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Math 104

Janine Paskiewicz

MTH 104 – Lesson Planning

May 2012

Collecting, Displaying and Analyzing Data Unit

Collecting, Displaying and Analyzing Data

In this unit students will learn how to:

• Select an appropriate representation for displaying relationships among data

• Choose among mean, median, mode or range to describe a set of data

• Make inferences and convincing arguments based on analysis of data

Key Terms:

• Frequency table

• Stem-and-leaf plot

• Line plot

• Mean

• Median

• Mode

• Range

• Outlier

• Bar graph

• Histogram

• Circle graph

• Sector

• Box-and-whisker plot

• Quartiles

• Line graph

LESSON PLAN 7-1

Frequency Tables, Stem-and-Leaf Plots, and Line Plots Objective: Learn to organize and interpret data in frequency tables, stem-and-leaf plots, and line plots Grade Level: 6th Grade Estimated Time: 90 minutes Mathematics Academic Standards: STANDARD E: STATISTICS AND PROBABILITY

Data Analysis and Statistics/ Probability Benchmark:

• E-3.6: I can make and analyze data in line and stem-and-leaf plots

Introduction & Development: IMAX® theaters, with their huge screens and powerful sound systems, make viewers feel as if they are in the middle of the action. In 2005, the classic IMAX film The Dream Is Alive had total box office receipts of over $149 million.

To see how common it is for an IMAX movie to attract such a large number of viewers, you could use a frequency table. A is a way to organize data into categories or groups. By including a column in your table, you can keep a running total of the number of data items.

Example One: Organizing and Interpreting Data in a Frequency Table

The list shows box office receipts in millions of dollars for 20 IMAX films. Make a cumulative frequency table of the data. How many films earned under $40 million?

76,51,41,38,18,17,16,15,13,13,12,12,10,10,6,5,5,4,4,2 Step 1: Choose a scale that includes all of the data values. Then separate the scale into equal intervals. Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column. Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row.

Learn to organize and interpret data infrequency tables, stem-and-leaf plots, and line plots.

Vocabulary

line plot

stem-and-leaf plot

cumulative frequency

frequency table

IMAX® theaters, with their hugescreens and powerful soundsystems, make viewers feel as if they are in the middle of theaction. In 2005, the classic IMAXfilm The Dream Is Alive hadtotal box office receipts of over $149 million.

To see how common it is for anIMAX movie to attract such a largenumber of viewers, you could use a frequency table. A is a way to organize data intocategories or groups. By including a column in your table, you can keep a running total of the number of data items.

Organizing and Interpreting Data in a Frequency Table

The list shows box office receipts in millions of dollars for 20 IMAX films. Make a cumulative frequency table of the data.How many films earned under $40 million?

76, 51, 41, 38, 18, 17, 16, 15, 13, 13, 12, 12, 10, 10, 6, 5, 5, 4, 4, 2

Step 1: Choose a scale that includes all of the data values. Thenseparate the scale into equal intervals.

Step 2: Find the number ofdata values in eachinterval. Write thesenumbers in the“Frequency” column.

Step 3: Find the cumulativefrequency for eachrow by adding all the frequency valuesthat are above or in that row.

The number of films that earned under $40 million is the cumulative frequency of the first two rows: 17.

cumulative frequency

frequency table

IMAX Films

Receipts Cumulative ($ million) Frequency Frequency

0–19 16 16

20–39 1 17

40–59 2 19

60–79 1 20

E X A M P L E 1

376 Chapter 7 Collecting, Displaying, and Analyzing Data

7-1 Frequency Tables, Stem-and-Leaf Plots, and Line Plots

The number of films that earned under $40 million is the cumulative frequency of the first two rows: 17. Example Two: Organizing and Interpreting Data in a Stem-and-Leaf Plot A stem-and-leaf plot uses the digits of each number to organize and display a set of data. Each leaf on the plot represents the right-hand digit in a data value, and each stem represents the remaining left-hand digits. The key shows the values of the data on the plot. The table shows the number of minutes students spent doing their Spanish homework. Make a stem-and-leaf plot of the data. Then find the number of students who studied longer than 45 minutes.

