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Graphing Scientific Data
Bio 211, Mr. Hoyt
Southwestern College
Chula Vista, CA,USA
Introduction
Why graph data? Scientists must be able
to communicate data to other scientists. Often, the most concise way to
do this is to present the data in the form of a graph. Therefore, when
reading a scientific paper, usually the first thing a scientist looks at
is the graph.
Additionally, graphing can allow transformation
of data in ways that can demonstrate aspects of the data more clearly and
meaningfully. You will do both of these in this exercise.
Learning Objectives
Upon completion of this lab you should
be able to:
1. Define
dependent variable
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independent variable
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scatter graph
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best fit line
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line graph
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extrapolation
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slope
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column graph
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distribution frequency
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2. Make a well constructed and labeled
scatter graph with a best-fit line, line graph and column graph.
3. Be able to use Cricketgraph™ or other
graphics package to construct a graph.
4.Be able to verbally describe a graph
of simple data.
5. Be able to calculate and interpret slope.
What Makes a Well Constructed
Graph?
1. On hand drawn graphs, always
use graph paper for accuracy or use graphing software such as Cricketgraph™
2. A descriptive title is important.
For example, you want to graph shoot length vs. time in an experiment in
which you manipulated the amount of light bean plants received each day.
You construct a nice graph and thenname it: Shoot Length.
What is the problem with this name? Well,
it doesn’t describe the experiment. Someone looking at the graph will have
to read the full experiment before understanding the graph and that takes
a lot of time. A much better title would have been " Shoot Length in Bean
Plants with Various Day Lengths". Now there is no question as to what the
graph represents.
3. Scale and Label your axes accurately.
Space the intervals evenly along the axes and use a maximum value on each
axis which is only slightly greater that the greatest data value for that
axis. This gives your graph the greatest sensitivity and doesn’t waste
space. Label your axes.
4. Put independent variable (usually
time) on the horizontal or "X" axis. The independent variable is
usually a scale that measures the progress of the experiment. The dependent
variable is usually placed on the vertical or "Y" axis. The dependent
variable is usually what is being measured as the experiment proceeds.
5. Do not make up data. Plot data points
only at coordinates where data was collected.
6. Extrapolate data only when called for.
Extrapolation is an assumption made when a trend in an experiment
is clear. For example, if a line on a graph extends upward at a 48 degree
angle and does not deviate from that angle, you would probably be correct
in assuming that the line will continue on at 48 degrees. Say that you
need information about the experiment at a certain coordinate that is beyond
the last data point collected in the experiment. You could extend the
line on the graph at the same 48-degree angle to the coordinate that you
need,
assuming that that would be the results of the experiment
at that coordinate. Realize that this may not be a good assumption.
Types of Graphs
1. The scatter graph
The scatter graph is a simple graph
of data points between two axes. See Figure 1 for an example. Usually the
independent variable is placed on the horizontal axis and the dependent
variable is placed on the vertical axis.
Figure 1: scatter graph 
As you can see, the data is hard to interpret
in the graph in Figure 1 due to the scattering of the data points. To help
interpret the data in a scatter graph, a line is often used to show trends
in the data. Often the most useful line to show trends in data in a scatter
graph is a best-fit line (also known as a best fit curve).
A best fit line is a line on a graph which best represents the trend in
a set of data points when the data points themselves have considerable
variability in value. This variability may be due to minor inconsistencies
in measurement or factors inherent in the experiment itself. See Figure
2 for a graph of the same data in Figure 1 but with a best fit line.
The calculation of a best-fit line is complex
but to keep it simple, it is a method of averaging of the data points to
give a line which best depicts the data. Cricketgraph™ can easily do it
for you.
Figure 2: scatter graph with a best-fit
line
2. The line graph
There are times when using a best-fit
line on a scatter graph is not very useful. Often a best-fit
line, since it is an average, does not accurately represent what is really
happening. For example, if you graph the number of sunspots (eruptions
on the surface of the sun) that appear over a period of time, it will not
be well represented by a scatter graph with a best-fit line. The reason
is the number of sunspots is known to oscillate in 11-year cycles. See
Figure 3. Does this graph represent the data well?
