1.1.2 Variables and Data

We start with examples of quantitative relationships. Think for a moment about each of the following questions. You are not expected to know answers to these questions, just to be willing to think about them.

The United States has a serious dropout problem. What is the relationship between state expenditures on teacher salaries and high school graduation rates?
Will the world be seriously overpopulated in 20 years?
For adults, high blood pressure is linked to weight. Is there a similar relationship for children or adolescents?

These questions are different in many respects, but answering each requires collection, organization, and interpretation of data. Each requires analysis of the relationship between two variables. In the first question, those variables are the state expenditure on teacher salaries and the high school graduation rate. In the second question, the variables are time and population. And in the third, the variables are blood pressure and weight.

We can classify possible relationships between pairs of variables in four categories:

• One variable may have a causative effect on the other. For example, we expect that blood pressure in adults of the same height depends in some way on weight — higher weight causes higher blood pressure — but probably not the other way around.

• Other times there is a relationship between the variables, but it is not one of cause and effect. For example, at any given time, some number is the actual population of the world — but we would not consider either time or population to be a cause of the other.

• We might find that there is no relationship at all between two variables. For example, we do not expect a relationship between the distance from a student's home to college and her height.

• Finally, we may not know if there is a relationship between two variables. For example, there might be some relationship between the annual dollar amount of imports from Mexico to the U. S. and the annual dollar amount of exports from the U. S. to Mexico — but, without any data, we have no way of knowing.

Checkpoint 1

To determine whether a relationship exists between two variables, we must analyze pairs of data — each pair consisting of a value of the first variable and a corresponding value of the second variable. Sometimes these data are gathered from a well-designed, carefully controlled scientific experiment, as might be the case for a study of blood pressure or crop yields. Other times we want to analyze data that already exist in the world around us, such as census data on populations.

Activity 2

Table 1 shows both average spending per pupil and high school graduation rates for each of the fifty states and for the District of Columbia. Study this list of paired data to determine whether you think increased spending on students translates into higher graduation rates.

Note 2 – Data sources

Comment on Activity 2

Contents for Chapter 1