Introduction to Graphs
Examine the following table and graph:
Grade Distribution for Students Enrolled in Science Class
1. Both of these figures display the same information but in different
ways. Which figure is easier to understand? Explain why you think so.
2. If you need to get specific data, such as the exact number of stu-
dents who earned a B, which figure would you use? Explain your
answer.
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A B C D F
Number of students
Grade
Grade Distribution of Students Enrolled in Science Class
Grade Number of students
A22
B79
C50
D9
F2
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Introduction to Graphs, continued
Choosing the Right Graph
Data tables provide an organized way of viewing information, and
graphs are pictures of the information in a data table. Sometimes it is
faster and easier to interpret data by looking at a graph. It is important
to choose the type of graph that best illustrates your data. The following
table summarizes the best uses for three of the most common graphs:
Type of graph
Bar graph
Pie graph
Line graph
Best use for this graph
A bar graph is best used for comparing
data quickly and easily, such as the grade
distribution of students enrolled in science
class or the growth of plants in different
pots.
A pie graph is best used for showing
percentages, such as the percentage
of the student body who picked certain
entrees for lunch or the percentage of
your allowance that will go toward pur-
chasing various things.
A line graph is best used for looking at
changes over time, such as the number
of bathing suits sold each month during
the year or the change in your sister’s
height throughout the year.
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Number of students
Grade
Corn chip pie
15%
Cosmic pizza
63%
Chicken Kiev
18%
Beef stuff
4%
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J F M A M J J A S O N D
Number of bathing suits sold
Month
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Grade Distribution of Students Enrolled in Science Class
Percentage of Students Picking Various Lunch Entrees
Number of Bathing Suits Sold Each Month
Choose the Graph
What graph type do you think best presents each set of data? Explain.
1. The percentage of rabbits preferring various foods
2. Albert’s grades for each month of the school year
3. The pH of solutions in experimental test tubes
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Introduction to Graphs, continued
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Grade in
Month science class
September 98
October 94
November 88
December 78
January 82
Food Percentage preferring that food
Skippy’s Rabbit Chow 32
Homemade rabbit food 13
Happy Rabbit 10
Joe’s Special Food for Rabbits 44
Premium Rabbit Nutrition Diet 1
Test-tube number pH
1 6.7
27.1
37.4
47.1
57.0
Grade in
Month science class
February 83
March 86
April 81
May 97
Grasping Graphing
When you bake cookies, you must use the right ingredients to make the cookies turn out
right. Graphs are the same way. They require the correct ingredients, or components, to
make them readable and understandable.
Bar and Line Graphs
• First, set up your graphs with an x-
axis and a y-axis. The x-axis is hori-
zontal, and the y-axis is vertical as
shown in the example at right. The
axes represent different variables in
an experiment.
• The x-axis represents the independent
variable. The independent variable is
the variable whose values are chosen
by the experimenter. For example, the
range of grades is the independent
variable.
• The y-axis represents the dependent
variable. The values for the depend-
ent variable are determined by the
independent variable. If you are
grouping students by grades, the
number of students in each group
depends on the grade they get.
• Next choose a scale for each of the
axes. Select evenly spaced intervals
that include all of your data, as
shown on the grade-distribution bar
graph. When you label the axes, be
sure to write the appropriate units
where they apply.
• Next, plot your data on the graph.
Make sure you double-check your
numbers to ensure accuracy.
• Finally, give your graph a title. A title
tells the reader what he or she is
studying. A good title should explain
the relationship between the vari-
ables. Now your graph is complete!
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y-axis
x-axis
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Number of students
Grade
Grade Distribution of Students Enrolled in Science Class
Independent variable
Dependent variable
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Grasping Graphing, continued
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Amount of daily sunlight Average height of plants
exposure (min) (cm)
50 14.8
60 14.9
95 15.2
75 15.1
110 16.5
135 17.3
100 16.1
30 11.0
Pie Graphs
When you convert data to show percentages, you can use a pie graph.
Pie graphs are shaped like a circle. The size of each “pie slice” is deter-
mined by the percentage it will represent. A full pie is equal to
100 percent, half a pie is equal to 50 percent, and so on.
Like bar and line graphs, pie graphs have independent and depend-
ent variables. The independent variable is whatever the pie or slice of
pie represents. The dependent variable is the size of the pie slice, the
percentage of the whole it represents.
Percentage of Students Picking Percentage of Students Picking Percentage of Students Picking
Various Lunch Entrees Various Lunch Entrees Various Lunch Entrees
Your Turn
For each table (a) identify the independent and dependent variable,
(b) determine the type of graph to use, and (c) provide a title.
1.
a.
b.
c.
25%
25% 25%
50%
50%
100%
25%
2.
a.
b.
c.
Give It a Try
Graph the data below inyour ScienceLog. Don’tforget to do the following:
• Select the appropriate graph type.
• Identify the independent and the dependent variable.
• Choose an appropriate scale.
• Label the axes.
• Give your graph a title.
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Grasping Graphing, continued
Student Number of jelly
beans consumed
Anthony 15
Keiko 28
Leigh Ann 58
Adam 22
Katie 12
Juan 17
Amount of fertilizer Average height of
added to soil (g) plants (cm)
5 13.2
10 14.1
15 14.9
20 15.4
25 16.5
30 17.3
35 16.1
40 11.0
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Interpreting Your Data
Imagine that you are at home taking care of your brother’s dog,
Sparky. At 7
P.M., Sparky starts barking. “He might be hungry,” you
think to yourself. What are some other reasons that Sparky might
bark?