Step 1: Order the data from least to greatest. Since the data values range from 21 to 64, use tens digits for the stems and ones digits for the leaves. Step 2: List the stems from least to greatest on the plot. Step 3: List the leaves for each stem from least to greatest. Step 4: Add a key and title the graph.

One student studied for 47 minutes, 2 students studied for 48 minutes, and 1 student studied for 64 minutes. A total of 4 students studied longer than 45 minutes.

A uses the digits of each number to organize and display a set of data. Each leaf on the plot represents the right-hand digit in a data value, and each stem represents the remaining left-hand digits. The key shows the values of the data on the plot.

Organizing and Interpreting Data in a Stem-and-Leaf Plot

The table shows the number of minutes students spent doing theirSpanish homework. Make a stem-and-leaf plot of the data. Thenfind the number of students who studied longer than 45 minutes.

Step 1: Order the data from least to greatest. Since the data valuesrange from 21 to 64, use tens digits for the stems and onesdigits for the leaves.

Step 2: List the stems from least to greatest on the plot.

Step 3: List the leaves for each stem from least to greatest.

Step 4: Add a key and title the graph.


Similar to a stem-and-leaf plot, a can be used to show howmany times each data value occurs. Line plots use a number line andX’s to show frequency. By looking at a line plot, you can quickly seethe distribution, or spread, of the data.

line plot

stem-and-leaf plot

Minutes Spent Doing Homework

38 48 45 32 29 48

32 45 36 22 21 6435 45 47 26 43 29

The stems arethe tens digits.

The stem 5 hasno leaves, sothere are nodata values inthe 50’s.

The leaves are the ones digits.

The entries in the second rowrepresent the datavalues 32, 32, 35,36, and 38.

2E X A M P L E


Key: 3!2 means 32

Stems Leaves

23456

1 2 6 9 92 2 5 6 83 5 5 5 7 8 8

4

Key: 2!7 means 27

Stems Leaves

23

4 7 90 6

7-1 Frequency Tables, Stem-and-Leaf Plots, and Line Plots 377

To represent 5minutes in the stem-and-leaf plot in Example 2, youwould use 0 as thestem and 5 as the leaf.

A uses the digits of each number to organize and display a set of data. Each leaf on the plot represents the right-hand digit in a data value, and each stem represents the remaining left-hand digits. The key shows the values of the data on the plot.

Organizing and Interpreting Data in a Stem-and-Leaf Plot

The table shows the number of minutes students spent doing theirSpanish homework. Make a stem-and-leaf plot of the data. Thenfind the number of students who studied longer than 45 minutes.

Step 1: Order the data from least to greatest. Since the data valuesrange from 21 to 64, use tens digits for the stems and onesdigits for the leaves.

Step 2: List the stems from least to greatest on the plot.

Step 3: List the leaves for each stem from least to greatest.

Step 4: Add a key and title the graph.


Similar to a stem-and-leaf plot, a can be used to show howmany times each data value occurs. Line plots use a number line andX’s to show frequency. By looking at a line plot, you can quickly seethe distribution, or spread, of the data.

line plot

stem-and-leaf plot


38 48 45 32 29 48

32 45 36 22 21 6435 45 47 26 43 29

The stems arethe tens digits.

The stem 5 hasno leaves, sothere are nodata values inthe 50’s.

The leaves are the ones digits.

The entries in the second rowrepresent the datavalues 32, 32, 35,36, and 38.

2E X A M P L E


Key: 3!2 means 32

Stems Leaves

23456

1 2 6 9 92 2 5 6 83 5 5 5 7 8 8

4

Key: 2!7 means 27

Stems Leaves

23

4 7 90 6

7-1 Frequency Tables, Stem-and-Leaf Plots, and Line Plots 377

To represent 5minutes in the stem-and-leaf plot in Example 2, youwould use 0 as thestem and 5 as the leaf.

