Preparing Graphs
Often in science you will find it convenient to organize data into forms that are easily
interpreted visually. Graphs are an effective way to display information. Often, they can reveal a
relationship between variables more clearly than data in a table. The type of graph you draw will
depend upon the type of data you are working with. Choose the one that best fits the purpose.
A few basic guidelines apply to all graphs (an example is provided in Figure 1):
- Use graph paper or a clean sheet of white paper and a sharp pencil, a compass, or a ruler so that
your lines will be clear and as accurate as possible.
- Title your graph using the same or a similar title to that of a data table or experiment upon
which the graph is based. The title should be at the top of the graph. A statement of the two
variables is often used as a title; for example, "Solubility versus Temperature for Sodium
Chloride."
- Draw and label each axis, indicating any units used. For example, you might label
an axis as Distance (m). The independent variable, or manipulated variable, is plotted along the
horizontal (x, abscissa) axis; the dependent variable, or responding variable, is plotted along the
vertical (y, ordinate) axis. For example, if you are measuring the temperature at various times, time
is the manipulated variable. Therefore, time will be placed on the horizontal axis and temperature
will be placed on the vertical axis. Include the unit in parentheses on each axis label, for example,
"Time (s)." The point where the two axes meet is called the origin of the graph.
- Choose a scale that reflects the data you have gathered. As a general rule, the data points
should be spread out so that at least one half of the graph paper is used. This makes it easier to
interpret your graph. For example, you could make each square on the graph paper representative
of one, two, five, or ten units. The scale does not have to be the same for both axes, but make
sure you label the axes clearly to avoid confusion. It is not necessary to start the scale at zero; your
graph just has to be able to include your smallest and largest figures. Choose a scale that is easy to
read and has equal divisions. Each division (or square) must represent a small simple number of
units of the variable; for example, 0.1, 0.2, 0.5, or 1.0.
- For example, imagine that you have collected data on the average height of students in the
school versus their age and your results are as follows.
| Height (cm) |
Age (years) |
| 122 |
12 |
| 137 |
13 |
| 145 |
14 |
| 152 |
15 |
| 168 |
16 |
| 175 |
17 |
- You want to plot the height on the y axis and the age on the x axis. For the height of the students,
your largest value is 175 cm and your smallest is 122 m, the range you need is 53 cm (175 cm -
122 cm = 53 cm). Imagine also that you have 20 lines of graph paper to use. To find the increase
in value for each line of graph paper, simply divide the range by the number of lines. In our
example,
53 cm ÷ 20 lines = 2.65 m/line, which is rounded up to 3.
- This means that every line on your graph paper would correspond to an increase of 3 cm in height.
Follow the same procedure for the x axis. This ensures that your entire range would fit on the
graph. You do not need to label every division line on the axis. Scales on graphs are labeled in a
way similar to the way scales on rulers are labeled.
- When plotting points:
- a) Mark each point clearly with an X or dot with a small circle around it.
- b) If there is a clear pattern among the points, draw a "best-fit" line (continuous smooth curve or
straight line), which is a line that comes as close as possible to most of the points. Using a sharp
pencil, draw a line that best represents the trend shown by the collection of points. Do not force
the line to go through each point. Uncertainty of experimental measurements may cause some of
the points to be misaligned. If the collection of points appears to fall in a straight line, use a ruler
to draw the line. The chart on the graph paper is the "graph" and the lines drawn between points
are "curves", even if they are straight lines.
- c) Be suspicious of a data point that is obviously not part of the pattern. Double check the location
of such points, but do not eliminate the point from the graph if it does not align with the rest. If
the data points are in ink and the line is in pencil, it is easy to change the position of the line if your
first curve does not fit the points to your satisfaction.
- d) If there is no evident or expected relationship between the variables, connect the points with
short, straight lines, much like a connect-the-dots picture.
- e) If two or more sets of data are plotted on one graph, use different symbols, colours, or lines to
distinguish them.
- f) To extend your data to find values between measured points (interpolation) or to find values
beyond measured points (extrapolation), use a dotted line.
- g) If any comments are required, do not write them along the curves. Place any necessary
information in a legend below the graph.
- When more than one curve is placed on a graph, use different symbols or colors to differentiate
between curves. All the points on one curve should be plotted with the same symbol or color
which should be distinctly different from those used in plotting the other curves.
Although a graph is constructed using a limited number of measured values, the pattern may be used to extend the
empirical information. The scattering of points gives a visual indication of the uncertainty in the experiment. A point that
is obviously not part of the pattern may require a re-measurement to check for an error or may indicate the influence of
an unexpected variable.
Remember that line graphs are not the only type available to you. Consider the different ways the data is represented
throughout this text. Always choose the type of graph that best represents your findings. The examples which follow
will introduce you to the various types of graphs most commonly used.
| A line graph is used to show trends in data over equally spaced intervals of
time. It is useful for a long series of data, or comparison of two or
more series of data.
|
| An area graph is also used to
show trends in data over time. It is useful for emphasizing the
magnitude of changes of time, as ... Note that an area graph is the equivalent of a stacked bar
graph, for continuous data.
|
| A column bar graph is used to compare the magnitude of, or differences between items,
where the emphasis is on variations over time. It is useful for one or more series of
data over time.
|
| A horizontal bar graph is used to compare differences
between items, where the emphasis is more on the
differences and less on variations over time. It is useful
for ranking items by magnitude, or a direct comparison
of size between items.
Items are normally ranked from largest to smallest.
|
| A pie graph is used to show the relative proportions of several
components of one data series. The number of components in a pie graph
should be no more than five or six. A pie graph is useful for seeing the
percentage relationship between components. It can also be used to
show the change in component proportion at different times, using two
pie graphs. It is important to ask yourself whether a pie graph is the best
way to represent your data.
|
| A scatterplot is used to show any correlation between two different numeric
variables (where a variable is something that has been measured or observed). It is
useful for large amounts of data, or establishing any
possible relationship between variables. It is commonly used with scientific data.
|
- There are also several general "rules" to follow when preparing your graph. The following is not
exhaustive, but may give you some guidance:. Click on a "rule" to see any extra information.
- Avoid 3D graphics if you want people to be able to read quantities. Use this form only where a
general impression is sufficient, and then ensure that the title reinforces the message.
- If you use symbols instead of lines or bars in a graph, creating a pictograph, make sure that you
use multiples of the same size symbol, rather than different sized symbols.
- Label x and y axes, with units (use 'thousands' rather repeat zeros everywhere).
- Keep the number of legend items to 5 maximum; direct labeling is preferred if that will work OK
with your format and data.
- Ensure that you use a direct title.
- Ensure you take note of the time periods when using discontinuous data.
- Think about font styles and sizes for impact - don't just use the default settings.
- Thicker lines on many charts will dramatically improve the graphic quality of the information.