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 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.

Grade 6 310

Tickets Sold

Grade 7 215 Grade 8 285

350 300 250 200 150 100 50 Tickets Sold

Step 3: Title the graph and label the axes.

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 Club Memberships Art Music Science Boys Girls

12 8 6 14 16 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 Boys Girls Club Memberships Band Chess

9 11 14 7

Year Book

16 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 Club Memberships 16 14 12 10 8 6 4 2 0 Chess Club Band Year Book

Determine appropriate scales for both sets of data.

Boys Girls

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.

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 arch arch loop arch arch whorl loop loop whorl whorl 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 arch loop arch arch arch whorl loop loop whorl whorl arch whorl arch loop

Number of Fingerprint Patterns

Whorl Arch Loop l l l l l l l l l l l l l 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 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 arch loop arch whorl loop whorl loop whorl whorl whorl 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 Step 1: Make a column for each fingerprint pattern.

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

Number of Fingerprint Patterns

Whorl Arch Loop 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 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 14 10 11 15 16 15 11 10 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 x x x x x 5 6 7 8 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.

5 7 7 14 Cans Collected 11 14 14 5 11 15 5 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 7 14 11 14 14 5 11 15 5 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 x x x x x x x 5 6 7 8 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.

12 5

Pages Read Last Weekend

15 22 40 34 19 37 7 18

Example 5 Continued Use the data in the table to make a frequency table with intervals Number Frequency Pages Read Last Weekend

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

Frequency

3 2 3 31–40 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.

Number Frequency Pages Read Last Weekend

1–10 2 11–20 4 21–30 1 31–40 3 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.

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 Frequency

1–10 3 11–20 2 21–30 3 31–40 2 Step 1: Choose an appropriate scale and interval.

4 Number Miles Driven on Saturday 3

Step 2: Draw a bar for the number of students in each interval. The bars should touch but not overlap.

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.