Lesson 2: Constructing Line Graphs
and Bar Graphs
Selected Content Standards
Benchmarks Addressed:
D-1-M
Systematically collecting, organizing, describing, and displaying data
in charts, tables, plots, graphs, and/or spreadsheets
D-2-M
Analyzing, interpreting, evaluating, drawing inferences, and making
estimations, predictions, decisions, and convincing arguments based
on organized data (e.g., analyze data using concepts of mean, median,
mode, range, random samples, sample size, bias, and data extremes)
GLEs Addressed:
Grade 5
28. Use various types of charts and graphs, including double bar graphs,
to organize, display, and interpret data and discuss patterns verbally
and in writing (D-1-M) (D-2-M) (P-3-M) (A-4-M)
29. Compare and contrast different scales and labels for bar and line
graphs (D-1-M)
Grade 6
29. Collect, organize, label, display, and interpret data in frequency
tables, stem-and-leaf plots, and scatter plots and discuss patterns in
the data verbally and in writing (D-1-M) (D-2-M) (A-3-M)
30. Describe and analyze trends and patterns observed in graphic
displays (D-2-M)
Lesson Focus
This lesson continues instruction on how to construct the various types of
graphs. In this lesson, students learn to construct line graphs and bar
graphs from tables. They will be expected to analyze various types of
graphs given to them in a contextual form.
GEE 21 Connection
Students will be required to:
• Organize data in a frequency table
• Construct, label, and scale line graphs and bar graphs.
• Interpret and summarize a set of experimental data presented in a table,
line graph, or bar graph in context.
• Draw conclusions from a variety of graphs, charts, and tables.
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Translating Content Standards into Instruction
This lesson will teach a student how to choose the best display for data and
how to set up a graph that displays the data clearly. Two types of graphs will
be covered in this lesson – the line graph and the bar graph. In addition, we
will look at frequency tables. This is another method of organizing data. They
can be used to draw frequency polygons, a type of line graph. In order for the
students to understand each type of display, the lesson should be activity
based. Clear and concise instructions for constructing each graph will be
available, and students should have a chance to construct their own. Once
students have learned each construction they should be presented with some
different types of data and asked how that data could best be displayed.
Students should be given a chance to see data displayed in a table and on the
resulting graph. The teacher should talk about the various aspects of the graph
used. Students should also get a chance to generate a graph of the their own.
A. Frequency Tables and Line Graphs
Line graphs are sometimes called broken-line graphs. A line graph usually
displays data that are measured rather than counted. A graph of this sort uses
line segments to show changes and relationships between quantities. A small
amount of data can be graphed individually. A large amount of data can be
organized in a frequency table and shown in a line graph called a frequency
polygon. Both are shown below.
This is an example of a table with a small amount of data and its accompanying
graph. The table below gives the lows over a seven-day period in South
Louisiana as a cold front moved through the state. (This is also available on
Teacher Blackline #1 for lesson #2.)
Day
Temperature
October
October
October
October
October
October
October
(Degrees Fahrenheit)
73o
71o
71o
60o
42o
35o
41o
22
23
24
25
26
27
28
How to Construct a Line Graph
1. On a sheet of graph paper draw a horizontal and vertical axis.
2. Make a decision as to what to put on the horizontal and vertical
axis. The measurement data is usually put on the vertical axis.
Time usually goes on the horizontal axis.
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3. Decide how you will scale and label each axis.
a. The scales will probably be different on each axis. The tic
marks should be equally spaced on each axis. Normally, each
axis begins with zero. However, if the measurement data is
large and we want to show the details of that data, we need to
mark the lower part of the vertical axis with a jagged line to
show that numbers lower than the numbers we are interested in
are being omitted. For instance, we might be showing dollar
value of sales from $50,000 to $100,000. We would draw a
jagged piece from the origin with our first number being
50,000.
b. Each axis should be labeled so that the viewer knows what
information is being represented.
4. Plot each point and then connect the points in order with line
segments.
5. Select an appropriate title and write it above the graph.
Once you have gone over the information above and shown the students
how to draw a line graph, hand out Student Worksheet #1. The price of the
gasoline is in dollars and cents. They should understand that the scaling on
the vertical axis does not have to be to the nearest penny. They can scale by
$.10 or $.20 without loss of accuracy.
B. Making a frequency table
Statisticians use a frequency table to organize large amounts of data. To make
such a table
1. List the classes of data.
2. Tally the data. Each number should fall into a single class. This may be a
single number or it may be a range of numbers.
