Lessons 6.4 and 6.5
BAR GRAPHS
LINE PLOTS
FREQUENCY TABLES
HISTOGRAMS
Learn to display and analyze data in bar
graphs.
Learn to organize data in line plots,
frequency tables, and histograms.
Vocabulary
bar graph
double-bar graph
frequency
frequency table
line plot
histogram
A bar graph can be used to display and
compare data. A bar graph displays
data with vertical or horizontal bars.
Example 1: Reading a Bar Graph
Use the bar graph to answer each question.
Which biome in the
graph has the least
average summer
temperature?
Find the lowest bar.
The coniferous forest has
the least average summer
temperature.
Example 1B: Reading a Bar Graph
Use the bar graph to answer each question.
Which biomes in the
graph have an average
summer temperature of
30C or greater?
Find the bar or bars
whose heights measure
30 or more than 30.
The grassland and the
rain forest have average
summer temperatures of
30C or greater.
White board practice:
Use the data to make a bar graph.
Tickets Sold
Grade 6
Grade 7
Grade 8
310
215
285
White board practice: Solution
Use the data to make a bar graph.
Step 3: Title the graph and label
the axes.
Tickets Sold
Grade 6
Grade 7
Grade 8
310
215
285
Tickets Sold
350
300
Tickets
Step 1:Find an appropriate scale
and interval. The scale
must include all of the
data values. The interval
separates the scale into
equal parts.
Step 2:Use the data to
determine the lengths of
the bars. Draw bars of
equal width. The bars
cannot touch.
250
200
150
100
50
0
Grade
6
Grade
7
Grade
Grade
8
A double-bar graph shows two
sets of related data.
Example 2: Problem Solving Application
Make a double-bar graph to compare the data in
the table.
Club Memberships
Club
Art
Music Science
Boys
12
6
16
Girls
8
14
4
Understand the Problem
You are asked to use a graph to compare the
data given in the table. You will need to use all of
the information given.
Example 2 Continued
Determine appropriate scales
for both sets of data.
Use the data to determine the
lengths of the bars. Draw bars
of equal width. Bars should be
in pairs. Use a different color
for boy memberships and girl
memberships. Title the graph
and label both axes.
Include a key to show what
each bar represents.
White board practice:
Make a double-bar graph to compare the data in
the table.
Club Memberships
Club
Band
Chess
Year Book
Boys
9
14
16
Girls
11
7
15
Understand the Problem
You are asked to use a graph to compare the
data given in the table. You will need to use
all of the information given.
White board practice: Solution
Determine appropriate scales
for both sets of data.
Club Memberships
Memberships
16
14
12
10
Boys
Girls
8
6
4
2
0
Chess
Club
Band
Use the data to determine the
lengths of the bars. Draw bars
of equal width. Bars should be
in pairs. Use a different color
for boy memberships and girl
memberships. Title the graph
and label both axes.
Year Book
Include a key to show what
each bar represents.
The frequency of a data value is the
number of times it occurs.
A frequency table tells the number of
times an event, category, or group occurs.
Example 3: Using Tally Marks to Make
a Frequency Table
Students in Mr. Ray’s class recorded their
fingerprint patterns. Which type of pattern do
most students in Mr. Ray’s class have?
whorl loop
whorl loop
arch
arch
loop
loop
arch
whorl arch
arch
whorl arch
whorl
loop
Make a table to organize the data.
Students in Mr. Ray’s class recorded their
fingerprint patterns. Which type of pattern do
more students in Mr. Ray’s class have?
whorl loop
whorl loop
arch
arch
loop
loop
arch
whorl arch
arch
whorl arch
whorl
Step 2: For each fingerprint,
make a tally mark in the
appropriate column.
loop
Number of Fingerprint
Patterns
Whorl
llll
Step 1: Make a column for each
fingerprint pattern.
Arch
Loop
llll l
llll
Most students in Mr. Ray’s
class have an arch
fingerprint.
White board practice:
Students in Ms. Gracie’s class recorded their
fingerprint patterns. Which type of pattern do
more students in Ms. Gracie’s class have?
whorl loop
whorl loop
arch
whorl loop
whorl
loop
whorl whorl arch
arch
whorl arch
loop
Make a table to organize the data.
White board practice: Solution
Students in Ms. Gracie’s class recorded their
fingerprint patterns. Which type of pattern do
more students in Ms. Gracie’s class have?
whorl loop
whorl loop
arch
whorl loop
whorl
loop
whorl whorl arch
arch
whorl arch
loop
Number of Fingerprint
Patterns
Whorl
Arch
Loop
llll ll
llll
llll
Step 1: Make a column for each
fingerprint pattern.
