Lessons 6.4 and 6.5

BAR GRAPHSLINE PLOTS

FREQUENCY TABLESHISTOGRAMS

Lessons 6.4 and 6.5

Learn to organize data in line plots, frequency tables, and histograms.

Learn to display and analyze data in bar graphs.

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 30C 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 30C or greater.

White board practice:

Use the data to make a bar graph.

285215310

Grade 8Grade 7Grade 6

Tickets Sold

White board practice: Solution

Use the data to make a bar graph.

285215310

Grade 8Grade 7Grade 6

Tickets SoldStep 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.

Step 3: Title the graph and label the axes.

Grade 6

Grade 7

Grade 8

0

50

100

150

200

250

300

350Tickets Sold

Grade

Tic

kets

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.

4148Girls

16612Boys

ScienceMusicArtClub

Club Memberships

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.

15711Girls

16149Boys

Year BookChessBandClub

Club Memberships

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.

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.

0

2

4

6

8

10

12

14

16

Chess Band Year Book

Boys

Girls

Club

Club Memberships

Mem

ber

ship

s

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 whorl

loop arch whorl arch

arch whorl arch 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 whorl

loop arch whorl arch

arch whorl arch loop

Step 1: Make a column for each fingerprint pattern.

Step 2: For each fingerprint, make a tally mark in the appropriate column.

LoopArch Whorl

Number of Fingerprint Patterns

l l l l l l l l l l l l l

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?

Make a table to organize the data.

whorl loop whorl loop

arch whorl loop whorl

loop whorl whorl arch

arch whorl arch loop

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?

Step 1: Make a column for each fingerprint pattern.

whorl loop whorl loop

arch whorl loop whorl

loop whorl whorl arch

arch whorl arch loop

Step 2: For each fingerprint, make a tally mark in the appropriate column.

LoopArch Whorl

Number of Fingerprint Patterns

l l l l l l l l l l l l l l

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

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.

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.

111015151014

101116111410

Tennis Balls Collected

x x x x

5 6 7 8 9 10 11 12 13 14 15 16

x x x

x x

x x x

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.

1115514147

511141175

Cans Collected

Write board Practice: Solution

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.

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.

1115514147

511141175

Cans Collected

x x x

5 6 7 8 9 10 11 12 13 14 15 16

xx

x xx

x x x x

Example 5: Making a Frequency Table w/ Intervals

Use the data in the table to make a frequency table with intervals.

183734225

719401512

Pages Read Last Weekend

Example 5 Continued

Use the data in the table to make a frequency table with intervals

Frequency

31–4021–3011–201–10Number

Pages Read Last Weekend

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.

2 4 1 3

Step 1: Choose equal intervals.

Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” row.

White board practice:

Use the data in the table to make a frequency table with intervals.

382134275

71992917

Number of Miles Driven on Saturday

White board practice: Solution

Use the data in the table to make a frequency table with intervals.

Frequency

31–4021–3011–201–10Number

Number of Miles Driven on Saturday

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.

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.

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.

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.

Frequency31–4021–3011–201–10Number

Pages Read Last Weekend

2 4 1 3

White board practice:

Use the frequency table from your last white board practice to make a histogram.

Frequency

31–4021–3011–201–10Number

Number of Miles Driven on Saturday

3 2 3 2

White board practice: Solution

Use the frequency table from your last white board practice to make a histogram.

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.

0

1

2

3

4

1- 10 11- 20 21- 30 31- 40

Number Miles Driven on Saturday

Number of Miles

Peop

le

Frequency

31–4021–3011–201–10Number

Number of Miles Driven on Saturday

3 2 3 2

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.

2. Which animal was least popular among students?

3. Which pet was more popular to twice as many students as rabbits were? dog

bird

Student Pet Survey

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.