Reading: Graphing Techniques
Revised 3/6/12
GRAPHING TECHNIQUES
Mathematical relationships between variables are determined by graphing experimental data.
For example, the linear relationship between the concentration and the absorption of dilute
colored solutions leads to Beer’s Law (A=εCl). Once the mathematical relationship is known,
experimental quantities can often be calculated from the slope or y-intercept of a graph. For
example, reaction enthalpy can be determined from the slope of a plot of ln k vs. inverse T.
Furthermore, extrapolation of graphical data trends can be used to find information about
conditions difficult to achieve in the laboratory, such as high or low temperatures and pressures.
Plotting Variables
A line graph consists of two axes at right angles. The horizontal x-axis, or abscissa, is typically
chosen to represent the independent variable which is intentionally manipulated by the
experimenter. The vertical y-axis, or ordinate, is chosen to represent the dependent variable
which changes as the independent variable is manipulated.
Example: A student wishes to measure the relationship between volume and temperature of a
gas. If the student purposely increases the temperature and measures the resultant changes in gas
volume, he should graph the values for T on the x-axis and the resulting values for V on the yaxis. If the student reverses the experiment and purposely increases the volume of the gas and
measures the resultant temperature, the variables are then reversed: V is plotted on the x-axis
and T is plotted on the y-axis.
Selecting a Title and Labeling the Axes
The title must describe the type of reaction or system being investigated, chemicals used, and
special conditions of the experiment. Examples: "Beer’s Law Plot for Co(NO3)2(aq) at 510 nm"
or "Cooling Curve for Lauric Acid/Unknown Mixture". Do not state x vs. y in the title, that is
easily determined by labeling the axes. Axes must be labeled with the name (or symbol) of the
variable and include the units (if any). Examples:
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Temperature (°C) or V (mL).
Reading: Graphing Techniques
Revised 3/6/12
Choosing an Appropriate Scale
The scale of the graph should be chosen so the data completely fills the graph and is not
restricted to one small region or corner. Examples are shown in Figure 1. Note that the scale
does not have to begin with zero.
Absorbance vs. Wavelength
for a Metal Complex Ion
0.5
Absorbance
0.4
0.3
0.2
0.1
0
225
325
425
525
625
725
Wavelength (nm)
Absorbance vs. Wavelength
for a Metal Complex Ion
Absorbance vs. Wavelength
for a Metal Complex Ion
Absorbance
Absorbance
0.5
0.4
0.3
0.2
0.1
0
0
500
1000
1500
2000
2500
3000
2.5
2
1.5
1
0.5
0
225
325
425
525
625
Wavelength (nm)
Wavelength (nm)
Figure 1: The three plots are from the same data set, but use different scales for the dependent
and independent variables. The top graph represents the data range most clearly. Note that each
graph contains a title and the axes are labeled. Absorbance is unitless but the units for
wavelength are given in nanometers.
Drawing Data Points
Data points can be represented either as a circle, dot, or bar. The size of the circle or bar is often
used to represent the deviation or error in the data point. Recorded data should be included on
the plot as a separate table. (Figure 2)
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Reading: Graphing Techniques
Revised 3/6/12
Data points from other experimenters should be represented with different symbols.
legend citing the source of the additional data points. Example:
Include a
• My data, ♦ Kim Nguyen's
data, † Sam Patel's data
Use a solid line through the data points and a dashed line when extrapolating or extending
beyond the collected data points.
Drawing Lines or Curves
Draw (have a computer program draw) a smooth curve or line when connecting data points.
"Dot-to-dot" connections should be avoided. If the data points do not exactly fit on the line, a
best-fit line in which an equal number of data points lie an equal distance above and below the
line should be drawn. The best fit line "smoothes" the data and helps eliminate random error.
(Figure 2) Use a computer graphing program to generate the line and its equation.
V (L) P (atm) 1/P (atm-1)
4.89
0.50
2.00
3.06
0.80
1.25
2.44
1.00
1.00
1.96
1.25
0.80
1.63
1.50
0.67
Figure 2: Linear plot with a best fit line, including a data table.
Computer Generated Plots
All graphs must be computer generated. Caution: A computer plot must be scaled correctly,
have labels, and all other expected information. Keep in mind the old addage: "garbage in,
garbage out". Good data is necessary for good results. You must use the computer graphing
program correctly and obtain a useful graph.