Now suppose that this is the fourth night in a row you’ve taken care of
Sparky. You have noticed that every night at about 7
P.M., Sparky starts
barking. “Ah-ha!” you say to yourself, “There is a pattern here!”
Hidden Patterns
When you collect raw data, patterns are often camouflaged as random
numbers. Part of conducting a successful experiment is analyzing your
data to find any hidden patterns. Two common data patterns you
might see on your graph during an experiment are as follows:
• linear (Your data tend to form a straight line.)
• repeating (Your data cycle repeatedly through the same general
points.)
On the graph below, identify the examples of these two patterns.
a.
b.
b.
a.
0.5
0.4
0.3
0.2
0.1
1 2 3
cm
3
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10 20 30 40 50 60 70 80
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Interpreting Your Data, continued
Graph It!
One of the best ways to identify a pattern is to draw a graph. A graph
turns random data into a pattern that gives specific information.
Mary tested how fast blocks of clay dry under a bright light. She
recorded the time it took different-sized blocks to dry.
Volume of block (cm
3
)
Time to dry (min)
Graph her data in the space below.
Describe the shape of the pattern that emerges from Mary’s data. Mary
hypothesized that the drying time for a clay block was directly pro-
portional to the block’s volume. In other words, her hypothesis pre-
dicted that her data would form a straight line. Was her hypothesis
correct? Explain your answer.
27 8 43 125 16 166 64 91
5 3 7 21 4 37 9 14
Mary had one additional data point
with values of 142 cm
3
and 39 min-
utes. Because this point was different
from her other data points, she de-
cided she had made an error while
performing that trial. To understand
her thinking, plot that point on your
graph above.
TRY THIS!
If you are having trouble telling
whether Mary’s data form a straight
line, try drawing a line from her
lowest data point to the highest
data point. If her data form a
straight line, most of the points
should fall on or be very close to
the line you just drew.
TROUBLESHOOTING
Recognizing Bias in Graphs
Graphs can be used to display your data at a glance. However, graphs can
distort your results if you are not careful. The picture that results may
not be objective, or without bias or distortion. Look at the first graph.
How Much Rain Really Fell?
In the graph below, it appears as though March had drastically more
rainfall compared with an average month. But did that really happen?
Wait! March’s rainfall was only 0.4 cm above average. On the graph,
that looks like a large increase. On the ground, a 0.4 cm increase is
not that much. This graph is biased because it exaggerates the differ-
ence between the two lines. Because the interval between 27.8 cm to
28.7 cm on the y-axis is so small, the difference in rainfall seems very
large and noticeable.
If you increase the interval between numbers on the y-axis, the scale
becomes larger. That makes the difference between the two lines smaller,
as shown below.
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This Year’s Rainfall Versus Average Rainfall
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Amount of rainfall (cm)
Month
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Average rainfall
This year‘s rainfall
January February March
This Year’s Rainfall Versus Average Rainfall
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Recognizing Bias in Graphs, continued
Refer to the graphs on the previous page to answer the following questions:
1. What is the range of values on the y-axis in the second graph?
2. How does the difference between the two lines in the second graph
compare with the difference between the two lines in the first
graph? Which graph is a more accurate picture of the data? Explain.
A Matter of Scale
Here is another example of how the choice of the scale can alter a graph.
In an experiment, seven students tried to mix a solution of salt water
so that its concentration would be exactly 7.00%. When the teacher
tested the concentration of their solutions, he got the following results:
Concentrations of Students’ Solutions
The teacher created the following graph to show the students’ results:
Does this graph give you a clear picture of how the concentrations
varied? Not really. The bars look so much alike that it’s hard to tell the
differences between them.
Bruno Cali Shaun Chazz Jessie Janet Tonya
7.02% 6.99% 7.00% 7.08% 6.97% 7.01% 6.99%
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8.0
7.5
7.0
6.5
6.0
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Concentration %
Student
Concentrations of Students’ Solutions
Name
Concentration
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Recognizing Bias in Graphs, continued
Suppose the teacher decreased the scale of the y-axis. The graph
would then look like the one below. The variation in the students’
results looks much greater, even though it hasn’t changed. This graph
makes it easier to see the small differences.
Graphs with an Attitude
The data in the chart below were recorded by a student measuring the
thickness of four rock layers.
Using the above data, create two graphs in the space below. First
show how similar the measurements are. (Hint: Make the scale of the
y-axis larger. This makes the difference between the measurements
seem smaller.) In your second graph, emphasize the fact that layer C
was slightly thicker than the other layers.
Your Graphs:
ABCD
11.2 10.8 13.5 11.1
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7.1
7.0
6.9
Bruno Cali Shaun Chazz Jessie Janet Tonya
Concentration %
Student
Concentrations of Students’ Solutions
Thickness of Rock Layers
Layer
Thickness
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Recognizing Bias in Graphs, continued
Identifying Bias on Your Own
Graph 1
1. This graph shows that test plant D grew much taller than the other
plants. How is this information misleading?
Graph 2
2. This graph shows that Kendra received a much lower grade in science
class during the fourth quarter. Do you think what appears to be such a
large drop in her grades should worry Kendra? Explain your reasoning.
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52.5
52.0
51.5
51.0
50.5
50.0
49.5
49.0
48.5
A B C D E
Height (cm)
Test plant
Height of Test Plants
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Kendra's score
Quarter
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Kendra’s Scores in Science Class
for Each Quarter