Example Three: Organizing and Interpreting Data in a Line Plot Similar to a stem-and-leaf plot, a line plot can be used to show how many times each data value occurs. Line plots use a number line and X’s to show frequency. By looking at a line plot, you can quickly see the distribution, or spread, of the data. Make a line plot of the data. How many miles per day did Trey run most often?

Step 1: The data values range from 2 to 16. Draw a number line that includes this range. Step 2: Put an X above the number on the number line that corresponds to the number of miles Trey ran each day.

The greatest number of X’s appear above the number 5. This means that Trey ran 5 miles most often. Complete Lesson 7-1 Practice A with the class for additional instruction Assessment:

• Students’ participation in examples • Completion of Practice B & C

Think and Discuss

1. Tell which you would use to determine the number of data values ina set: a cumulative frequency table or a stem-and-leaf plot. Explain.

Organizing and Interpreting Data in a Line Plot

Make a line plot of the data. How many miles per day did Trey runmost often?

Step 1: The data values range from 2 to 16. Draw a number line thatincludes this range.

Step 2: Put an X above the number on the number line thatcorresponds to the number of miles Trey ran each day.

The greatest number of X’s appear above the number 5. This meansthat Trey ran 5 miles most often.

Number of Miles Trey Ran Each Day During Training

5 6 5 5 3 5 4 4 6

8 6 3 4 3 2 16 12 12

E X A M P L E 3

0

x x xxx

xxx

xxxx

xxx

xxx

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Number of miles

7-1 ExercisesExercisesKEYWORD: MS7 Parent

KEYWORD: MS7 7-1

Number of Electoral Votes for Select States (2004)

CA 55 GA 15 IN 11 MI 17 NY 31 PA 21

NJ 15 IL 21 KY 8 NC 15 OH 20 TX 34

GUIDED PRACTICE


1. Make a cumulative frequency table of the data. How many of the stateshad fewer than 20 electoral votes in 2004?

2. Make a stem-and-leaf plot of the data. How many of the states had morethan 30 electoral votes in 2004?

3. Make a line plot of the data. For the states shown, what was the mostcommon number of electoral votes in 2004?

See Example 2

See Example 3

See Example 1

Think and Discuss

1. Tell which you would use to determine the number of data values ina set: a cumulative frequency table or a stem-and-leaf plot. Explain.

Organizing and Interpreting Data in a Line Plot

Make a line plot of the data. How many miles per day did Trey runmost often?

Step 1: The data values range from 2 to 16. Draw a number line thatincludes this range.

Step 2: Put an X above the number on the number line thatcorresponds to the number of miles Trey ran each day.

The greatest number of X’s appear above the number 5. This meansthat Trey ran 5 miles most often.

Number of Miles Trey Ran Each Day During Training

5 6 5 5 3 5 4 4 6

8 6 3 4 3 2 16 12 12

E X A M P L E 3

0

x x xxx

xxx

xxxx

xxx

xxx

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Number of miles

7-1 ExercisesExercisesKEYWORD: MS7 Parent

KEYWORD: MS7 7-1

Number of Electoral Votes for Select States (2004)

CA 55 GA 15 IN 11 MI 17 NY 31 PA 21

NJ 15 IL 21 KY 8 NC 15 OH 20 TX 34

GUIDED PRACTICE


1. Make a cumulative frequency table of the data. How many of the stateshad fewer than 20 electoral votes in 2004?

2. Make a stem-and-leaf plot of the data. How many of the states had morethan 30 electoral votes in 2004?

3. Make a line plot of the data. For the states shown, what was the mostcommon number of electoral votes in 2004?

See Example 2

See Example 3

See Example 1

LESSON PLAN 7-2

Mean, Median, Mode and Range Objective: Learn to find the mean, median, mode, and range of a data set Grade Level: 6th Grade Estimated Time: 90 minutes Mathematics Academic Standards: STANDARD E: STATISTICS AND PROBABILITY


• E-5.6: I can find the range, mean, median (odd number of data), and mode of a data set

Introduction & Development: To crack secret messages in code, you can list the number of times each symbol of the code appears in the message. The symbol that appears the most often represents the mode. The mode, along with the mean and the median, is a measure of central tendency used to represent the “middle” of a data set.