Using Excel for Graphing
The following are guidelines for acquiring a graph using Excel, including a best-fit line (called a
trendline in the program). Be judicious about the data included. If a points lies far outside a
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Reading: Graphing Techniques
Revised 3/6/12
reasonable value, provide two plots for grading: one with the data point and one without. Also,
you should perform a Q-Test and report the confidence level for rejecting the data point. (See
Reading: Analysis of Errors.)
Instructions for graphing with 97-2003 Excel:
(1) Enter data points to be graphed in two adjacent columns. Data for the x axis should be in
the left column and data for the y axis should be in the right column.
(2) Highlight the two columns of data by holding down the left mouse button and dragging the
mouse over the column heading letters.
(3) Go to the Insert menu and select Chart. The Chart Wizard window should appear.
(4) In the first window, Step 1 of 4, select XY Scatter for Chart Type and Scatter for Subchart
Type (the choice without any lines connecting the data points). Click the Next button at the
bottom of the Chart Wizard window.
(5) In the second window, Step 2 of 4, make sure Series in Columns is chosen and then click
the Next button.
(6) In the third window, Step 3 of 4, there are five tabs: titles, axes, gridlines, legend, and data
labels. In the Title tab enter the Chart Title and the Labels for the x and y axes (make sure
that you include units). In the Gridlines tab check Major Gridlines for both x and y axes.
And, in the Legend tab uncheck Show Legend. Click the Next button.
(7) In the fourth window, Step 4 of 4, determine whether you want your graph on the same sheet
with your data, or on a new sheet. Click the Finish button. The chart should appear.
(8) Click on the data points so that only they are highlighted. Go to the Chart menu and choose
Add Trendline. In the Add Trendline window, under the Type tab, choose the correct line
type (which is usually linear for g chem. lab). Under the Options tab, check Display
Equation on Chart and Display R-squared Value on Chart. Click OK.
Notes:
1) You may change locations, sizes, gridline units, fonts, et cetera of your chart by clicking
to highlight the areas you wish to change.
2) R-squared values indicate how well the trendline fits the data. If the slope is positive, the
ideal fit is 1. If the slope is negative, the ideal fit is -1.
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Reading: Graphing Techniques
Revised 3/6/12
To extrapolate (extend) a data line:
Click on the line so that it is highlighted. Go to the “Chart” menu and choose “Add Trendline”.
Click on the “Options” tab. Under “Forecast” choose the number of periods necessary – either
forward or backward.
Instructions for graphing with 2007 Excel:
(1) Enter data points to be graphed in two adjacent columns. Data for the x axis should be in
the left column and data for the y axis should be in the right column.
(2) Highlight the two columns of data by holding down the left mouse button and dragging the
mouse over the column heading letters.
(3) Click on the Insert tab and select Scatter icon in the Charts section. Choose the Scatter
with Only Markers chart type (the top left choice). The plot of data will appear.
(4) Click on the plot that just appeared. Chart Tools should appear at the very top of the screen
in the middle. Choose the Layout tab.
a. In the Analysis section choose Trendline. Choose More Trendline Options at
the bottom of the pull down window. Choose the Trend/Regression Type and
click on the box next to Display Equation on chart.
b. In the Label section choose Chart Title. Choose Above Chart and enter a title
in the field that appears at the top of the plot. In the same section choose Axis
Titles. Enter the titles.
c. If the initial and final values of either axis needs to be changed, click on the Axis
button in the Axis section and make the necessary changes. Gridlines can be
altered by clicking on the Gridline button in the Axis section.
To extrapolate (extend) a data line:
Click on the line so that it is highlighted. The “Chart Tools” will show up on to the middle/right
of the top tool bar. Choose the “Layout” menu/tab. Go to the “Trendline” and choose “More
Trendline Options”. Under “Forecast” enter the number of periods necessary – either forward or
backward.
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Reading: Graphing Techniques
Revised 3/6/12
To change the x and y axes minimum and maximum values:
Click on the plot so that "Chart Tools" is visible in top tool bar. Choose the “Layout” menu/tab.
Click on "Axes" and choose "Primary Horizontal Axis", click on "More Primary Horizontal Axis
Options". Set either or both the Minimum and Maximum to "Fixed" and then change the value
in the field directly to the right. Repeat the process for the vertical axis (go to "Axes" and choose
"Primary Vertical Axis", et cetera).
Instructor Reviewed Information on the Web:
Please report any links that are no longer active.
Graphing with Excel, North Carolina State University:
http://www.ncsu.edu/labwrite/res/gt/gt-reg-home.html
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