Bio chemistry

NEED ACTIVIY 2 AND 3 DONE 

ACTIVITY 2

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Computer Graphing

Linear Regression

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Introduction to Graphing

Investigation
Manual

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INTRODUCTION TO GRAPHING

Table of Contents

Overview
Objectives
Time Requirements

3 Background
7 Materials
7 Safety
7 Activity
9 Activity 2
11 Activity

3

Overview
Scientific investigation requires the analysis and interpretation of
data. Knowing how to graph and what the different components
mean allow for an accurate analysis and understanding of data. In
this investigation you will practice creating graphs and use some
simple statistical tools to analyze graphs and datasets.

Objectives
• Create graphs from datasets, both by hand and electronically.
• Analyze the data in the graphs.
• Compare the slope of trendlines to interpret the results of an

experiment.

Time Requirements
Activity 1: Graphing by Hand ………………………………….. 20 minutes
Activity 2: Computer Graphing………………………………… 20 minutes
Activity 3: Linear Regression …………………………………… 20 minutes

Key
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Background
Science requires the collection of data to test
hypotheses in order to see if it supports or
does not support ideas behind the experiment.
Collecting data creates a record of observations
from experiments that is needed to ensure the
ideas in a hypothesis are accurate. This allows
the scientist to better understand the processes
they are investigating. Sharing data is critical
since it allows other scientists to examine the
experimental setting and draw conclusions
based on the data obtained. It also allows for
the replication and comparison of data obtained
in the experiment to confirm results and conclu-
sions. This will aid in the understanding of a
scientific principle.

Table 1, shows data from a study of plants. Two
types of plants, wheat and rye, were grown
over 8 weeks, and the height of the plants were
measured in centimeters (cm).

Table 1.

The aim of this experiment was to examine
growth rates of the two plant types in
comparison with each other in order to
find out which grows under a certain set of
environmental circumstances.

When looking at an experiment, the
experimenter is typically looking at variables that
will impact the result. A variable is something
that can be changed within an experiment.
An independent variable is something the
experimenter has control over and is able
to change in the experiment. Time can be a
common independent variable as the total
duration of the experiment can be changed or
the intervals at which data is collected can be
changed. A dependent variable changes based
on its association with an independent variable.
In the data from Table 1, the measured height of
the plant was the dependent variable. The aim of

Height in cm
Week Wheat Plant 1 Wheat Plant 2 Wheat Plant 3 Rye Plant 1 Rye Plant 2 Rye Plant 3

1 2.0 3.0 0.0 0.0 1.0 0.

0

2 3.0 3.0 2.0 1.0 2.0 1.0
3 5.0 5.0 3.0 1.0 2.0 2.0
4 6.0 6.0 4.0 2.0 3.0 3.0
5 7.0 7.0 5.0 3.0 4.0 3.0
6 9.0 8.0 7.0 3.0 4.0 3.0
7 10.0 9.0 7.0 4.0 5.0 4.0
8 10.0 10.0 7.0 5.0 6.0 5.0

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average=

average = ___ 3 __ _

average= 10 + 10 + 7 = 9 cm
3

CAR@UNA~
INTRODUCTION TO GRAPHING

Background continued
experiments is to determine how an independent
variable impacts the dependent variable. This
data can then be used to test the hypothesis
which has been made at the beginning of the
experiment.

Data can be presented in different ways. One
way is to organize it into a table as it is being
collected. When working with a limited amount
of data points, this can be the best option; for
larger studies, the data in data tables can be
overwhelming and difficult to interpret. To help
see the trends in large data sets, a scientist
may rely on summary statistics and graphical
representations of the data.

Summary Statistics
Summary statistics are methods of taking many
data points and combining them into just a few
numbers. The most common summary statistic
is an average, or arithmetic mean. An average
is the sum of a group of numbers, divided by
how many numbers were in the set. To find
the arithmetic mean you find the sum of the data
to be averaged and divide by the number of
data points. For instance: If we wanted to find
the average wheat plant height in week 8 from
the above data we would perform the following
calculations:

Equation 1:

In this equation, x1 indicates the first number in
a data set, x2 would be the second number, and
so on. x n is the last number in the set. The “n”
is the number of items in the set. So a dataset
with 8 numbers would go up to x8. This is the

same “n” that the sum of the numbers is divided
by. Using equation 1 for the wheat plant height
in week 8 would give the following equation.