• The mean is the sum of the data values divided by the number of data items. • The median is the middle value of an odd number of data items arranged in

order. For an even number of data items, the median is the mean of the two middle values.

• The mode is the value or values that occur most often. When all the data values occur the same number of times, there is no mode.

• The range of a set of data is the difference between the greatest and least values

Example One: Finding the Mean, Median, Mode, and Range of a Data Set Find the mean, median, mode, and range of the data set.

2,1,8,0,2,4,3,4

Example Two: Choosing the Best Measure to Describe a Set of Data The line plot shows the number of hours 15 people exercised in one week. Which measure of central tendency best describes these data? Justify your answer. Mean:

The mean is 4.2. Most of the people exercised fewer than 4 hours, so the mean does not describe the data set best. Median:

0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 5, 7, 7, 14, 14 The median is 2. The median best describes the data set because a majority of the data is clustered around the data value 2. Mode: The greatest number of X’s occur above the number 1 on the line plot. The mode is 1.

To crack secret messages in code, you canlist the number of times each symbol of thecode appears in the message. The symbolthat appears the most often represents themode, which likely corresponds to the letter e.

The mode, along with the mean and themedian, is a measure of central tendencyused to represent the “middle” of a data set.

• The is the sum of the data values divided by the number of data items.

• The is the middle value of an odd number of data itemsarranged in order. For an even number of data items, the median isthe mean of the two middle values.

• The is the value or values that occur most often. When allthe data values occur the same number of times, there is no mode.

The of a set of data is the difference between the greatest andleast values.

Finding the Mean, Median, Mode, and Range of a Data Set

Find the mean, median, mode, and range of the data set.

2, 1, 8, 0, 2, 4, 3, 4mean:2 ! 1 ! 8 ! 0 ! 2 ! 4 ! 3 ! 4 " 24 Add the values.

24 # 8 " 3 Divide the sum by the

The mean is 3. number of items.

median:0, 1, 2, 2, 3, 4, 4, 8 Arrange the values in order.

!2 !

23

! " 2.5

The median is 2.5.

mode:0, 1, 2, 2, 3, 4, 4, 8 The values 2 and 4 occur twice.

The modes are 2 and 4.

range: 8 $ 0 " 8 Subtract the least value from

The range is 8. the greatest value.

range

mode

median

mean

Learn to find the mean, median, mode, and range of a data set.

Vocabulary

outlier

range

mode

median

mean

E X A M P L E 1

7-2 Mean, Median, Mode, and Range 381

7-2 Mean, Median, Mode,and Range

Navajo Code Talkers used the Navajolanguage as the basis of a code inWorld War II.

The mean issometimes called the average.

There are two middle values,so find the mean of thesevalues.

Often one measure of central tendency is more appropriate for describinga set of data than another measure is. Think about what each measuretells you about the data. Then choose the measure that best answers thequestion being asked.

Choosing the Best Measure to Describe a Set of DataThe line plot shows the number of hours 15 people exercised inone week. Which measure of central tendency best describesthese data? Justify your answer.

mean:

! !61

35! ! 4.2

The mean is 4.2.

Most of the people exercised fewer than 4 hours, so the mean doesnot describe the data set best.

median:0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 5, 7, 7, 14, 14The median is 2.

The median best describes the data set because a majority of thedata is clustered around the data value 2.

mode:The greatest number of X’s occur above the number 1 on the line plot.The mode is 1.

The mode represents only 4 of the 15 people. The mode does notdescribe the entire data set.

0 " 1 " 1 " 1 " 1 " 2 " 2 " 2 " 3 " 3 " 5 " 7 " 7 " 14 " 1415

2E X A M P L E

0

xxx

xxx

xxxx

xxx

xx

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Number of hours


Measure Most Useful When

mean the data are spread fairly evenly

median the data set has an outlier

mode the data involve a subject in which many data points ofone value are important, such as election results

In the data set in Example 2, the value 14 is much greater than theother values in the set. An extreme value such as this is called an

. Outliers can greatly affect the mean of a data set.outlier

The mode represents only 4 of the 15 people. The mode does not describe the entire data set. In the data set in Example 2, the value 14 is much greater than the other values in the set. An extreme value such as this is called an outlier. Outliers can greatly affect the mean of a data set.

