Representing Data
In representing our data we move from reporting data to showing trends and patterns in the
physical, chemical, and biological phenomena we observe. As we make decisions about the types of
data we collect, we simultaneously need to think about how we will analyze and represent the data.
Data representations are driven by the types of data collected. Qualitative data describes
your observations in words or pictures and quantitative data describes the experiment in terms of
numbers. These data are often displayed in tables.
Graph data whenever possible. Relationships are more easily identified in a graphic
presentation as compared to a table. Some data that cannot be graphed on coordinates can be
expressed in pictorial form using other graphics such as a histogram. Supplement each graphic with
a brief descriptive text following the general guidelines described above.
 The title of your graph should be centered and placed just above the graph. Label both
the x-axis and the y-axis. Be sure to indicate the units used in the experiment. Multiple
data points should be graphed to provide a comparison among the experimental
conditions.
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
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To choose the type of graph that will best display your data, decide if your independent
variable is continuous or discrete.
Continuous variables are those measured on an ongoing scale such as length,
temperature or time. The values range on a continuum, for example from 0 to 100 mm,
or 0 to 100 °C, or 0 to 60 min. The intervals between numbers on a continuous scale are
equal. That is, the distance from 1 to 3 mm is the same as from 13 to 16 mm.
Categorical/ Discrete variables are described by separate categories. There is no
continuum between the categories; there are no values between the categories.
Examples of discrete variables include, dog breeds (greyhounds, pit bulls or terriers) or
makes of car (BMW, Honda or Ford). In science, types of antibiotics are an example of
categorical variables.
Types of Graphs. For continuous variables use a line graph. The Independent Variable
(descriptive or predictive variables) belongs on the horizontal (x) axis and the Dependent
Variable (outcome variable) belongs on the vertical (y) axis. Choose appropriate scales
for each axis to include all the values for the DV and the IV. You do not have to start at
zero; line breaks may be used for data that would normally not fit on the graph. If
appropriate draw a best-fit-line; a line that does not necessary connect the points but one
that best represents a general trend in the data. Best-fit-lines are often not used in scatter
plots. An X-Y scatter plot shows relationships or a correlation between 2 variables.
For categorical/ discrete variables use a bar graph. The independent variable (IV) is
placed on the horizontal (x) axis. The dependent variable (DV) is placed on the vertical
(y) axis. Make sure the bars are evenly spaced and label each bar. Histograms
(frequency distributions) are used when data can be organized into clumps.
A circle/pie graph is used when displaying parts of a whole, for example displaying
percentages. Each wedge should be labeled with the word or data that corresponds.
Bar Graphs
Line Graph
Figure 1. Effect of Antibiotics A and B on
Bacterial Growth
Figure 2. Mass of Potato vs Time
0.39
100
90
80
70
60
50
40
30
20
10
0
Antibiotic a
0.38
Antibiotic b
Mass (grams)
Inhibition (mm)
EXAMPLES
None
0.37
0.36
0.35
0.34
0.50%
0.33
1.00%
0.32
1
2
3
Time (days)
4
0
5
10
Time (minutes)
15
In addition to graphing, data can be represented in pictorial form such as maps. Or sometimes
diagrams are embedded in graphs.
Representing Data
 What are different types
of data representations?
 What is the purpose of
representing our data?
 In your experience, what
are some attributes of
graphs that you
appreciate?
EXTRAS
Ways to describe data. Five ways to describe data may be reported in this section including tables,
observations, sample calculations and graphs.
1. Tables. Organize the data from your experiment into charts or tables. Be sure to use a ruler
if you are hand drawing the table or chart. Consider using a computer program such as
Excel, SPSS or Word.
 Record your numerical data and observations (scientific drawings, photographs, audio
tapes, videos, written notes).

Use the proper metric units and use the “significant figures” to reflect the accuracy of the
instrument used to obtain the data. This means that if you are using an electric scale that
has an accuracy of 2 decimal places, then report your results using 2 decimal places. For
example, report 3.00 grams, not 3 grams.

Describe the data in a few sentences. Remember to state the exact results, but do not
make inferences or draw conclusions.
EXAMPLE
Table 1
Changes in Potato Mass Over Time
% Salt
Initial Mass
Mass at 5 min
(NaCl)
(grams)
(grams)
0.5%
0.34
0.34
1.0%
0.37
0.37
Mass at10 min
(grams)
0.35
0.38
Final Mass at 15 min
(grams)
0.35
0.39
The data listed above show the mass of 1 cm of potato cube over time. For the 0.5%
solution, mass ranged from 0.34 g to 0.35 g from initial time period the final time period.
In the 0.5% and the 1.0% salt solution, mass increased slightly over time.
2. Observations. Observations are descriptions or scientific drawings of findings that are not
based on numbers. Examples include a growth appearing in a bacterial experiment or the
color and height of a chemical responding to a flame. An observation is different from an
inference; it describes what the object or event looks like, not the reason you think a change
happened.
3. Sample Calculations. Displaying your calculations is an important way to show how you
derived your data. When writing sample calculations, first show the formula or steps for the
calculation, then show an example using the numbers. Box or underline your final answer.
It is not necessary to show all calculations; one example of each type is sufficient.
EXAMPLE
Table 2
Percent Change in Mass
% Salt
1.0 %
% Change in mass = (mass final – mass initial) x 100
% Change in mass = (0.39g – 0.37 g) x 100
% = 0.02 x 100
% = 2.0 %
The change of mass at 15 minutes was calculated as the percentage change compared to
the initial mass. In the 1.0% salt solution, the change was positive; the mass of the
potato increased.
4. Statistics. Running programs with basic statistics are often helpful for summarizing your
data and drawing conclusions from the data. Many calculators and computer programs can
run simple statistics. Helpful analysis may include descriptive and analytic statistics:
 Average, Mean (or other measures of central tendency)
 Standard Deviations from the mean
 Probability (especially in genetics)
 Percentages (the part of the whole)
 Correlation is measured in terms of r or r2 and ranges from –1 to +1. A value of one
is a perfect correlation and a value of zero is represents no correlation. This statistic
is most useful with larger sample sizes.
 t-tests