Georgia Performance 9A Scatter Plots M8D4 - …9A Scatter Plots LESSON Two sets of data can be...

ex plo rat i o n

Scatter Plots9A

1. The table shows the numbers of pages in some paperbackbooks and the books’ prices. Plot the data on the graphprovided.

Copyright © by Holt, Rinehart and Winston. 250 Holt MathematicsAll rights reserved.

Number of pages

Pric

e ($

)

100 200

3

2

1

300 400 500

TV hours

Out

side

hou

rs

10 2

4

3

2

1

3 4

Pages Price ($)

300 2.25

200 1.75

130 1.65

450 3.00

180 1.75

75 1.25

250 2.50

TV hours Outside hours

2.0 1.5

0.5 3.5

1.5 1.5

1.0 2.5

2.5 0.5

1.5 2.0

2.0 0.5

2. The table shows the number of hours some people spentoutside and spent watching TV in one day. Plot the data on the graph provided.

Think and Discuss

3. Explain what the shape of a graph tells you about the databeing displayed.

Georgia Performance

Standards

M8D4.b


Activity

Scatter plots are used to show relationships between two variables.The data displayed on the graph may resemble a line. If the slope ofthe line is positive, there is a positive correlation between the twosets of data; if the slope of the line is negative, a negativecorrelation would exist. If the plot on the graph is scattered in such away that it does not approximate a line, there is no correlationbetween the sets of data.

Using the data in the table, determine if studying longer will affectthe grades on students’ math exams.

On the y-axis, place scores from 0–100. On the x-axis, place hoursstudied from 0–8. Place one “point” on the graph for each row on thedata table. Your scatter plot will look similar to this.

Sco

re

10 2 3Hours Studied

4 6 85 7

Math Exam Score

100

80

60

40

20

0

Hands-On LabScatter Plots9A

LESSON

Name Date ClassName Date ClassName Date Class

Hours Studied Score

3 80

5 90

2 75

6 80

7 90

1 50

2 65

7 85

1 40

7 100


Think and Discuss

The data displayed on the graph resembles a line rising from left toright. What type of correlation does this show between the two setsof data? What does this mean in terms of the data compared?

Hands-On LabScatter Plots, continued9A

LESSON

Name Date Class


Try This

Plot the following points on the graph below:

(0.5, 1.5), (1, 0.5), (1, 2), (1, 4), (2, 1), (2.5, 2), (2.5, 3),

(3, 4), (4, 1.5), (4, 3), (4, 3.5), (5, 2), (5, 3.5), (5, 5)

What type of correlation between data is represented on the scatterplot below?

1 2 3 4 5

5

4

3

2

1

0

Hands-On LabScatter Plots, continued9A

LESSON

Name Date Class


Activity

The 4th grade class has collected information from Internet research tomake a scatter plot with. The class tracked the age of gym students and thenumber of pushups they were able to do. The data they collected is in thetable below and they will use it with a spreadsheet program to make ascatter plot.

First they open a worksheet in the spreadsheet program and enter the datain the top left corner of a new worksheet. Then they highlight the data andselect the Chart menu on the toolbar at the top of the document.

Select the Scatter Plot option and follow the instructions to select data andlabels for the chart. The class makes the ages the X axis of the plot and thenumber of pushups the Y axis on the plot.

Age 10 19 15 20 13 17 16 12 14 15 18

Pushups 3 36 20 21 10 28 22 13 17 25 32

Technology Lab 1Scatter Plots9A

LESSON

Name Date Class

Copyright © by Holt, Rinehart and Winston. 255 Holt MathematicsAll rights reserved.Copyright © by Holt, Rinehart and Winston. 255 Holt MathematicsAll rights reserved.

Think and Discuss

1. Do the data show a general correlation? If so, what is it?

2. If you extended the scatter plot data to cover the pushups doneby people in their 20s, 30s, 40s, 50s, and 60s, would you expectthe same correlation to hold and the same trend to continue?

Try This

You can choose to add a trendline that will show if there is acorrelation between the points on the scatter plot. This trendline isthe same as the line of best fit.