What the best fit line in Figure 3 really
shows is an average of the number of sun spots over roughly a 120 year
period. This doesn’t tell you much about the actual number of sunspots
in any one year. Now look at Figure 4. This is a graph of the same data
treated as a line graph (i.e. connect the dots). I think you will
agree that the line graph in Figure 4 is more representative of the data
because it makes it easy to see what happened from year to year.
Figure 3: scatter graph with a best-fit
line
Figure 4: line graph
3. Calculation of Slope
Graphical data can be manipulated in
many different ways that can yield useful information. One way that a scatter
graph with best-fit line or a line graph can be useful is in the determination
of slope. Slope is a way of expressing the rate at which the experimental
data is changing.
Slope is defined as the "rise over the run"
or numerically,
m= y2 - y1/ t2 - t1
where m= slope
y1 = a data point at time 1
y2 = a data point at time 2
t1 = time 1 and t2 = time 2
This gives you the rate at which
your data is changing (an example could be how fast an enzyme is making
a product). The slope can be calculated for the whole experiment or for
a particular time frame in the experiment.
For example, return to Figure 1. How
do you calculate the slope between age 4 and age 14? Well t1 = 4 years
and t2 = 14 years. y1 = the data point at time 1 which is 0 points, and
y2 = the data point at time 2 which is about 95 points. Plug the numbers
into the slope equation and you should get
m= 95 points - 0 points / 14 years
- 4 years
m = 9.5 points per year
This is the average rate at which the
math score should increase per year. However, you can see that the increase
in score is not the same for each year. What if you want to determine the
rate of increase of the score between 12 and 14 years old? Slope can do
that too because slope can be applied to a small portion of the graph.
Just make t2 =
14 years and t1 = 12 years. Make y2 =
95 points and y1 = about 60 points. If you got about 17 points per year,
go on to the column graph!
4. The Column Graph
This is a type of graph that shows
frequency distributions well. A frequency distribution measures
how many of a certain thing falls into a specific category. For example,
you are interested in the age of the Pacific Yew Trees in a forest. This
tree is important as a source of anticancer drugs. You go out into the
forest and take core samples of many yew trees. Then you count the rings
in the core samples to give you the age of each tree. Now you are ready
to construct a column graph.
Construction of a Column Graph
1) Divide your data into convenient categories.
E.g. First age category: 0 to 50yrs, Second age category: 51 to 100yrs,
Third: 101 to 150yrs, etc.
2) Draw out the axes of a graph with
the age categories on the "X" axis. In this case, age is the independent
variable.
3) Label the "Y" axis as "# of individuals"
and scale the axis appropriately. Now count the number of individuals in
each age category and draw a bar to that height on the "Y" axis. As this
is what is being measured, it is the dependant variable.
4) Don’t forget a descriptive title. For
an example of a column graph, see Figure 5.
Figure 5: column graph
What you have produced is a graph with
age categories and in each of these age categories is the number of yew
trees of that age. You have created a graph of the frequency distribution
of the ages of the yew trees in that forest. It is now very easy to see
which age is the most common age of the yew trees in the forest you surveyed.
Now you are ready to tackle some graphs
on you own!
Graphing Assignments
Work individually but you may discuss
methods with your fellow students. Construct good and complete graphs with
data provided. Use descriptive labels and titles! You may be called on
to place your graphs on the board for discussion.
Assignment 1
a. Plot the first plant’s root grow as
a line graph using the data provided. Make the graph by hand in the manner
described in the first few pages of this exercise.
b. For the first plant you should calculate
slope to determine the growth rate over the whole experiment and for the
time interval between day 8 and day 12.
c. Plot the second plant’s root growth on
the same graph. This makes it easy to compare data from plant 1 to
plant 2. For the second plant you should also include slope calculations
to determine the growth rate over the whole experiment and for the time
interval between day 8 and day 12.
d. Using the same data, use Cricketgraph™
to make a single scatter graph with a best-fit line for both plants. Label
and title.