Since there are 3 wheat plants in week 8, there
are 3 numbers that would be added together
(x1 x2 x3) divided by the number of plants (3).

In science it is important to know how much
variation is found in the data collected. The
most common measurement of variation is the
standard deviation. To calculate the standard
deviation:

1. Calculate the average of a data set.
2. Calculate the difference between each data

point and the average.
3. Square the result.
4. Find the average of these squares. This

yields the variance (σ2).
5. Taking the square root of the variance gives

the standard deviation (SD) as seen in
Table 2.

The standard deviation is an indication of the
distribution of your data. In the example above,
the average height of the plants was 9 cm. The
standard deviation was 1.4 cm. Statistically this
indicates that 68% of the data was within
1.4 cm of the average. In this way it is a useful
tool to gauge how close the results on an
experiment are to each other.

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Table 2.

Height at Week 8 (cm) Difference from Average Differ ence Squared
Wheat Plant 1 10 10 – 9 = 1 (1)2 =

1

Wheat Plant 2 10 10 – 9 = 1 (1)2 = 1

Wheat Plant 3 7 7 – 9 = -2 (-2)2 =

4

Average (10+ 10+ 7) (1 + 1 + 4)
=9cm Variance = =2

3 3

Standard Deviation = -)variance = J2 = 1 .4

Interpreting Graphs in Scientific Literature that the variance in Gr oups 1 and 2 is much
and Popular Press gr eater than in Groups A and B (Figure 2).
Graphs are an excellent way to summarize

This information can be conveyed in the graph and easily visualize data. Car e must be taken
by the use of error bars. Error bars are a graph-when interpreting data from a graph or chart.
ical representation of the variance in a dataset. Information can be lost in summarization and

this may be critical to our
interpr etation. For example, Figure 1.
in Figure 1, the average age
of 4 groups of people was
graphed using a bar graph. A Average Age
bar graph is most useful when 4

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allows for differ ences to be 35
more easily seen at a glance.

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1 and 2 is much greater than

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between Groups A and B.
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However, if we look at a graph 0
of all the data that went into

Group 1 Group 2 Group A Group B

the average age, we can see

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All Data Points

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INTRODUCTION TO GRAPHING

Background continued
The chart below uses the
standard deviations from the
data to show the variance of
the data. There are multiple
ways to represent variance,
so it is important that the
caption of the figure tells the
reader what measure is being
represented by the error bars
(Figure 3).

Standard deviation is highly
influenced by outliers, or
data points that are highly
unusual compared to the
rest of the data, so scientists
frequently use confidence
intervals to represent vari-
ance on graphs. Confidence
intervals express the proba-
bility that a data point will fall
within the error bars, so error
bars with a 99% confidence
interval say that 99% of the
data will fall between the
error bars. Confidence inter-
vals are typically published
at 99%, 95%, or 90%. The
main point is that when error
bars overlap, as they do
when comparing Group 1
with Group 2, it is not strong
evidence that there is a
difference between the two
groups, even if the averages
are far apart. A real differ-
ence is more likely between
Group A and Group B.

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Figure 2.

Figure 3.

■

ACTIVITY

Materials
Needed but not supplied:
• Graphing Software (Excel®, Open Office®, etc.)
• Printer to print graphing paper

Safety
There are no safety concerns for this lab.

ACTIVITY 1
A Graphing by Hand

A common method to look at data is to create
an x,y scatter graph. In this first activity, you will
create two graphs of the data from Table 1.

1. Print 2 copies of the graphing sheet found on
page 13.

2. Title the first graph “Wheat plant height by
week.”

3. Title the second graph “Rye plant height by
week” and set aside for later.

4. At the bottom of the graph there is a space to
label the x-axis. The x-axis runs from left to
right, with smaller numbers starting on the left
and the numbers increasing as you move to
the right.