1. Click on the chart to select it.

2. From the main menu, choose Chart, and then choose AddTrendline from the Chart menu.

3. In the Add Trendline dialog box, choose Linear.

4. Click OK. A trendline appears, showing the line of best fitcalculated by the spreadsheet software.

Technology Lab 1Scatter Plots, continued9A

LESSON

Name Date Class

You have learned that the sides of similar triangles are in proportion.You can verify that for yourself by measuring several similartriangles and seeing how accurately your measurements agree withthe proportions the triangles should show. If your measurements areaccurate, the heights of the triangles should be a linear function ofthe bases.

Activity

On a piece of 8.5 in. by 11 in. paper, use a centimeter ruler to drawfour baselines with the following lengths: 4 cm, 5 cm, 6 cm, and 7 cm. Using a protractor, draw a ray at a 30° angle starting from theleft end of the 4-cm line segment. From the right side of the 4-cmsegment, draw a vertical segment intersecting the ray you just drew.Do the same with the other line segments to create four similartriangles.

Measure the vertical line segments of the four triangles andcomplete the table below.

Use a graphing calculator to plot the data as a scatter plot.

1. Press 1 to enter statistical editing mode.

2. Under the heading L1, enter the bases of the four triangles.

3. Under the heading L2, enter the four heights of the triangles inthe same order.

4. Press to summon up the Stat Plots window. Press 1to modify Plot 1.

5. Under “Plot 1,” use the arrow keys to move the cursor to On andpress . After Type, select the Scatter Plot icon (the firstentry), and choose L1 as the XList and L2 as the YList. ForMark, select the � sign (second choice).

ENTER

Y�2nd

STAT

Base (cm) 4 5 6 7

Height (cm)

4 cm 5 cm 6 cm 7 cm


Technology Lab 2Collect Data and Match to a Linear Function9A

LESSON

Name Date Class


6. Press . Set Xmin as 0, Xmas as 7.5, Ymin as 0, and Ymaxas 7.5.

7. Press . Your measurements appear as a scatter plot.

8. Press and press 3 to enter the equation y � x /�3�.

9. Press again to see how well the linear function you justentered agrees with the data you obtained by measuring.

Think and Discuss

1. This activity calls for a centimeter ruler. Would an inch ruler bejust as good? Explain.

2. How do you know that the four triangles you drew are similartriangles?

Try This

1. If the scatter plot and the function line are not showing, pressto display them. Press and use the forward and back

arrow keys to check the y-values of the four points you plottedon the scatter plot. Then press the Down arrow to shift the traceonto the function line closest to each of your four plotted points.Read the y-value of the point as plotted on the function line andcompare it with your measurement for that point. Were youclose?

TRACEGRAPH

GRAPH

x22nd�ENTERY�

GRAPH

WINDOW

Technology Lab 2Collect Data and Match to a Linear Function, continued9A

LESSON

Name Date Class


Name Date Class

Review for MasteryScatter Plots9A

LESSON

Two sets of data can be graphed as points in a scatter plot.If there is a relationship between the data sets, a line of best fitcan be drawn.

Make a scatter plot. Include a line of best fit if there is acorrelation. Describe the correlation.

1.

The values for time are: increasing

distance are:

So, there is a correlation.

2.

The values for the number of workers are:

the number of days are:

So, there is a correlation.

Time (hours) 1 2 2.5 6

Distance (miles) 50 150 175 270

Number of Workers 6 4 2 1

Number of Days 1 2 5 7

Positive correlation:both sets of dataincrease together.

Negative correlation:values of one setincrease while values ofthe other set decrease.

No correlation: pointsneither increase nordecrease together.


Name Date Class

Homework and PracticeScatter Plots9A

LESSON

1. Use the given data to make a scatter plot.

Do the data sets have a positive, a negative, or no correlation?

6. Use the data to predict the percent of U.S. Households with acomputer in 1998.

In 1998, about % of U.S. households had acomputer.