Data for assignment 1
| Plant 1 |
|
Plant 2 |
|
|
|
|
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| root length |
age in days |
root length |
age in days |
| 1cm |
0 |
0.5cm |
0 |
| 3 |
3 |
1 |
2 |
| 5 |
6 |
2 |
5 |
| 6.5 |
8 |
3 |
8 |
| 7 |
10 |
5 |
10 |
| 8.5 |
13 |
8 |
12 |
| 9 |
14 |
9.5 |
14 |
Questions for Assignment 1
a. From the hand drawn graph, what is
the slope of the root growth rate for plant 1 over the 14-day period and
from day 8 to day 12? Remember to state the slopes in the form of a rate.
b. From the hand drawn graph, what is the
slope of the root growth rate for plant 2 over the 14-day period and from
day 8 to day 12? Remember to state the slopes in the form of a rate.
c. From your line graphs, describe the
difference in growth rate of the roots of plant 1 and plant 2.
d. Compare the line graphs with the scatter
graphs. Which graph type best represents this data and why?
Assignment 2
a. This time construct a column
graph using Cricketgraph™ for the California Live Oak, using the data provided
for assignment 2.
b. Construct a column graph using Cricketgraph™
for the Coulter Pine, using the data provided for assignment 2.
Data for assignment 2 (a count of frequency
of age of 2 species of trees in 10 square Km. of forest near the summit
of Mount Palomar in San Diego County, CA)
| Calif. Live Oak |
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Coulter Pine |
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| # of Trees |
Age |
# of Trees |
Age |
| 27 |
0 to 25yrs |
1 |
0 to 25yrs |
| 12 |
26 to 50 |
2 |
26 to 50 |
| 8 |
51 to 75 |
8 |
51 to 75 |
| 45 |
76 to 100 |
33 |
76 to 100 |
| 56 |
101 to 125 |
43 |
101 to 125 |
| 121 |
126 to 150 |
29 |
126 to 150 |
| 237 |
151 to 175 |
40 |
151 to 175 |
| 261 |
176 to 200 |
36 |
176 to 200 |
| 234 |
201 to 225 |
38 |
201 to 225 |
| 278 |
226 to 250 |
23 |
226 to 250 |
| 302 |
251 to 275 |
18 |
251 to 275 |
| 345 |
276 to 300 |
2 |
276 to 300 |
| 326 |
301 to 325 |
0 |
301 to 325 |
| 288 |
326 to 350 |
1 |
326 to 350 |
| 218 |
351 to 375 |
0 |
351 to 375 |
| 223 |
376 to 400 |
0 |
376 to 400 |
| 103 |
401 to 425 |
0 |
401 to 425 |
| 2 |
426 to 450 |
0 |
426 to 450 |
| 0 |
451 to 475 |
0 |
451 to 475 |
| 0 |
476 to 500 |
0 |
476 to 500 |
Questions for assignment 2
a. Are these column graphs good for determining
the age interval which contains the greatest and least number of California
Live Oaks and Coulter Pines in this forest? Why or why not?
b. Are these column graphs good for determining
the average age of California Live Oaks in this forest? Why or why not?
c. Describe the difference in the frequency
distribution of ages of the California Live Oaks and the Coulter Pines
in this forest.
Assignment 3
a. Using Cricketgraph™, make a line graph
for the data provided.
Data for assignment 3 (length of small
intestine in mouse embryos during development; each data point is an average
of 10 mouse embryos)
| Length of small intestine |
Days post conception |
| 0 |
1 |
| 0 |
2 |
| 0 |
4 |
| 0.05cm |
5 |
| 0.2cm |
6 |
| 1.2cm |
9 |
| 2.3cm |
11 |
| 3.8cm |
14 |
| 4.1cm |
16 |
| 4.3cm |
18 |
| 4.4cm |
19 |
Questions for assignment 3
a. Calculate the slope of the line for
the whole experiment, between day 5 and 9 and between day 9 and 14. State
the three rates of the development.
b. Does the over all rate of development
mean very much or is there a way of stating the rate of development for
this experiment that might be more meaningful?
c. Do you think that the data in this graph
could be easily extrapolated to day 23? Why or why not?
This lab exercise was developed in
part with the support of National Science Foundation (Division of Undergraduate
Education) grant # DUE 9552290
and California Community College Chancellor’s
Office (Curriculum and Instructional Resources Division, Special Projects)
grant # FII 95-621-001.
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