Example Three: Exploring the Effects of Outliers on Measures of Central Tendency The table shows the number of art pieces created by students in a glass-blowing workshop. Identify the outlier in the data set, and determine how the outlier affects the mean, median, and mode of the data. Then tell which measure of central tendency best describes the data with and without the outlier.

The outlier is 14.

Often one measure of central tendency is more appropriate for describinga set of data than another measure is. Think about what each measuretells you about the data. Then choose the measure that best answers thequestion being asked.

Choosing the Best Measure to Describe a Set of DataThe line plot shows the number of hours 15 people exercised inone week. Which measure of central tendency best describesthese data? Justify your answer.

mean:

! !61

35! ! 4.2

The mean is 4.2.

Most of the people exercised fewer than 4 hours, so the mean doesnot describe the data set best.

median:0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 5, 7, 7, 14, 14The median is 2.

The median best describes the data set because a majority of thedata is clustered around the data value 2.

mode:The greatest number of X’s occur above the number 1 on the line plot.The mode is 1.

The mode represents only 4 of the 15 people. The mode does notdescribe the entire data set.

0 " 1 " 1 " 1 " 1 " 2 " 2 " 2 " 3 " 3 " 5 " 7 " 7 " 14 " 1415

2E X A M P L E

0

xxx

xxx

xxxx

xxx

xx

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Number of hours


Measure Most Useful When

mean the data are spread fairly evenly

median the data set has an outlier

mode the data involve a subject in which many data points ofone value are important, such as election results

In the data set in Example 2, the value 14 is much greater than theother values in the set. An extreme value such as this is called an

. Outliers can greatly affect the mean of a data set.outlier

Exploring the Effects of Outliers on Measures of CentralTendency

The table shows the number of artpieces created by students in aglass-blowing workshop. Identifythe outlier in the data set, anddetermine how the outlier affectsthe mean, median, and mode of thedata. Then tell which measure ofcentral tendency best describes thedata with and without the outlier.The outlier is 14.

Without the Outlier With the Outlier

mean: mean:

! 3 ! 4.8

The mean is 3. The mean is about 4.8.The outlier increases the mean of the data by about 1.8.

median: median:1, 2, 3, 4, 5 1, 2, 3, 4, 5, 14

!3 "

24

! ! 3.5

The median is 3. The median is 3.5.The outlier increases the median of the data by 0.5.

mode: mode:There is no mode. There is no mode.The outlier does not change the mode of the data.

The median best describes the data with the outlier. The mean andmedian best describe the data without the outlier.

5 " 1 " 3 " 4 " 14 " 2!!!

65 " 1 " 3 " 4 " 2!!!

5

Think and Discuss

1. Describe a situation in which the mean would best describe adata set.

2. Tell which measure of central tendency must be a data value.

3. Explain how an outlier affects the mean, median, and mode of adata set.

Name Number of Pieces

Suzanne 5

Glen 1

Charissa 3

Eileen 4

Hermann 14

Tom 2

E X A M P L E 3


Since all the datavalues occur the samenumber of times, theset has no mode.

Complete Lesson 7-2 Practice A with the class for additional instruction Assessment:


Exploring the Effects of Outliers on Measures of CentralTendency

The table shows the number of artpieces created by students in aglass-blowing workshop. Identifythe outlier in the data set, anddetermine how the outlier affectsthe mean, median, and mode of thedata. Then tell which measure ofcentral tendency best describes thedata with and without the outlier.The outlier is 14.

Without the Outlier With the Outlier

mean: mean:

! 3 ! 4.8

The mean is 3. The mean is about 4.8.The outlier increases the mean of the data by about 1.8.

median: median:1, 2, 3, 4, 5 1, 2, 3, 4, 5, 14

!3 "

24

! ! 3.5

The median is 3. The median is 3.5.The outlier increases the median of the data by 0.5.

mode: mode:There is no mode. There is no mode.The outlier does not change the mode of the data.

