Download - LESSON PLAN 7-5 7-5 Box-and-Wh Box-and-Whisker …jpaskiewiczportfolio.weebly.com/uploads/1/8/0/3/18038065/standard... · 394 Chapter 7 Collecting, Displaying, and Analyzing Data

LESSON PLAN 7-5

Box-and-Whisker Plots Objective: To display and analyze data in box-and- whisker plots Grade Level: 6th Grade Estimated Time: 90 minutes Mathematics Academic Standards: STANDARD E: STATISTICS AND PROBABILITY

Data Analysis and Statistics/ Probability Benchmark:

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

Introduction & Development: Carson is planning a deep-sea fishing trip. He chooses a fishing charter based on the number of fish caught on different charters. A box-and-whisker plot uses a number line to show the distribution of a set of data. To make a box-and-whisker plot, first divide the data into four parts using quartiles. The median, or middle quartile, divides the data into a lower half and an upper half. The median of the lower half is the lower quartile, and the median of the upper half is the upper quartile. Example One: Making a Box-and-Whisker Plot Use the data to make a box-and-whisker plot.

26, 17, 21, 23, 19, 28, 17, 20, 29

Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles.

Learn to display andanalyze data in box-and-whisker plots.

Vocabulary

interquartile range

upper quartile

lower quartile

box-and-whisker plot

Carson is planning a deep-sea fishing trip. He chooses a fishing charter based on the number of fish caught on different charters.

A uses a number line to show the distribution of a set of data.

To make a box-and-whisker plot, first divide the data into four parts using quartiles. The median, or middle quartile,divides the data into a lower half and an upper half. The median of the lower half is the , and the median of the upper half is the .

Making a Box-and-Whisker Plot

Use the data to make a box-and-whisker plot.

26, 17, 21, 23, 19, 28, 17, 20, 29

Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upperquartiles.

Step 2: Draw a number line. Above the number line, plot a point foreach value in Step 1.

Step 3: Draw a box from the lower to the upper quartile. Inside thebox, draw a vertical line through the median. Then draw the“whiskers” from the box to the least and greatest values.

upper quartilelower quartile


15 20 25 3010

17Leastvalue

Greatestvalue

Lower quartileMedian

Upper quartile

17 19 20 21 23 26 28 29

= 1817 + 192

= 2726 + 282

394 Chapter 7 Collecting, Displaying, and Analyzing Data

7-5 Box-and-Whisker Plots

15 20 25 3010

E X A M P L E 1

To find the median of a data set with aneven number ofvalues, find the meanof the two middlevalues.

Step 2: Draw a number line. Above the number line, plot a point for each value in Step 1.

Step 3: Draw a box from the lower to the upper quartile. Inside the box, draw a vertical line through the median. Then draw the “whiskers” from the box to the least and greatest values.

The interquartile range of a data set is the difference between the lower and upper quartiles. It tells how large the spread of data around the median is. You can use a box-and-whisker plot to analyze how data in a set are distributed. You can also use box-and-whisker plots to help you compare two sets of data. Example Two: Comparing Box-and-Whisker Plots The box-and-whisker plots below show the distribution of the number of fish caught per trip by two fishing charters.

Which fishing charter has a greater median?

The median number of fish caught on Reel-to-Reel Charters, about 54, is greater


Vocabulary

interquartile range

upper quartile

lower quartile







26, 17, 21, 23, 19, 28, 17, 20, 29






15 20 25 3010

17Leastvalue

Greatestvalue


Upper quartile

17 19 20 21 23 26 28 29

= 1817 + 192

= 2726 + 282



15 20 25 3010

E X A M P L E 1



Vocabulary

interquartile range

upper quartile

lower quartile







26, 17, 21, 23, 19, 28, 17, 20, 29






15 20 25 3010

17Leastvalue

Greatestvalue


Upper quartile

17 19 20 21 23 26 28 29

= 1817 + 192

= 2726 + 282



15 20 25 3010

E X A M P L E 1


The of a data set is the difference between thelower and upper quartiles. It tells how large the spread of data aroundthe median is.

You can use a box-and-whisker plot to analyze how data in a set aredistributed. You can also use box-and-whisker plots to help you comparetwo sets of data.

Comparing Box-and-Whisker Plots

The box-and-whisker plots below show the distribution of thenumber of fish caught per trip by two fishing charters.

Which fishing charter has a greater median?The median number of fish caught on Reel-to-Reel Charters,about 54, is greater than the median number of fish caughton Mud Puppy Charters, about 51.