3. Count the tally marks to list the frequency of each class.
In the example for this lesson, the class will be a single number.
Example: Mrs. Johnson took a poll of her class as to their favorite sandwich.
Once the choices were tallied, the four favorite sandwiches were listed and
students were asked to pick which one they liked the best. The results were as
follows:
Type of sandwich
Tally
Number
Tuna fish
|||| |
6
Ham and cheese
|||| |||| |
11
Toasted cheese
||||
5
Roast Beef
|||| ||||
9
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Information such as that on page 17 is better shown as a bar graph.
Instructions for such a graph are given below. Students can learn to construct a
frequency table and a bar graph by using the same exercise in the example
above. Ask the students to list their favorite sandwich, list the 4 favorites, and
then have the students pick their favorite from the four. Count the votes by
setting up a frequency table as shown on page 17. After the students have
learned to construct a bar graph with the example below, they can construct a
bar graph with the four favorite sandwiches above. You could use favorite ice
creams, favorite desserts, or favorite snacks in place of sandwiches, if you
prefer.
Student Worksheet #2 has a table that the students should use to build a bar
graph using the data provided on total salaries paid by the NBA teams in the
midwest division of the Western Conference.
C. Bar Graphs
Bar graphs display categorical data clearly. Categorical data are data that can
be grouped or categorized such as favorite colors, makes of cars, or students’
favorite pets. A bar graph uses horizontal or vertical bars to compare the
number of items in each category.
How to Construct a Bar Graph
1. Begin by drawing a vertical and horizontal axis. Select a
convenient scale for measuring the numbers in each category.
Round large numbers. Use tic marks to indicate points on a
scale. This will go on the vertical axis, if the bars are vertical
and on the horizontal axis, if the bars are horizontal.
2. Label the remaining axis with the names of the categories.
There will be one bar for each category measured. Each bar
should be of the same width and equally spaced. Draw each bar
marking each length or height with the number in the category.
3. Label each axis.
4. Select an appropriate title and put it at the top of the page.
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The table below is on Teacher Blackline #2. Use it to show the students how
to construct a bar graph. Stress the importance of correct scaling on the
frequency axis. Be sure students understand that the graph is not complete
until the vertical and horizontal axes are labeled with the correct information
and the graph is given a title.
Favorite Student After School Activity
Use Computers
Activity
Earn Money
Play Sports
Series1
Talk on Phone
Visit with friends
0
50
100
150
200
Number
Activity
Number
Visit with
175
friends
Talk on phone
168
Play sports
120
Earn money
120
Use Computers
65
The students at a local high
school were polled concerning
their favorite activity. Their
choices are listed above.
Sources of Evidence of Student Learning
Evidence that the student has a grasp of the material will be through teacher
observation of their work as they construct each of the graphs. It is important
that they understand how to construct each of these graphs. The open-ended
problems on the GEE 21 could very well be the type of problem that asks
students to organize and display data in one of the required graphs.
GEE 21 Connection
These benchmarks may be assessed either by multiple-choice questions or a
free response question. Below are examples of what students might see in a
multiple-choice question. These were taken from the Illinois and Texas state
tests, either of which can be accessed on the Louisiana Department of
Education web site. An (*) indicates the correct answer.
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1. During which 10-year period did automobile sales increase the most?
A.
B.
C.
D.
E.
Vehicles Sold
1940-1950
1950-1960*
1960-1970
1970-1980
1980-1990
Year
Illinois Standards Achievement Test
2. The emergency room staff at a hospital sees more patients on Friday and
Saturday nights than on other nights. The following graph shows the
average number of patients seen by the emergency-room staff on each
night of the week for the past year.
Texas Assessment of Academic Skills
Which is the best estimate of the average number of patients seen per
night from Sunday through Thursday?
A. 60
B. 70 *
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C. 80
20
D. 90
Data Analysis, Probability and Discrete Math
3. The graph shows the gasoline efficiency of several cars.
Which statement is supported by the data?
A. Car 1 can travel only half the distance of Car 4 on the same amount of
gas.
B. The median value for efficiency of all the cars is 30 miles per gallon.
C. All the cars meet the federal guideline for fuel efficiency of at least 21
miles per gallon.