The median best describes the data with the outlier. The mean andmedian best describe the data without the outlier.

5 " 1 " 3 " 4 " 14 " 2!!!

65 " 1 " 3 " 4 " 2!!!

5

Think and Discuss

1. Describe a situation in which the mean would best describe adata set.

2. Tell which measure of central tendency must be a data value.

3. Explain how an outlier affects the mean, median, and mode of adata set.

Name Number of Pieces

Suzanne 5

Glen 1

Charissa 3

Eileen 4

Hermann 14

Tom 2

E X A M P L E 3


Since all the datavalues occur the samenumber of times, theset has no mode.

LESSON PLAN 7-3

Bar Graphs and Histograms Objective: To display and analyze data in bar graphs and histograms Grade Level: 6th Grade Estimated Time: 90 minutes Mathematics Academic Standards: STANDARD E: STATISTICS AND PROBABILITY


• E-1.6: I can display and analyze data in frequency tables and histograms • E-2.6: I can display and analyze data in bar and line graphs

Introduction & Development: Hundreds of different languages are spoken around the world. The graph shows the numbers of native speakers of four languages. A bar graph can be used to display and compare data. The scale of a bar graph should include all the data values and be easily divided into equal intervals. Example One: Interpreting a Bar Graph Use the bar graph to answer each question. Which language has the most native speakers? The bar for Mandarin is the longest, so Mandarin has the most native speakers. About how many more people speak Mandarin than speak Hindi?

About 500 million more people speak Mandarin than speak Hindi.


Learn to display andanalyze data in bargraphs and histograms.

Vocabulary

histogram

double-bar graph

bar graph

Hundreds of different languages are spoken around the world. The graph shows the numbers of native speakers of four languages.

A can be used to display and compare data. The scale of a bar graph should include all the data values and be easily divided into equal intervals.

Interpreting a Bar Graph

Use the bar graph to answer each question.

Which language has the most native speakers?The bar for Mandarin is the longest, so Mandarin has the mostnative speakers.

About how many more people speak Mandarin than speak Hindi?About 500 million more people speak Mandarin than speak Hindi.

You can use a to compare two related sets of data.

Making a Double-Bar Graph

The table shows the lifeexpectancies of people in threeCentral American countries. Make a double-bar graph of the data.Step 1: Choose a scale and

interval for the verticalaxis.

Step 2: Draw a pair of bars foreach country’s data. Usedifferent colors to showmales and females.

Step 3: Label the axes and givethe graph a title.

Step 4: Make a key to show whateach bar represents.

double-bar graph

bar graph

Country Male Female

El Salvador 67 74

Honduras 63 66

Nicaragua 65 70

80

60

40

20

0El Salvador Honduras Nicaragua

Age

Life Expectancies inCentral America

FemaleMale

Honduras

Nicaragua

ElSalvador

E X A M P L E 1

2E X A M P L E

Most Widely Spoken Languages

English

Hindi

Mandarin

Spanish

0 1,000200 400 600 800

Number of speakers (millions)

7-3 Bar Graphs and Histograms

Example Two: Making a Double-Bar Graph You can use a double-bar graph to compare two related sets of data. The table shows the life expectancies of people in three Central American countries. Make a double-bar graph of the data.

Step 1: Choose a scale and interval for the vertical axis. Step 2: Draw a pair of bars for each country’s data. Use different colors to show males and females. Step 3: Label the axes and give the graph a title. Step 4: Make a key to show what each bar represents. Example Three: Making a Histogram A histogram is a bar graph that shows the frequency of data within equal intervals. There is no space between the bars in a histogram. The table below shows survey results about the number of CDs students own. Make a histogram of the data.

Step 1: Make a frequency table of the data. Be sure to use a scale that includes all of the data values and separate the scale into equal intervals. Use these intervals on the horizontal axis of your histogram. Step 2: Choose an appropriate scale and interval for the vertical axis. The greatest value on the scale should be at least as great as the greatest frequency.

A is a bar graph that shows the frequency of data withinequal intervals. There is no space between the bars in a histogram.