Which fishing charter has a greater interquartile range?The length of the box in a box-and-whisker plot indicates theinterquartile range. Reel-to-Reel Charters has a longer box, soit has a greater interquartile range.

Which fishing charter appears to be more predictable in thenumber of fish that might be caught on a fishing trip?The range and interquartile range are smaller for Mud PuppyCharters, which means that there is less variation in the data.So the number of fish caught on Mud Puppy Charters is morepredictable.

interquartile range

Think and Discuss

1. Describe what you can tell about a data set from abox-and-whisker plot.

2. Explain how the range and the interquartile range ofa set of data are different. Which measure tells you moreabout central tendency?

2E X A M P L E

20 30 40 50 60 70 80

= Reel-to-Reel Charters

= Mud Puppy Charters

Number of fish

7-5 Box-and-Whisker Plots 395

than the median number of fish caught on Mud Puppy Charters, about 51. Which fishing charter has a greater interquartile range?

The length of the box in a box-and-whisker plot indicates the interquartile range. Reel-to-Reel Charters has a longer box, so it has a greater interquartile range.

Which fishing charter appears to be more predictable in the number of fish that might be caught on a fishing trip?

The range and interquartile range are smaller for Mud Puppy Charters, which means that there is less variation in the data. So the number of fish caught on Mud Puppy Charters is more predictable.

Complete Lesson 7-5 Practice A with the class for additional instruction Assessment:

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

LESSON PLAN 7-6

Line Graphs Objective: To display and analyze data in line 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 bar and line graphs Introduction & Development: You can use a line graph to show how data changes over a period of time. In a line graph, line segments are used to connect data points on a coordinate grid. The result is a visual record of change. Line graphs can be used for a variety of reasons, including showing the growth of a cat over time. Example One: Making a Line Graph Make a line graph of the data in the table. Use the graph to determine during which 2-month period the kitten’s weight increased the most. Step 1: Determine the scale and interval for each axis. Place units of time on the horizontal axis. Step 2: Plot a point for each pair of values. Connect the points using line segments. Step 3: Label the axes and give the graph a title. The graph shows the steepest line segment between 2 and 4 months. This means the kitten’s weight increased most between 2 and 4 months.

Learn to display andanalyze data in linegraphs.

Vocabulary

double-line graph

line graph

To plot each point,start at zero. Moveright for the timeand up for theweight.

7-6 Line Graphs


E X A M P L E 1

You can use a line graph to show how data changes over a period of time. In a

, line segments are used to connect data points on a coordinate grid. The result is a visual record of change.

Line graphs can be used for a variety of reasons, including showing the growth of a cat over time.

Making a Line Graph

Make a line graph of the data in the table. Use the graph todetermine during which 2-monthperiod the kitten’s weightincreased the most.

Step 1: Determine the scale andinterval for each axis. Place units of time on the horizontal axis.

Step 2: Plot a point for each pair of values. Connect the points using line segments.

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

The graph shows the steepest line segment between 2 and 4 months.This means the kitten’s weight increased most between 2 and 4 months.

line graph

Age (mo) Weight (lb)

0 0.2

2 1.7

4 3.8

6 5.1

8 6.0

10 6.7

12 7.2

Growth Rate of a Kitten8

6

4

2

02 40 6 8 10 12

Wei

ght (

lb)

Age (mo)

Learn to display andanalyze data in linegraphs.

Vocabulary

double-line graph

line graph

To plot each point,start at zero. Moveright for the timeand up for theweight.

7-6 Line Graphs


E X A M P L E 1

You can use a line graph to show how data changes over a period of time. In a

, line segments are used to connect data points on a coordinate grid. The result is a visual record of change.

Line graphs can be used for a variety of reasons, including showing the growth of a cat over time.

Making a Line Graph

Make a line graph of the data in the table. Use the graph todetermine during which 2-monthperiod the kitten’s weightincreased the most.

Step 1: Determine the scale andinterval for each axis. Place units of time on the horizontal axis.

Step 2: Plot a point for each pair of values. Connect the points using line segments.

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

The graph shows the steepest line segment between 2 and 4 months.This means the kitten’s weight increased most between 2 and 4 months.

line graph

Age (mo) Weight (lb)

0 0.2

2 1.7

4 3.8

6 5.1

8 6.0

10 6.7

12 7.2

Growth Rate of a Kitten8

6

4

2

02 40 6 8 10 12

Wei

ght (

lb)

Age (mo)

Example Two: Using a Line Graph to Estimate Data You can use a line graph to estimate values between data points. Use the graph to estimate the population of Florida in 1990. To estimate the population in 1990, find the point on the line between 1980 and 2000 that corresponds to 1990. The graph shows about 12.5 million. In fact, the population was 12.9 million in 1990. Example Three: Making a Double-Line Graph A double-line graph shows change over time for two sets of data. The table shows the normal daily temperatures in degrees Fahrenheit in two Alaskan cities. Make a double-line graph of the data.

