Notes on Guidelines for Constructing Tables
and Graphs
(Notes from Students and Research Practical Strategies for Science Classrooms and Competitions 4th edition
J. Cothron et al 2006 and references therein)
Data Tables
1. Title: Needs to reflect the PURPOSE of the experiment
2. Independent Variable: The part of the experiment that the experimenter
changes on purpose.
3. Dependent Variable: What the experimenter is observing based on the
changes to the independent variable.
4. You may organize your data using the Independent variable (example—
highest to lowest, lowest to highest or alphabetical). You should NEVER
organize your data using the dependent data.
The effect of Submersion Time on the Height a Liquid Rose in a Paper Towel Strip
Independent
variable (X)
Time Paper
Towel is
submerged
10
15
20
25
30
35
40
Dependent Variable (Y) for independent trials
11
14
14
15
16
17
19
Height liquid rose in towel (mm)
Trials
1
2
3
10
11
14
13
14
14
15
16
16
16
17
18
20
19
Note: Headings in shaded box are NOT included in formal tables.
Colum for Derived
Quantity (Y)
(Usually an
average)
Mean height
(mm)
11
14
14
15
16
17
19
Constructing Line Graphs
Graphs communicate in pictorial form data collected in an experiment. Graphs are
better at communicating data than tables.
Basic steps to constructing a graph:
1.
2.
3.
4.
5.
6.
Title: Needs to reflect the PURPOSE of the experiment
Draw and Label the Axes
Write Data Pairs
Determine Scales for Axes
Plot Data pairs
Summarize trends
Draw and Label Axes
1. Draw a vertical and horizontal line
2. Labe the X Axis with the INDEPENDENT VARIABLE (in our example that
would be Time paper towel submerged)
3. Labe the Y Axis with the DEPENDENT VARIABLE (in our example that would
be AVERAGE Height liquid rose in paper towel (mm) not you will graph only
the Derived Quantity when it is available.)
4. It is important to ALWAYS add the units in parenthesis on the appropriate
Axis.
Determine the Scales for Axes
The following is a helpful guideline to determining the proper scale for your axes.
1. Find the difference between the largest and smallest variable.
2. Obtain a reasonable number of intervals divide by 5. (5 is used only because
it is easy to work with and it usually gives you a good interval to work with—
too small of an interval will make the graph crowed but too large an interval
makes the data difficult to plot.)
3. Round the answer to the nearest convenient counting number. Any number
that is easily counted in multiples works well (for example 0.5, 2, 5, or 10)
Example Scales:
For Submersion Time (x-axis)
Largest Value
Smallest Value
Difference
Difference divided by 5
Quotient rounded to counting number
40 sec.
10 sec.
30 sec.
30 sec. / 5= 6 sec.
6 sec. rounded to 5 sec.
For Average Height Liquid Rose (y-axis)
Largest Value
Smallest Value
Difference
Difference divided by 5
Quotient rounded to counting number
19 mm
11 mm
8 mm
8 mm / 5 = 1.6 mm
1.6 rounded to 2 (OR 1.5—your choice)
Develop a scale for each axis using the rounded quotient as the interval.
a. Begin with an interval that allows the smallest value to be graphed
(THIS DOES NOT HAVE TO BE ZERO) for example if the smallest value
is 11 start with 10.
b. End with an interval that allows the largest value to be graphed for
example if the largest value is 40 you may use 40 but if it is 41 you
should use 45 (if your intervals are 5).
c. It is important to note that the x and y axis do NOT need to use the
same scale and they DO NOT have to start with zero!!! If you do this it
could result in your data being misrepresented and incorrect
conclusions could be made.
Plot Data Pairs
Do this by locating the value of the independent variable on the x axis and the value
of the dependent variable on the y axis and drawing and imaginary line until the
both meet.
Summarize trends
Sometimes we want to draw a line-of-best-fit (trend line)—this shows a basic
trend. To do this you do NOT connect the dots--- you draw a line which has about
the same number of dots above the line as below the line and the distance of the
points above the line is roughly equal to the distance of the points below the line.
(In general in the middle of the points.) There are more mathematically accurate
ways to determine the line-of-best-fit (trend line) that you can use a graphing
calculator or graphing software (such as excel) to complete if available.
You do not always need to draw a line-of-best-fit (trend line)—sometimes we want
to see the individual peeks and valleys to look for patterns. You will make this
decision based of the question you are asking with your data.
Sometimes you want to do both connect the dots and then draw a best-fit line over it
to show an over all trend.
In the end you should always include a basic conclusion statement (descriptive
sentence—example The greater the time a paper towel is submerged in a liquid the
farther the liquid will travel up the paper towel.) that describes the basic trend that
the data shows. Be careful to only conclude the information in the graph not a
conclusion for the entire study (this is most important when you are dealing with
studies that involve more than one set of data).
Constructing a Bar Graph
Average water absorbed by different brands of paper towel
Brand of paper towel
Average water absorbed (mL)
American Paper Towel
34
Basic Towels
17
Ceci’s Towels
24
Don’s All purpose paper towels
36
Everyone’s Favorite Towels
27
Flower’s Paper Towels
25
This is very much like making a line graph with only a few differences.
1. Title: Needs to reflect the PURPOSE of the experiment
2. Draw and label the X (Independent Variable) and Y (Dependent variable)
axes.
3. Write data pairs for the values of the Independent and Dependent Variables.
4. Subdivide the x-axis to depict the DISCRETE values of the Independent
variables.
5. Determine the appropriate scale for the y-axis.
6. Draw a bar for each discrete value on the x-axis that extends to the
appropriate value on the y-axis. Leave a space between each bar.
7. Summarize the graph with a descriptive sentence.
When to use a Line Graph or a Bar Graph
The appropriate type of graph is determined by the data taken.
Data can be classified as discrete or continuous.
Discrete data are categorical or counted (examples – days of the week, gender,
kind of animal) Use a bar graph for this type of data.
Continuous data are associated with measurement involving standard scale
with equal intervals (examples height of plants in cm, amount of fertilizer in
grams, length of time in seconds). When data may be any value in a continuous
range of measurement a line graph is best to use. Line graphs may also be used at
times to infer data not specifically plotted on the graph (when line-of-best-fit is
determined).
Use the following tables when creating a table or graph to help determine if it
is complete.
Checklist for Evaluating Data Tables
Criteria
Completed
Title (Does it describe the data given in the table with respect to independent and
dependent variables?)
Vertical column for independent variable
Title / unit for independent variable
Values of independent variable ordered
Vertical column for dependent variable
Title/unit for dependent variable
Dependent variable column subdivided for multiple trials (when done)
Dependent variables correctly entered
Vertical column for derived quantity (when applicable)
Unit of derived quantity included
Derived quantity correctly calculated
Checklist for Evaluating Line Graphs
Criteria
Completed
Title (Does it describe the data given in the table with respect to independent and
dependent variables?)
X axis correctly labeled including units
Y axis correctly labeled including units
X axis correctly subdivided into scale
Y axis correctly subdivided into scale
Data pairs correctly plotted
Data trend summarized with a line-of-best-fit (when appropriate)
Data trend summarized with sentences
Checklist for Evaluating Bar Graphs
Criteria
Title (Does it describe the data given in the table with respect to independent and
dependent variables?)
X axis correctly labeled including units
Y axis correctly labeled including units
X axis correctly subdivided – discrete values
Y axis correctly subdivided into scale
Vertical bars for data pairs correctly drawn
Data trend summarized with sentences
Completed