Making a Histogram

The table below shows survey results about the number of CDsstudents own. Make a histogram of the data.

Step 1: Make a frequency table of the data. Be sure to use a scale that includes all of the data values and separate the scale into equal intervals. Use these intervals on the horizontal axis of your histogram.

Step 2: Choose an appropriate scale andinterval for the vertical axis. Thegreatest value on the scale shouldbe at least as great as the greatestfrequency.

Step 3: Draw a bar for each interval. The height of the bar is thefrequency for that interval. Barsmust touch but not overlap.

Step 4: Label the axes and give the graph a title.

histogram

Think and Discuss

1. Explain how to use the frequency table in Example 3 to find thenumber of students surveyed.

2. Explain why you might use a double-bar graph instead of twoseparate bar graphs to display data.

3. Describe the similarities and differences between a bar graph anda histogram.

Number of CDs Frequency

1–5 22

6–10 34

11–15 52

16–20 35

CD Survey Results

60

50

40

30

20

10

0

1–516–20

11–156–10

Freq

uenc

y

Number of CDs

Number of CDs

1 lll 5 llll l 9 llll l 13 llll llll 17 llll llll2 ll 6 lll 10 llll llll 14 llll llll l 18 llll ll3 llll 7 llll lll 11 llll llll l 15 llll llll l 19 ll4 llll l 8 llll ll 12 llll llll 16 llll llll l 20 llll l

E X A M P L E 3

7-3 Bar Graphs and Histograms 387



Vocabulary

histogram

double-bar graph

bar graph














double-bar graph

bar graph

Country Male Female

El Salvador 67 74

Honduras 63 66

Nicaragua 65 70

80

60

40

20


Age


FemaleMale

Honduras

Nicaragua

ElSalvador

E X A M P L E 1

2E X A M P L E


English

Hindi

Mandarin

Spanish

0 1,000200 400 600 800





Vocabulary

histogram

double-bar graph

bar graph














double-bar graph

bar graph

Country Male Female

El Salvador 67 74

Honduras 63 66

Nicaragua 65 70

80

60

40

20


Age


FemaleMale

Honduras

Nicaragua

ElSalvador

E X A M P L E 1

2E X A M P L E


English

Hindi

Mandarin

Spanish

0 1,000200 400 600 800




Making a Histogram






histogram

Think and Discuss





1–5 22

6–10 34

11–15 52

16–20 35

CD Survey Results

60

50

40

30

20

10

0

1–516–20

11–156–10

Freq

uenc

y

Number of CDs

Number of CDs


E X A M P L E 3


Step 3: Draw a bar for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap. Step 4: Label the axes and give the graph a title.




Making a Histogram






histogram

Think and Discuss





1–5 22

6–10 34

11–15 52

16–20 35

CD Survey Results

60

50

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E X A M P L E 3


LESSON PLAN 7-4

Reading and Interpreting Circle Graphs Objective: To read and interpret data presented in circle graphs Grade Level: 6th Grade Estimated Time: 90 minutes Mathematics Academic Standards: STANDARD E: STATISTICS AND PROBABILITY


• E-2.6: I can display and analyze data in box-and-whisker plots and circle graphs

Introduction & Development: A circle graph, also called a pie chart, shows how a set of data is divided into parts. The entire circle contains 100% of the data. Each sector or slice, of the circle represents one part of the entire data set. The circle graph compares the number of species in each group of echinoderms. Echinoderms are marine animals that live on the ocean floor. The name echinoderm means “spiny-skinned.”

Learn to read andinterpret data presentedin circle graphs.

Vocabulary

sector

circle graph

A , also called a pie chart, shows howa set of data is divided into parts. The entire circlecontains 100% of the data. Each , or slice,of the circle represents one part of the entire data set.

The circle graph compares the number of species in each groupof echinoderms.Echinoderms are marineanimals that live on theocean floor. The nameechinoderm means“spiny-skinned.”

Life Science Application

Use the circle graph to answer each question.

Which group of echinoderms includes the greatest number ofspecies?The sector for brittle stars and basket stars is the largest, so thisgroup includes the greatest number of species.