Step 2: For each fingerprint, make
a tally mark in the appropriate
column.
Most students in Ms. Gracie’s
class have a whorl fingerprint.
A line plot uses a number line and x’s
or other symbols to show frequencies
of values.
Example 4: Making a Line Plot
Students collected tennis balls for a project.
The number of balls collected by the
students is recorded in the table. Make a line
plot of the data.
Tennis Balls Collected
10
14
11
16
11
10
14
10
15
15
10
11
Step 1: Draw a number line.
Step 2: For each tennis ball, use an
x on the number line to represent
how many were collected.
x
x x
x x
x x
5 6
7 8
x x
x x x
9 10 11 12 13 14 15 16
White board practice:
Students collected aluminum cans for a
project. The number of cans collected by the
students is recorded in the table. Make a line
plot of the data.
Cans Collected
5
7
11
14
11
5
7
14
14
5
15
11
Write board Practice: Solution
Students collected aluminum cans for a
project. The number of cans collected by the
students is recorded in the table. Make a line
plot of the data.
Cans Collected
5
7
11
14
11
5
7
14
14
5
15
11
Step 1: Draw a number line.
Step 2: For each aluminum can,
use an x on the number line to
represent how many were collected.
x
x
x
x
x
5 6
7 8
x
x
x
x
x
x x
9 10 11 12 13 14 15 16
Example 5: Making a Frequency Table w/ Intervals
Use the data in the table to make a frequency
table with intervals.
Pages Read Last Weekend
12
15
40
19
7
5
22
34
37
18
Example 5 Continued
Use the data in the table to make a frequency
table with intervals
Pages Read Last Weekend
Number
Frequency
1–10
2
11–20
4
21–30
1
31–40
3
Step 1: Choose equal intervals.
Step 2: Find the number of data values in each interval.
Write these numbers in the “Frequency” row.
This table shows that 2 students read between 1 and 10
pages, 4 students read between 11 and 20 pages, 1
person read between 21 and 30 pages, and 3 people read
between 31 and 40 pages last weekend.
White board practice:
Use the data in the table to make a frequency
table with intervals.
Number of Miles Driven on Saturday
17
29
9
19
7
5
27
34
21
38
White board practice: Solution
Use the data in the table to make a frequency
table with intervals.
Number of Miles Driven on Saturday
Number
1–10
11–20
21–30
31–40
Frequency
3
2
3
2
Step 1: Choose equal intervals.
Step 2: Find the number of data values in each interval.
Write these numbers in the “Frequency” row.
This table shows that 3 people drove between 1 and 10
miles, 2 people drove between 11 and 20 miles, 3 people
drove between 21 and 30 miles, and 2 people drove
between 31 and 40 miles on Saturday.
A histogram is a bar graph that shows
the number of data items that occur
within each interval.
Example 6: Making a Histogram
Use the frequency table in Example 5 to make a histogram.
Pages Read Last Weekend
Number
Frequency
1–10
2
Step 1: Choose an
appropriate scale and interval.
Step 2: Draw a bar for the
number of students in each
interval. The bars should
touch but not overlap.
Step 3: Title the graph and
label the axes.
11–20
4
21–30
1
31–40
3
White board practice:
Use the frequency table from your last white board practice
to make a histogram.
Number of Miles Driven on Saturday
Number
1–10
11–20
21–30
Frequency
3
2
3
31–40
2
White board practice: Solution
Use the frequency table from your last white board
practice to make a histogram.
Number of Miles Driven on Saturday
Number
1–10
11–20
21–30
31–40
Frequency
3
2
3
2
Step 2: Draw a bar for the
number of students in each
interval. The bars should touch
but not overlap.
4
People
Step 1: Choose an appropriate
scale and interval.
Number Miles Driven on
Saturday
3
2
1
0
Step 3: Title the graph and label
the axes.
1- 10
11- 20
21- 30
31- 40
Number of Miles
Lesson Quiz:
1. Students listed the number of days they spent
on vacation in one year. Make a tally table with
intervals of 5.
2, 18, 5, 15, 7, 10, 1, 10, 4,
16, 7, 11, 17, 3, 8, 14, 13, 10
Use the bar graph to answer each question.
Student Pet Survey
2. Which animal was least popular among students?
bird
3. Which pet was more popular to twice as many
students as rabbits were? dog
4. Use your tally table from problem 1 to make a
frequency table.
5. Richard listed the number of books lent by
their school library each day. Create a tally
table with intervals of 5.
3, 18, 6, 14, 8, 10, 1, 10, 4, 17, 8, 11, 17, 4, 8,
14, 14, 10
2. Create a frequency table
for the given data.