Solution : 

Positive and basically linear :

The students who are taller read at a higher level.

Example 3 :

Jack recorded his height at different ages. The scatter plot shows the his height at different ages. Describe the association between age and height and give a possible reason for it.

Positive and basically linear :

When Jack gets older, his height gets increased. But if the data continued for increasing age, we can see that Jack’s height will stop increasing.

Reflect

1. Based on the association shown in the scatter plot in example 1, what might happen if David increased the price to $14 ?

It is likely that no one would buy the product.

2. In example 3, if the data continued for increasing age, we can see that Jack’s height will stop increasing. why ?

Naturally, height of human being will stop increasing at a particular age. Even if age gets increased, after a particular age, height will not increase. 

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