2. The type of car a person drives andthe color of their hair.

4. The number of innings completed ina baseball game and the number ofruns scored.

3. The number of people working on ajob and the hours to completion.

5. The number of shares of stockowned and the amount received individends.

Total FatSandwich Calories Grams

Chicken Breast 318 2

Chicken Teriyaki 374 1.5

Club 323 2

Cold Cut 441 7

Ham 288 1.5

Meatball 527 10

Roast Beef 293 2

Tuna 445 6

Turkey Breast 281 1.5

Veggie 226 1To

tal F

at G

ram

s

Calories

12

10

8

6

4

2

00 100 200 300 400 500 600

Percent of U.S. Households with a Computer

Year 1985 1990 1995 2000

Percent 8.2% 15% 24.1% 51%

2 N D P R I N T

Homework and Practice 8I1. 15 in. and 1 in.

2. 1350 in2 and 6 in2

3. 3375 in3 and 1 in3

4. 20 in. and 1 in.

5. 2400 in2 and 6 in2

6. 8000 in3 and 1 in3

7. 18.75 in. by 7.5 in.

8. 480 cubes

Chapter 8 Big Ideas1. Multiply half the sum of the base lengths

by the height.

2. Multiply the radius (6) by 2π.

3. Use the formula V � �13

�πr 2h, where r is

the radius and h is the height.

4. Find the area of each circular base, πr 2,and add them together with the lateralarea, 2πrh. For this cylinder, r � 3 in.and h � 7 in.

Chapter 9 Project Recording Sheet

Check students’ graphs.

Pizza Pizzazz, Taste of New York,Speedworks, Momma Mildred’sDirect losses: Taste of New York, $630;Momma Mildred’s, $1680; Speedworks,$930; Pizza Pizzazz, $570; losses willincrease.

Exploration 9A1.

2.

3. Sample: it shows the relationshipbetween the two groups of data.

Hands-On Lab 9AThink and DiscussPositive correlation; as hours spent studyingincreases, scores increase.

Try ThisCheck students’ graphs. There is nocorrelation.

Technology Lab 1, 9AThink and Discuss

1. yes; positive

2. No, athletic abilities tend to fall off inlater years.

Try ThisCheck students’ work.

TV hours

Out

side

hou

rs

10 2

4

3

2

1

3 4

Number of pages

Pric

e ($

)

100 200

3

2

1

300 400 500

Company Mean Median Mode

Taste of New York 4.2 4 4

MommaMildred’s 11.2 12 7

Speedworks 6.2 7 8

PizzaPizzazz 3.8 4 2


Answer Key


Technology Lab 2, 9AThink and Discuss

1. Sample: No; markings on a centimeterruler are closer together and thereforemore accurate.

2. They are all 30°-60°-90° triangles.

Review for Mastery 9A1. increasing; positive;

2. decreasing; increasing; negative;

Homework and Practice 9A1.

2. no correlation

3. negative correlation

4. positive correlation

5. positive correlation

6. 36

Exploration 9B1–3. Check students’ work. �

14

� cup of water

weighs approximately 2 ounces, so eachcolumn of the table should increase by 2.

4. scatter plot

5. Possible answer: Each time the amount

of water increases by �14

� cup, the weight

increases by 2 oz. This is a linearrelationship.

Review for Mastery 9B1.

78°F

Homework and Practice 9B1–5. Students’ trend lines and estimates may

vary. Possible answers given.

1.

2. 500 sec

3. 750 sec

4.

5. 12 oz

6. Check students’ work.

20181614121086420

14

12

34 1

Volume (cups)

Weight of Water

Wei

gh

t (o

z.)

114 11

2 136 2

900800700600500400300200

10 20 300 40 50

Number of Laps

Tim

e (s

ec)

85

80

75

70

65

607:40 8:40 9:40 10:40 11:40

Time

Temperature Over Time

Tem

per

atu

re

Tota

l Fat

Gra

ms

Calories

12

10

8

6

4

2

00 100 200 300 400 500 600

8

6

4

2

2Workers

4 6 8

Day

s

300

200

100

2Time (hours)

4 6 8

Dis

tan

ce (

mile

s)

Answer Key

Georgia Performance 9A Scatter Plots M8D4 - …9A Scatter Plots LESSON Two sets of data can be...

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