(Note:  This section is taken directly from Physics:  A Laboratory Approach, by Dr. Harold Tiller, published by Contemporary Publishing Company of Raleigh, Inc., 1995.)

Purpose

We draw graphs to present a set of results so that they can be easily and quickly understood by ourselves and others. A graph that allows someone to grasp the idea quickly and clearly is good, but one that requires an effort to understand is not satisfactory.

Advantages of Graphs

1. Curves strike an average among the observed points so that the curve itself is more accurate than any one
data point.

2. Graphs enable us to detect observations which are definitely in error (gross error).

3. Graphs enable us to easily recognize relationships between the variables, e.g., straight line, hyperbola,
parabola, exponential, etc.

4. Graphs allow interpolation between observed points, as if an infinite number of observations had been
made.

5. Graphs permit extrapolation in order to predict results which would occur for conditions other than those actually used in an experiment.

6. Graphs permit a clear comparison of experimental results with theoretical predictions.

Methods of Plotting Graphs

In plotting a graph, the independent variable should be plotted along the horizontal axis (abscissa), while the dependent variable should be plotted on the vertical axis (ordinate). You may plot the graphs of more than one dependent quantities on the same sheet, but only if all the quantities plotted have the same independent variable.

A graph should occupy a single sheet of paper. Don't put two graphs on one page. The scales selected should be from 60% to 100% of the sheet in both directions. The scales selected should be easy to read. Satisfactory values for one scale division are 1, 2, 5, 10, or factors of 10 of these values. Don't crowd too many values on the scale. Figure 1 shows a graph with the horizontal axis too crowded. Figure 2 shows the same graph with fewer values, and is easier to read. On the border of the graph sheet, the scale should be clearly indicated, so that the values can be read easily. The quantity should be indicated both by name and units. Increases in positive values of each variable should read upward on the vertical axes and to the right on the horizontal axes.

It is not necessary to have the same units on both axes. In physics labs, the units are almost always different. See Figure 2 for an example of this. It is usually better to include the origin on the scales. Don't "suppress the zero point" on a scale unless its inclusion unduly cramps the actual graph plot.

In most cases, it is better to use the short side of the sheet as the horizontal axis. Never use the side of the graph paper on which the report is to be bound at the bottom of the page.

In plotting graphs, each point should be carefully and clearly marked by either a dot, a dot with a small circle around it, a cross, or some similar mark. When two or more sets of data are plotted on the same sheet, use different markings for each set, To distinguish between two curves that are close together, use different types of lines, such as dotted, broken, or different colored lines, and write the name of the dependent quantity close to each curve.

Don't draw the graph line "point to point. " A smooth curve should be drawn, which need not pass directly through each experimental point recorded. The graph curve itself should be a fine pencil line averaging through the plotted points. If the "curve" is a straight line, use a straightedge to draw in the graph line. To detect trends in plotted data points or to check a graph curve to see whether it strikes a good average through the plotted points, hold the graph sheet in a horizontal position at about eye level and sight along the data points and graph curve. It should be easy to see if the best fit is a straight line. Figure 2 shows a "best fit" straight line for its graph.

Notice that the line is dotted in the upper right of the graph. If you extrapolate (extend) the line, you must draw a dotted line to show that you don't have data in this region. Some graphs don't have straight lines as their best fit. Figure 3 shows a graph for which a curved line would best fit.

Logarithmic Functions and Semi-log Paper

In many cases, the dependent variable changes logarithmically when the independent variable changes. Figure 4 shows an example of an exponential curve. The logarithm of the dependent variable must be plotted instead of the arithmetic data. Sometimes, it is desirable to plot the graph on a special kind of paper called semi-log paper, which automatically plots the logarithm for you.

On semi log paper, the y axis is divided into a logarithmic scale rather than the arithmetical scale found on the x axis. (On log log paper, useful in some instances, both axes are divided into logarithmic scales.)

A sheet of semi log paper may contain from one to five cycles on the log portion. Each cycle corresponds to the characteristic of the logarithm of the number being plotted, while the subdivisions within the cycle correspond to the mantissa of the logarithm of the same number. Figure 5 shows data plotted on semi-log paper.

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