Plot a point for each temperature in Nome and connect the points. Then, using a different color, plot a point for each temperature in Anchorage and connect the points. Make a key to show what each line represents.


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

You can use a line graph to estimate values between data points.

Using a Line Graph toEstimate Data

Use the graph to estimate thepopulation of Florida in 1990.To estimate the population in1990, find the point on the linebetween 1980 and 2000 thatcorresponds to 1990.The graph shows about 12.5 million. In fact, thepopulation was 12.9 million in 1990.

A shows change over time for two sets of data.

Making a Double-Line Graph

The table shows the normal daily temperatures in degrees Fahrenheit in two Alaskan cities. Make adouble-line graph of the data.

Plot a point for eachtemperature in Nome andconnect the points. Then,using a different color, plot a point for eachtemperature in Anchorageand connect the points.Make a key to show whateach line represents.

double-line graph

Florida Population

20

15

10

5

01920 1940 1960 1980 2000

Popu

latio

n (m

illio

ns)

Year

Month Nome Anchorage

Jan 7 15

Feb 4 19

Mar 9 26

Apr 18 36

May 36 47

Jun 46 54Average Temperatures

60

50

40

30

20

10

0Jan

Nome

Feb Mar Apr May Jun

Tem

pera

ture

( °F)

MonthAnchorage

Anchorage

Nome

Russia

CanadaAlaska

Gulf of Alaska

Think and Discuss

1. Describe how a line graph would look for a set of data thatincreases and then decreases over time.

2. Give an example of a situation that can be described by a double-line graph in which the two sets of data intersect at least once.

2E X A M P L E

E X A M P L E 3

7-6 Line Graphs 403








double-line graph

Florida Population

20

15

10

5

01920 1940 1960 1980 2000

Popu

latio

n (m

illio

ns)

Year


Jan 7 15

Feb 4 19

Mar 9 26

Apr 18 36

May 36 47


60

50

40

30

20

10

0Jan

Nome

Feb Mar Apr May Jun

Tem

pera

ture

( °F)

MonthAnchorage

Anchorage

Nome

Russia

CanadaAlaska

Gulf of Alaska

Think and Discuss



2E X A M P L E

E X A M P L E 3

7-6 Line Graphs 403








double-line graph

Florida Population

20

15

10

5

01920 1940 1960 1980 2000

Popu

latio

n (m

illio

ns)

Year


Jan 7 15

Feb 4 19

Mar 9 26

Apr 18 36

May 36 47


60

50

40

30

20

10

0Jan

Nome

Feb Mar Apr May Jun

Tem

pera

ture

( °F)

MonthAnchorage

Anchorage

Nome

Russia

CanadaAlaska

Gulf of Alaska

Think and Discuss



2E X A M P L E

E X A M P L E 3

7-6 Line Graphs 403

LESSON PLAN 7-7

Misleading Graphs Objective: To identify and analyze misleading graphs Grade Level: 6th Grade Estimated Time: 90 minutes Mathematics Academic Standards: STANDARD E: STATISTICS AND PROBABILITY


• E-4.6: I can determine if a graph is misleading Introduction & Development: Advertisements and news articles often use data to support a point. Sometimes the data is presented in a way that influences how the data is interpreted. A data display that distorts information in order to persuade can be misleading. An axis in a graph can be “broken” to make the graph easier to read. However, a broken axis can also be misleading. In the graph at right, the cost per minute for service with Company B looks like it is twice as much as the cost for service with Company A. In fact, the difference is only $0.10 per minute. Example One: Analyzing Misleading Graphs Both bar graphs show the percent of people in California, Maryland, Michigan, and Washington who use seat belts. Which graph could be misleading? Why?

Learn to identify andanalyze misleadinggraphs.

Advertisements and news articlesoften use data to support a point.Sometimes the data is presented ina way that influences how the datais interpreted. A data display thatdistorts information in order topersuade can be misleading.

An axis in a graph can be “broken”to make the graph easier to read.However, a broken axis can also bemisleading. In the graph at right,the cost per minute for service withCompany B looks like it is twice asmuch as the cost for service withCompany A. In fact, the differenceis only $0.10 per minute.

