A well-designed graph can convey information quickly and simply. Patterns that are not immediately evident in a list of numbers take shape when the data are graphed. In this section, you will develop graphing techniques that will enable you to display, analyze, and model data.

Identifying Variables

When you perform an experiment, it is important to change only one factor at a time. For example, Table 1-3 gives the length of a spring with different masses attached, as measured in the Mini Lab. Only the mass varies; if different masses were hung from different types of springs, you wouldn’t know how much of the difference between two data pairs was due to the different masses and how much to the different springs.

A variable is any factor that might affect the behavior of an experimental setup. The independent variable is the factor that is changed or manipulated during the experiment. In this experiment, the mass was the independent variable. The dependent variable is the factor that depends on the independent variable. In this experiment, the amount that the spring stretched depended on the mass. An experiment might look at how radioactivity varies with time, how friction changes with weight, or how the strength of a magnetic field depends on the distance from a magnet.

One way to analyze data is to make a line graph. This shows how the dependent variable changes with the independent variable. The data from Table 1-3 are graphed in black in Figure 1-15. The line in blue, drawn as close to all the data points as possible, is called a line of best fit. The line of best fit is a better model for predictions than any one point that helps determine the line. The problem-solving strategy on the next page gives detailed instructions for graphing data and sketching a line of best fit.