5. At the left of the graph there is a space to
label the y-axis. The y-axis runs from the
bottom to top of the graph, with smaller
numbers starting at the bottom and the size
of the numbers increasing as you move up.

6. You will now label each axis and decide which
pieces of data will be our x-values and our
y-values, respectively.

7. One method to determine which data should
be your x versus y axis is to think about the
goal of the experiment. The y-axis should be
for data that you measured for, the dependent
variable. In the data set in Table 1, the
scientists were measuring the height each
week. This means that the height is the
dependent variable.

8. Label the y-axis “Height (cm).” It is important
to always include the unit of measurement on
the axis. In this case the unit is centimeters
(cm).

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HEIGHT OF WHEAT PLANT BY WEEK

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TIME (WEEKS)

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ACTIVITY

ACTIVITY 1 continued
9. The x-axis is the independent variable, the

parameter of the experiment that can be
controlled. In this experiment the scientists
were controlling when they measured the
height.

10. Label the x-axis “Time (weeks).” This
indicates that a measurement was taken
each week.

11. Locate the lower left corner of the graph.
This will be the origin of your graph. The
origin on a graph is where both the values of
x and the values of y are 0. If the numbers
in a data set are all positive (i.e. there are no
negative numbers) it is a best practice to set
the origin in the lower left corner. This allows
the view of the data to be maximized.

12. The axes then need to be numerically
labeled. Referring to Figure 4, label each
axis from 0 to 14 along the darker lines.

Figure 4.

13. Starting with the “Wheat Plant 1” data in
Table 1, count over 1 (for week 1) on the
x-axis for time, then count up to 2 from there
to indicate 2 cm. Place a dot at this point

14. Repeat this process for the remaining data
points for “Wheat Plant 1.” Your graph
should now look like Figure 4.

15. Using this same process, graph the data
for “Wheat Plant 2” and “Wheat Plant 3” on
the same graph. You will need to be able to
distinguish the data from each set from each
other. Use different colors, or symbols to
make this differentiation.

16. When complete, compare your graph to
Figure 5. Your exact colors or symbols may
be different, but the data should be in the
same locations.

continued on next page
Figure 5.

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ACTIVITY 1 continued
17. You can now create a legend. The legend is

what shows another person what the points
on your graph represent. Refer to Figure 5
for an example legend for this graph.

18. Create your legend. It is below the x-axis
label as in Figure 5. The legend can be
anywhere on the graph, so long as it does
not interfere with the reading of the graph.

19. Create your own graph of the data for “Rye
plant height by week.” Use the process
outlined in this activity to graph all of the
data for each plant.

ACTIVITY 2
A Computer Graphing

Graphing by hand can be useful for observing
trends in small data sets. However, as the quan-
tity of the data grows it can be useful to graph
using a computer. This activity will give a general
outline of how to graph on a computer. Please
note Microsoft Excel® was used to generate
the figures for this activity. Your exact soft-
ware may look different or have slightly
different labeling than what you will see here.
You may need to refer to the documentation
of your exact program to determine how to
perform a particular step.

In this activity you will graph the data from
Table 1 into your computer.

1. Open a new workbook. This will open a new
sheet (Figure 6).

2. You will see a large sheet with lettered
columns and numbered rows. These letters
and numbers can be used to refer to a

specific cell (the box Figure 6.
where information
can be typed.) For
example the upper left
cell is A1 representing
column A, row 1.

3. Starting in cell A1
type “Week.” In cell
B1 type “Wheat Plant
1.” Continue across
putting each title in
a new cell in the first
row.

4. Move to row 2. Type the corresponding
numbers under the correct column.

5. Continue until your table looks like Table 1.
6. Select the data for Week thru Wheat Plant 3.

You can do this by clicking on cell A1 and
then dragging down and over to cell D9. All
of the data and titles should be selected for
the wheat plant (Figure 7).

Figure 7.