Social Studies Application

Both bar graphs show the percent of people in California,Maryland, Michigan, and Washington who use seat belts. Whichgraph could be misleading? Why?

Graph B could be misleading. Because the vertical axis on graph B isbroken, it appears that the percent of people in California who wearseat belts is twice as great as the percent in Michigan. In fact, it isonly 5% greater. People might conclude from graph B that the percentof people in California who wear seat belts is much greater than thepercents in the other states.

Cellular Phone Costs

1.10

1.00

Cost

per

min

ute

($)

Company A Company B

100

80

60

40

20

0CA MD WAMI

State

90

88

86

84

82

0CA MD WAMI

State

Seat Belt Use

Graph A Graph B

Perc

ent o

f peo

ple

Perc

ent o

f peo

ple

E X A M P L E 1


7-10 Misleading GraphsLearn to identify andanalyze misleadinggraphs.

Advertisements and news articlesoften use data to support a point.Sometimes the data is presented ina way that influences how the datais interpreted. A data display thatdistorts information in order topersuade can be misleading.

An axis in a graph can be “broken”to make the graph easier to read.However, a broken axis can also bemisleading. In the graph at right,the cost per minute for service withCompany B looks like it is twice asmuch as the cost for service withCompany A. In fact, the differenceis only $0.10 per minute.

Social Studies Application

Both bar graphs show the percent of people in California,Maryland, Michigan, and Washington who use seat belts. Whichgraph could be misleading? Why?

Graph B could be misleading. Because the vertical axis on graph B isbroken, it appears that the percent of people in California who wearseat belts is twice as great as the percent in Michigan. In fact, it isonly 5% greater. People might conclude from graph B that the percentof people in California who wear seat belts is much greater than thepercents in the other states.

Cellular Phone Costs

1.10

1.00

Cost

per

min

ute

($)

Company A Company B

100

80

60

40

20

0CA MD WAMI

State

90

88

86

84

82

0CA MD WAMI

State

Seat Belt Use

Graph A Graph B

Perc

ent o

f peo

ple

Perc

ent o

f peo

ple

E X A M P L E 1


7-10 Misleading Graphs

Graph B could be misleading. Because the vertical axis on graph B is broken, it appears that the percent of people in California who wear seat belts is twice as great as the percent in Michigan. In fact, it is only 5% greater. People might conclude from graph B that the percent of people in California who wear seat belts is much greater than the percents in the other states. Explain why each graph could be misleading.

Because the vertical axis is broken, the distance jumped in 1988 appears to be over two times as far as in 1984. In fact, the distance jumped in 1988 is less than 0.5 meter greater than in the other years.

The scale of the graph is wrong. Equal distances on the vertical axis should represent equal intervals of numbers, but in this graph, the first $18,000 in sales is larger than the next $18,000. Because of this, you can’t tell from the bars that Pizza Perfect’s sales were twice those of Pizza Express.


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

Analyzing Misleading Graphs

Explain why each graph could be misleading.

Because the vertical axis is broken, the distance jumped in 1988appears to be over two times as far as in 1984. In fact, the distance jumped in 1988 is less than 0.5 meter greater than in the other years.

The scale of the graph is wrong. Equal distances on the verticalaxis should represent equal intervals of numbers, but in thisgraph, the first $18,000 in sales is larger than the next $18,000.Because of this, you can’t tell from the bars that Pizza Perfect’s saleswere twice those of Pizza Express.

36,00027,00018,000

Sale

s ($

)

Pizza Sales

PizzaExpress

PizzaPalace

PizzaPerfect

Women‘s Long Jump

Dis

tanc

e (m

)

Year

7.5

7.3

7.1

6.9

01984 1988 1992 1996 2000

Think and Discuss

1. Explain how to use the scale of a graph to decide if the graph ismisleading.

2. Describe what might indicate that a graph is misleading.

3. Give an example of a situation in which a misleading graphmight be used to persuade readers.

2E X A M P L E

7-10 Misleading Graphs 423

Analyzing Misleading Graphs

Explain why each graph could be misleading.

Because the vertical axis is broken, the distance jumped in 1988appears to be over two times as far as in 1984. In fact, the distance jumped in 1988 is less than 0.5 meter greater than in the other years.

The scale of the graph is wrong. Equal distances on the verticalaxis should represent equal intervals of numbers, but in thisgraph, the first $18,000 in sales is larger than the next $18,000.Because of this, you can’t tell from the bars that Pizza Perfect’s saleswere twice those of Pizza Express.

