Graphs

The American Standards Association [11] outlines the do's and don'ts of making engineering graphs. Their thirteen rules for making graphs are presented here.

1. The graph should be designed to require minimum effort from the reader in understanding and interpreting the information it conveys.

2. The axes should have clear labels that name the quantity plotted, its units, and its symbol if one is in use.

3. Axes should be clearly numbered and should have tick marks for significant numerical divisions. Typically, ticks should appear in increments of 1, 2, or 5 units of measurement multiplied or divided by factors of ten (1, 10, 100, ...). Not every tick needs to be numbered; in fact, using too many numbers will just clutter the axes. Tick marks should be directed toward the interior of the figure.

4. Use scientific notation to avoid placing too many digits on the graph. For example, use $50 \times 10^3$ rather than 50,000. A particular power of ten need appear only once along each axis; avoid confusing labels such as ``Pressure, Pa x 10$^5$ ''.

5. When plotting on semilog or full-log coordinates, use real logarithmic axes; do not plot the logarithm itself (e.g., plot 50, not 1.70). Logarithmic scales should have tick marks at powers of ten and intermediate values, such as 10, 20, 50, 100, 200, ...

6. The axes should usually include zero; if you wish to focus on a smaller range of data, include zero and break the axis.

7. The choice of scales and proportions should be commensurate with the relative importance of the variations shown in the results. If variations by increments of ten are significant, the graph should not be scaled to emphasize variations by increments of one.

8. Use symbols such as $\circ$ , $\bigtriangleup$ and $\Box$ for data points. Do not use dots ($\cdot$ ) for data. Open symbols should be used before filled symbols. You may place a legend defining symbols on the graph (if space permits) or in the figure caption.

9. Place error bars on data points to indicate the estimated uncertainty of the measurement or else use symbols that are the same size as the range of uncertainty.

10. When several curves are plotted on one graph, different lines (solid, dashed, dash-dot, ...) should be used for each if the curves are closely spaced. The graph should include labels or a legend identifying each curve. Avoid using colors to differentiate curves, since colors are usually lost when the graph is photocopied. Theoretical curves should be plotted as lines without showing calculated points. Curves fitted to data do not need to pass through every measurement like a dot-to-dot cartoon; however, if a data point lies far from the fitted curve, a discrepancy may be indicated.

11. Lettering on the graph should be held to the minimum necessary for clarity. Too much text (or too much data) creates crowding and confusion.

12. Labels on the axes and curves should be oriented to be read from the bottom or from the right. Avoid forcing the reader to rotate the figure in order to read it.

13. The graph should have a descriptive but concise title. The title should appear as a caption to the figure rather than on the graph itself.

Science and engineering practice follows all of these rules except for a minor deviation of rule #3. Recommended practice by most engineering publications is to place the tick marks outside the graph. Also it is sometimes useful to number the scale in different increments than suggested in rule #3; angular degrees are best labeled 30, 60, 90, ..., inches in increments of six to easily convert to feet. Another exception is to rule #5. Decibels and earthquake strength expressed using the Richter scale should be represented using a linear scale as these units are already exponential. One final derrogation is that the Système International has prefixes. Use them.

Proper graphs indicate the origin of both axes. Only by showing the zero can the importance of a trend be compared to an invariable part of the function. Trends that have large y-axis intercepts and small slopes are best represented by a constant and not a line. However, most computer graphing packages do not allow a break in the scale to permit the indication of the zeros of the axes.

If you are using a computer graphing package, make sure that you are plotting engineering graphs. Some packages, such as Quattro Pro $^\mathrm{TM}$ or Excel $^\mathrm{TM}$ , have graph options that are not suitable for engineering graphs such as the x-y line graph. Do not use these options to plot your graph, since the x-axis scale will be irregular and the graph will be useless. A good way to be alerted to an irregular axis is to watch for oddly numbered ticks (e.g., 49.21, 37.17, 55.43) at equal spacing along the x-axis. These graphs may be useful in the financial world, but they are unacceptable in science and engineering.

In general, be careful with line graphs. Do not play connect-the-dots with your data points (rule #10). In most cases, a graph should show a continuous trend even though your experimental data show scatter about the trend. One line type that should be avoided is Excel $^\mathrm{TM}$ 's smoothed line. The line is forced (by using a spline) through the data points showing slopes that depend only on the uncertainties of each point. This is not a true trend line as it does not take into account the erroneous nature of the data point without error bars. Always qualify a trend line: fitted by eye, curve fit using least squares, etc. Never extend a trend line (extrapolate) beyond the error margins of the maximum and minimum data.

Figure 7.1: A Good Graph of How Writing Experience Affects Students' Grades

Two examples are given below; Figure 7.1 shows how the average grade assigned to written reports improves with the number of reports written by university students (fictitious data). The graph has a reasonable trend line fitted to the data, illustrating that the average grade increases with the number of reports written. Figure 7.2 shows the same data with a connect-the-dots plot. This accentuates discrepancies in the trend which are really due to inadequate sampling or scatter in the data. Avoid plots like the latter.

Figure 7.2: A Poor Graph of How Writing Experience Affects Students' Grades