GRAPHICAL REPRESENTATIONS OF EXPERIMENTAL DATA

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INTRODUCTION:
Plots are the most common way of presenting data. Often, it is the most effective way to
present the results of an investigation and the easiest way to understand and interpret these results.
This is true because a plot visually displays the relationship between two physical quantities, such
as pressure and temperature in this experiment. For a plot to be easily understood by all readers it
must follow a standardized format; the quintessential idea being that the plot be clear and concise
in their labeling. For our class we will be using the follow set of instructions to create plots
throughout the semester:
Instructions for Constructing a Data Plot
ORIENTATION
• Plots should be presented in landscape orientation and not portrait orientation, as shown below
in FIGURE 1.
FIGURE 1 – Two possible page orientations.
TITLE
• Describe which part of the experiment that the data comes from.
o Use words, not abbreviations or mathematical symbols.
AXES
• Describe the plotted variable.
o Use words, not abbreviations or mathematical symbols.
• Within parentheses, describe the units of the plotted variable.
o Use the appropriate abbreviation or mathematical symbols, not words.
CURVE FITTING
• Don’t use a series of straight-line segments to connect successive data points, as shown below
in FIGURE 2.
o This is often done in business but never done in science.
FIGURE 2 – Sample business graph with connected data points.
• An equation, in the form of a single and continuous curve, will attempt to “fit” the data points
to the desired mathematical behavior.
o This curve, called a best-fit line or a trendline, usually doesn’t pass through every data
point in the plot as seen in FIGURE 3 below.
FIGURE 3 – Sample trendline (in red) to plotted data points (in green).
Linear Trendlines
When the data appears to follow a straight-line it is considered to be linear in nature, and is the
easiest to analyze. All straight lines have an equation of the form
𝑦𝑦 = 𝑚𝑚𝑚𝑚 + 𝑏𝑏
where 𝑚𝑚 is the slope and 𝑏𝑏 is the y-intercept (where the line crosses the 𝑦𝑦-axis when 𝑥𝑥 = 0).
Nonlinear Trendlines
There are many different trendlines that can be fitted to data which are not linear. These curves are
classified as being nonlinear. The power law function 𝑦𝑦 = 𝑎𝑎𝑥𝑥𝑛𝑛 is one example of a nonlinear
curve, where 𝑎𝑎 a constant coefficient is and 𝑛𝑛 is an exponent to the variable 𝑥𝑥. Computer software,
such as Microsoft Excel or Google Sheets, will aide in determining the appropriate values for all
numerical coefficients. The theory within an experiment will aide in determining the appropriate
value of the function’s exponent.
PROCEDURE:
1. First Graph
a. Create a plot of pressure versus temperature using the data in the DATA TABLE
below.
• Give the plot an appropriate title, such as “Non-Ideal Gas Law Data”.
• Insert a linear trendline that isn’t forced to go through the origin.
• Display the trendline equation displayed and the 𝑅𝑅-squared value directly
beneath the graph’s title.
b. Save the graph as a PDF.
2. Second Graph
a. Create another plot using the same data as the first plot.
• Label the graph appropriately.
• Insert a quadratic trendline that isn’t forced to go through the origin.
• Display the trendline equation displayed and the 𝑅𝑅-squared value directly
beneath the graph’s title.
b. Save the graph as a PDF.
3. Third Graph
a. Create another plot using the same data as the first plot.
• Label the graph appropriately.
• Insert a cubic trendline that isn’t forced to go through the origin.
• Display the trendline equation displayed and the 𝑅𝑅-squared value directly
beneath the graph’s title.
b. Save the graph as a PDF.
DATA TABLE
VAPOR
TEMPERATURE
𝑇𝑇
( ℃ )
VAPOR
PRESSURE
𝑃𝑃
( 𝑃𝑃𝑃𝑃 )
10.5 19
20.2 29
30.1 37
40.2 81
50.1 119
60.7 155
70.5 265
80.9 369
90.0 522
100.3 753
Answer the following questions below using complete sentences:
1. 𝑅𝑅-squared can be treated as a statistical measure of how close the data are to the trendline.
R-squared has a minimum value of 0 and a maximum value of 1; the higher the 𝑅𝑅-squared value,
the better that the trendline “fits” the data. Based on this, which graph (of the three) has the most
accurate trendline?
2. Below is a scanned image of a scatter plot based on data collected, by a student, from a
different experiment. It has been scaled-down to a smaller size to better fit on this page. Identify
three mistakes that the student made in creating this graph.
(A)
(B)
(C)

 

 

Sample Solution

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