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# How Variables Relate Help

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By — McGraw-Hill Professional
Updated on Oct 25, 2011

## Introduction to How Variables Relate

Tables and graphs portray relationships between changeable quantities known as variables . Tables and graphs show how the values of variables compare with, and in some cases affect, one another. When a table or graph is well composed, it can reveal phenomena that would otherwise be impossible to see.

### This Versus That

Consider the following statements. Each of them represents a situation that could occur in everyday life.

• The outdoor air temperature varies with the time of day.
• The time the sun is above the horizon on June 21 varies with the latitude of the observer.
• The time required for a wet rag to dry depends on the air temperature.

All of these expressions involve something that depends on something else. In the first case, a statement is made concerning temperature versus time; in the second case, a statement is made concerning sun-up time versus latitude; in the third case, a statement is made concerning time versus temperature. Here, the term versus means “depending on.”

## Independent vs. Dependent Variables

### Independent Variables

An independent variable can change in value, but its value is not influenced by anything else in a given scenario. Time is often treated as an independent variable. A lot of things depend on time.

When two or more variables are interrelated, at least one of the variables is independent, but they are not all independent. A common and simple situation is one in which there are two variables, one of which is independent. In the three situations described above, the independent variables are time, latitude, and air temperature.

### Dependent Variables

A dependent variable can change in value, but its value is affected by at least one other factor in a situation. In the scenarios described above, the air temperature, the sun-up time, and time are dependent variables.

When two or more variables are interrelated, at least one of them is dependent, but they cannot all be dependent. Something that’s an independent variable in one instance can be a dependent variable in another case. For example, the air temperature is a dependent variable in the first situation described above, but it is an independent variable in the third situation.

## Scenarios Illustrated

The three scenarios described above lend themselves to illustration. In order, they are shown crudely in Fig. 2-1.

Figure 2-1A shows an example of outdoor air temperature versus time of day. Drawing B shows the sun-up time (the number of hours per day in which the sun is above the horizon) versus latitude on June 21, where points south of the equator have negative latitude and points north of the equator have positive latitude. Drawing C shows the time it takes for a rag to dry, plotted against the air temperature.

Fig. 2-1. Three “this-versus-that” scenarios. At A, air temperature versus time of day; at B, sun-up time versus latitude; at C, time for rag to dry versus air temperature.

The scenarios represented by Figs. 2-1A and C are fiction, having been contrived for this discussion. But Fig. 2-1B represents a physical reality; it is true astronomical data for June 21 of every year on earth.

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