36,00027,00018,000

Sale

s ($

)

Pizza Sales

PizzaExpress

PizzaPalace

PizzaPerfect

Women‘s Long Jump

Dis

tanc

e (m

)

Year

7.5

7.3

7.1

6.9

01984 1988 1992 1996 2000

Think and Discuss

1. Explain how to use the scale of a graph to decide if the graph ismisleading.

2. Describe what might indicate that a graph is misleading.

3. Give an example of a situation in which a misleading graphmight be used to persuade readers.

2E X A M P L E

7-10 Misleading Graphs 423

LESSON PLAN 7-8

Using Technology to Display Data Lab Objective: To identify and analyze misleading 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 bar and line graphs. I can display and analyze data in box-and-whisker plots and circle graphs.

Information and Technology Standards: STANDARD A: MEDIA AND TECHNOLOGY

Benchmark: • A2-3: Students use a computer and productivity software to organize and

create information including hyperlinks, graphics, pictures, images, and/or charts

Introduction & Development: There are several ways to display data, including bar graphs, line graphs, and circle graphs. A spreadsheet provides a quick way to create these graphs. Today you will use Microsoft Excel to enter data and create various types of displays. Activity One Use a spreadsheet to display the Kennedy Middle School Student Council budget shown in the table at right.

Step 1: Open the spreadsheet program, and enter the data as shown below. Enter the activities in column A and the amount budgeted in column B. Include the column titles in row 1.

Use Technology to Display Data

Use after Lesson 7-6

7-6

There are several ways to display data, including bar graphs, line graphs, and circle graphs. A spreadsheet provides a quick way to create these graphs.

Use a spreadsheet to display the Kennedy Middle School Student Council budget shown in the table at right.

Open the spreadsheet program, and enter the data asshown below. Enter the activities in column A and theamount budgeted in column B. Include the column titles in row 1.

Highlight the data byclicking on cell A1 anddragging the cursor tocell B6. Click the ChartWizard icon . Thenclick FINISH to choosethe first type of columngraph.

Activity

KEYWORD: MS7 Lab7

Student Council Budget

Activity Amount ($)

Assemblies 275

Dances 587

Spring Festival 412

Awards Banquet 384

Other 250


1

2

Step 2: Highlight the data by clicking on cell A1 and dragging the cursor to cell B6. Click the Chart Wizard icon. Then click FINISH to choose the first type of column graph.

Step 3: The bar graph of the data appears as shown. Resize or reposition the graph, if necessary.



7-6





Activity

KEYWORD: MS7 Lab7


Activity Amount ($)

Assemblies 275

Dances 587

Spring Festival 412

Awards Banquet 384

Other 250


1

2



7-6





Activity

KEYWORD: MS7 Lab7


Activity Amount ($)

Assemblies 275

Dances 587

Spring Festival 412

Awards Banquet 384

Other 250


1

2

The bar graph of the data appears as shown. Resize or reposition thegraph, if necessary.

To see a circle graph of the data, select the bar graph (as shown above).Click the Chart Wizard icon and choose “Pie,” which is the circle graph.Then click FINISH to choose the first type of circle graph.

1. Which graph best displays the Student Council budget? Why?

2. Would a line graph be an appropriate display of the Student Council budget data? Explain.

1. The table shows the number of points scored by members of a girls’ basketball team in one season. Use a spreadsheet to create a bar graph and a circle graph of the data.

2. Which type of graph is a better display of the data? Why?

Think and Discuss

Try This

Player Ana Angel Mary Nia Tina Zoe

Points Scored 201 145 89 40 21 8

7-6 Technology Lab 407

3

To see a circle graph of the data, select the bar graph (as shown above). Click the Chart Wizard icon and choose “Pie,” which is the circle graph. Then click FINISH to choose the first type of circle graph.



Activity Two


2. Which type of graph is a better display of the data? Why? Assessment:

• Students completion and correctness of the activity

The bar graph of the data appears as shown. Resize or reposition thegraph, if necessary.






Think and Discuss

Try This


Points Scored 201 145 89 40 21 8


3The bar graph of the data appears as shown. Resize or reposition thegraph, if necessary.






Think and Discuss

Try This


Points Scored 201 145 89 40 21 8


3

Download - LESSON PLAN 7-5 7-5 Box-and-Wh Box-and-Whisker …jpaskiewiczportfolio.weebly.com/uploads/1/8/0/3/18038065/standard... · 394 Chapter 7 Collecting, Displaying, and Analyzing Data

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