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Chart Title

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10 • • • •
8 • • • • •
6 • • •
4 • • • •
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• Wheat Plant 1 • Wheat Plant 2 • Wheat Plant 3

Height of Wheat Plant by Week

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Time (weeks)

• Wheat Plant 1 • Wheat Plant 2 • wheat Plant 3

CAR@UNA~
ACTIVITY

ACTIVITY 2 continued
NOTE: The next several
steps may vary greatly
depending on the exact
software you are using, but
the goal is the same.

7. Find the menu labeled
“Insert.”

8. Among the “Charts” find
“Scatter,” or “x,y Scatter,”
and click it.

9. A basic graph similar to
Figure 8 should appear.

10. Edit the chart title so that
it matches the one created
in Activity 1. This can
usually be accomplished
by clicking (or double
clicking) on the title and
then typing.

11. You can then add a label
to each axis. This step in
particular is very different
depending on your
software. You will typically
be looking for a menu
option titled “Axis Title.”
You will need to do this
twice, once for each axis.
Your graph should now
look like Figure 9. You will
use this graph again in
Activity 3.

Figure 8.

Figure 9.

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change in y
change in x

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week

ACTIVITY 3
A Linear Regression

Typically if you are graphing using an x,y scatter
plot you are looking for trends (a recognizable
pattern) in your data. In this activity you are
looking to see if there is a trend in height of
the plants over time. More specifically, you are
looking for the rate at which the plants grew.
This rate can be determined from the graph
produced in Activity 2.

1. In your graph from Activity 2, click on a point
from the Wheat Plant 1 dataset.

2. Right-click on the data point and select “Add
Trendline.”

3. Select “Linear.”
4. Select “Display Equation on chart.”
5. The equation displayed on the graph should

read y = 1.2381x + 0.9286. Write this in
“Wheat Plant 1 trendline equation” in the Data
Table.

This is the equation of the line. In its general
form is y = mx + b . The “m” symbol stands for
the slope of the line. The slope is how far the line
rises (y) over a certain distance (x.) The “b” is
called the y-intercept; this is the point at which
the line crosses the y-axis. For the equation from
step 6, this would mean that “1.2381” would be
the slope and “0.9286” would be the y-intercept.
This equation allows you to find the length of
a plant at a certain time. For example, if you
wanted to determine the height of the plant in

week 9, based on this equation the estimated
height would be 12.0715 cm.

Y = 1.2381 * 9 + 0.9286

Y = 12.0715 cm

Since the slope is calculated from
it uses the same units as the dataset. In this
case, this means that the slope has units of .
The slope then means that on average, Wheat
Plant 1 grew 1.2381 centimeters per week.

The y-intercept indicates that at week 0 the
plant was likely 0.9286 cm tall. However, in
this experiment the plants were all grown from
seeds, so at week 0 they should have a height of
0. This information can be added to a trendline
without having to add to a dataset.

6. Right click on the trendline and select
“Format Trendline.”

7. Select “Set Intercept” and set the number to
0. This is setting the y-intercept to 0. You can
do this whenever you know the exact value
of your dependent variable at the 0 for the
x-axis.

8. Write the new trendline in “Wheat Plant 1
trendline corrected” in the Data Table.

9. Using the same procedure, create a corrected
trendline for each additional wheat plant on
the graph. Write the corrected equation for
each in the data table.

10. Based on the corrected trend lines, which
wheat plant grew fastest? Record your
answer in the data table.

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ACTIVITY

ACTIVITY 3 continued
Data Table.

Wheat Plant 1 trendline equation

Wheat Plant 1 trendline corrected

Wheat Plant 2 trendline corrected

Wheat Plant 3 trendline corrected

Wheat plant with fastest growth

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Label (x-axis): _________________________________________________

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NOTES

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DISTANCE LEARNING

Introduction to Graphing
Investigation Manual

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866.332.4478

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Introduction to Graphing
Table of Contents
Overview
Objectives
Time Requirements
Key
Background
Summary Statistics
Interpreting Graphs in Scientific Literature and Popular Press
Materials
Safety
ACTIVITY 1
A Graphing by Hand
ACTIVITY 2
A Computer Graphing
ACTIVITY 3
A Linear Regression
Data Table.

NOTES