Approximately what percent of echinoderm species are sea stars?The sector for sea stars makes up about one-fourth of the circle.Since the circle shows 100% of the data, about one-fourth of100%, or 25%, of echinoderm species are sea stars.

Which group is made up of fewer species—sea cucumbers or sea urchins and sand dollars?The sector for sea urchins and sand dollars is smaller than thesector for sea cucumbers. This means there are fewer species ofsea urchins and sand dollars than species of sea cucumbers.

sector

circle graph

Species of Echinoderms

Sea stars

Sea lilies andfeather stars

Brittle stars andbasket stars

Sea urchinsand sand dollars

Seacucumbers

E X A M P L E 1


7-4 Reading and InterpretingCircle Graphs

Example One: Reading Circle Graphs Use the circle graph to answer each question. Which group of echinoderms includes the greatest number of species?

The sector for brittle stars and basket stars is the largest, so this group includes the greatest number of species.

Approximately what percent of echinoderm species are sea stars?

The sector for sea stars makes up about one-fourth of the circle. Since the circle shows 100% of the data, about one-fourth of 100%, or 25%, of echinoderm species are sea stars.

Which group is made up of fewer species—sea cucumbers or sea urchins and sand dollars?

The sector for sea urchins and sand dollars is smaller than the sector for sea cucumbers. This means there are fewer species of sea urchins and sand dollars than species of sea cucumbers.

Example Two: Interpreting Circle Graphs Leon surveyed 30 people about pet ownership. The circle graph shows his results. Use the graph to answer each question. How many people do not own pets?

The circle graph shows that 50% of the 30 people do not own pets.

50% of 30 = 0.5 x 30 =15

Fifteen people do not own pets How many people own cats only?

The circle graph shows that 20% of the 30 people own cats only.

20% of 30 = 0.2 x 30

=6 Six people own cats only

Interpreting Circle Graphs

Leon surveyed 30 people about pet ownership. The circle graphshows his results. Use the graph to answer each question.

How many people do not own pets?The circle graph shows that 50% of the 30 people do not own pets.50% of 30 ! 0.5 " 30

! 15Fifteen people do not own pets.

How many people own cats only?The circle graph shows that 20% of the 30 people own cats only. 20% of 30 ! 0.2 " 30

! 6Six people own cats only.

Choosing an Appropriate Graph

Decide whether a bar graph or a circle graph would best displaythe information. Explain your answer.

the percent of a nation’s electricity supply generated by each ofseveral fuel sourcesA circle graph is the better choice because it makes it easy to seewhat part of the nation’s electricity comes from each fuel source.

the number of visitors to Arches National Park in each of the lastfive yearsA bar graph is the better choice because it makes it easy to seehow the number of visitors has changed over the years.

the comparison between the time spent in math class and thetotal time spent in school each dayA circle graph is the better choice because the sector thatrepresents the time spent in math class could be compared to the entire circle, which represents the total time spent in school.

Think and Discuss

1. Describe two ways a circle graph can be used to compare data.

2. Compare the use of circle graphs with the use of bar graphs todisplay data.

Pet Survey Results

No pets50%

Dogs only20%

Cats only20%

Dogs and cats10%

2E X A M P L E

E X A M P L E 3

Arches National Park,located in southeasternUtah, covers 73,379acres. The park isfamous for its naturalsandstone arches.

Earth Science

7-4 Reading and Interpreting Circle Graphs 391

Example Three: Choosing an Appropriate Graph Decide whether a bar graph or a circle graph would best display the information. Explain your answer. The percent of a nation’s electricity supply generated by each of several fuel sources

A circle graph is the better choice because it makes it easy to see what part of the nation’s electricity comes from each fuel source.

The number of visitors to Arches National Park in each of the last five years

A bar graph is the better choice because it makes it easy to see how the number of visitors has changed over the years.

The comparison between the time spent in math class and the total time spent in school each day

A circle graph is the better choice because the sector that represents the time spent in math class could be compared to the entire circle, which represents the total time spent in school.



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