Physics Study Guide
Independent and Dependent Variable
Physics Study Guide
Independent and Dependent Variable
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.
| Table 1-3 Length of a Spring for Different Masses |
|
|---|---|
| Mass Attached to Spring (g) | Length of Spring (cm) |
| 0 | 13.7 |
| 5 | 14.1 |
| 10 | 14.5 |
| 15 | 14.9 |
| 20 | 15.3 |
| 25 | 15.7 |
| 30 | 16.0 |
| 35 | 16.4 |
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.
Plotting Line Graphs
Use the following steps to plot line graphs from data tables.
- Identify the independent and dependent variables in your data. The independent variable is plotted on the horizontal axis, the x-axis. The dependent variable is plotted on the vertical axis, the y-axis.
- Determine the range of the independent variable to be plotted.
- Decide whether the origin (0, 0) is a valid data point.
- Spread the data out as much as possible. Let each division on the graph paper stand for a convenient unit. This usually means units that are multiples of 2, 5, or 10.
- Number and label the horizontal axis. The label should include the units, such as Mass (grams).
- Repeat steps 2–5 for the dependent variable.
- Plot the data points on the graph.
- Draw the best-fit straight line or smooth curve that passes through as many data points as possible. This is sometimes called eyeballing. Do not use a series of straight line segments that connect the dots. The line that looks like the best fit to you may not be exactly the same as someone else’s. There is a formal procedure, which many graphing calculators use, called the least-squares technique, that produces a unique best-fit line, but that is beyond the scope of this textbook.
- Give the graph a title that clearly tells what the graph represents.