D. Each car can travel a minimum of 350 miles on a tank of gas.
E. The difference in gas mileage between the most efficient car and the
least efficient car is more than 15 miles per gallon.*
Texas Assessment of Academic Skills
Attributes of Student Work at the “Got-It” level
For the line graph• Students should be able to work independently with few questions for
classmates or teacher
• The scaling is displayed at equal intervals on both axes. Using graph
paper is so helpful.
• The graph is appropriately named.
• Both axes are labeled correctly.
• The data displayed is accurate.
For the bar graph• Students should be able to work independently with few questions for
classmates or teacher.
• There is one bar for each category and they are of equal width. Each bar
should be appropriately named.
• The scaling is displayed at equal intervals on both axes. Using graph
paper is also helpful.
• The graph is appropriately named.
• Both axes are labeled correctly.
• The data displayed is accurate.
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Finally, students should be able to look at data and tell which of the two graphs
would be appropriate. The bar graphs make comparisons among several items
in a given category. The line graphs are used to show the behavior of a
variable. Ask the students which graph should be used to display:
1. The number of points scored by the teams in the NBA in the last series of
games. (bar)
2. Manuel’s weight over a period of years. (line)
3. An automobile’s value as the gas mileage increases. (line)
4. Sales of different types of pizzas. (bar)
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Data Analysis, Probability and Discrete Math
Lesson 2: Constructing Line Graphs and Bar Graphs
Teacher Blackline #1
Making a line graph –
Day
October
October
October
October
October
October
October
22
23
24
25
26
27
28
Temperature
(Degrees
Fahrenheit)
73o
71o
71o
60o
42o
35o
41o
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Data Analysis, Probability and Discrete Math
Lesson 2: Constructing Line Graphs and Bar Graphs
Teacher Blackline #2
Making a bar graph –
Activity
Number
Visit with friends
Talk on phone
Play sports
Earn money
Use Computers
175
168
120
120
65
The students at a local high
school were polled concerning
their favorite activity. Their
choices are listed above.
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Lesson 2: Constructing Line Graphs and Bar Graphs
Student Worksheet #1
The table below shows the average price of gasoline over a twelve year period.
Gasoline Prices for Unleaded Regular
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
Price
$.69
$.94
$1.27
$1.41
$1.32
$1.22
$1.21
$1.19
$0.96
$0.93
$0.91
$0.99
$1.14
1. Make a line graph of the data.
2. Answer the following questions concerning the data.
a) What is the year with the highest annual cost? With the lowest annual
cost?
b) What is the greatest difference when comparing consecutive years? Why
might it be different each month?
c) What is the overall pattern?
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Lesson 2: Constructing Line Graphs and Bar Graphs
Student Worksheet #2
Below is a table showing the total salaries paid for each of the NBA teams in the
Pacific division in the Western Conference of the NBA. Use this to construct a
bar graph showing this information.
Sacramento
LA Lakers
Portland
Seattle
Phoenix
LA Clippers
Golden State
$46.3
$58.8
$86.5
$50.6
$53.5
$29.6
$41.8
million
million
million
million
million
million
million
Will your bars be horizontal or vertical?
• Vertical bars: Categories go on the horizontal axis
• Horizontal bars: Categories go on the vertical axis
Select a convenient scale for measuring the salaries. Use tic marks to indicate
points on the scale.
Label the remaining axis with the names of the teams. There will be one bar for
each team. Each bar should be of equal width. The bars should be equally
spaced.
Label each axis. Be sure that an observer knows what the numbers represent.
Select an appropriate title and put it at the top of the page.
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Lesson 2: Constructing Line Graphs and Bar Graphs
Answer Keys
Answers to problems on Teacher Blacklines are provided in the notes to the teacher.
Student Worksheet 2: The bar graph is shown below.
100
80
60
Series1
40
20
0
Sa
cr
am
LA ent
La o
ke
Po r s
rtl
an
Se d
at
Ph tle
LA oe
C nix
G lip
ol
p
d e ers
n
St
at
e
Team Salary (millions of
dollars)
NBA Teams and Their Salaries
Western Conference Pacific Division
Student Worksheet 1: The line graph is shown below.
Price of Gasoline
$1.60
$1.40
$1.20
Price
$1.00
$0.80
$0.60
$0.40
$0.20
$0.00
1 2 3 4 5 6 7 8 9 10 11 12 13
Year Beginning in 1978
2. a) 1981
b) A difference of $0.33 between 1979-80. The values are yearly averages so
the monthly values can be higher or lower than those shown.
c) The values fluctuate, but over time the prices increase.
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