lesson samples and surveys 9-1 - manchester high school · in a county survey, ... four out of five...

Copyright © by Holt, Rinehart and Winston. 181 Holt MathematicsAll rights reserved.

Samples and Surveys9-1

LESSON

Lesson Objectives

Identify sampling methods and recognize biased samples

Vocabulary

population (p. 462)

sample (p. 462)

biased sample (p. 463)

random sample (p. 462)

systematic sample (p. 462)

stratified sample (p. 462)

convenience sample (p. 462)

voluntary-response sample (p. 462)

Additional Examples

Example 1

Identify the sampling method used.

A. In a county survey, Democratic Party members whose names begin withthe letter D are chosen.

The is to survey members whose names begin with D.

B. A telephone company randomly chooses customers to survey about itsservice.

Customers are chosen by .


LESSON 9-1 CONTINUED

People that attend a

baseball game are more

likely to

the construction of a new

stadium.

Population Sample Possible Bias

Customers who make a

purchase might be more

in music than others in

the store.

Population Sample Possible Bias

Example 2

Identify the population and the sample. Give a reason why the samplecould be biased.

A. A record store manager asks customers who make a purchase how manyhours of music they listen to each day.

Try This

1. Identify the sampling method used.

In a county survey, families with 3 or more children are chosen.

2. Identify the population and the sample. Give a reason why the samplecould be biased.

People attending a baseball game were asked if they support theconstruction of a new stadium in the city.


Organizing Data9-2

LESSON

Lesson Objectives

Organize data in tables and stem-and-leaf plots

Vocabulary

stem-and-leaf plot (p. 467)

back-to-back stem-and-leaf plot (p. 468)

line plot (p. 467)

Venn diagram (p. 468)

Additional Examples

Example 1

Use a line plot to organize the math exam scores.

Find the least value, , and the greatest value, , in the data

set. Then draw a number line from to . Place an “x” above each number on the number line for each time it appears in the data set.

There are numbers in the data set

and x’s above the number line.50 55 60 65 70 80 10075 90 9585

xxx x

xx

xxx x

xx x

xxx

Student Test Scores

100 95 75 80

60 100 60 75

90 85 80 100

50 90 65 80



Example 2

List the data values in the stem-and-leaf plot.

The data values are

Example 3

Use the given data to make a back-to-back stem-and-leaf plot.

Example 4

Make a Venn diagram to show how many 8th grade students play soccer.

Draw two circles. Label one circle “8th Grader”and the other circle “Soccer Player”. The region that overlaps represents the characteristics that are shared by both sets of data.

145

202

517

19

Key: 1 2 means 12

Grade Sport Grade Sport

6 baseball 8 tennis

6 tennis 7 soccer

8 soccer 7 baseball

8 baseball 6 soccer

7 soccer 8 soccer

Survey Results

IL MA MI NY PA

1950 25 14 18 43 31

2000 19 10 15 29 19

U.S. Representatives forSelected States, 1950 and 2000


Measures of Central Tendency9-3

LESSON

Lesson Objectives

Find appropriate measures of central tendency

Vocabulary

mean (p. 472)

median (p. 472)

mode (p. 472)

outlier (p. 472)

range (p. 472)

Additional Examples

Example 1

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

21, 21, 28, 29, 30, 28, 32

mean: 21 � 21 � 28 � 29 � 30 � the values.

28 � 32 �

��189

�Divide by , the number of values.

median: 21 21 28 28 29 30 32 the values.3 values 3 values

mode: The values occur two times.

range: � �



Example 2

Determine and find the most appropriate measure of central tendency orrange for each situation. Justify your answer.

A. Competitors received the following scores for their performance in agymnastic competition: 9.0, 8.3, 8.5, 9.1, 8.2, 8.9, 8.2, 9.0, 8.8, 8.3, 9.2,9.0, 8.6. What score occurred most often?

Find the mode.

, , , , 8.5, 8.6, List the scores in .

8.8, 8.9, , , , 9.1, 9.2 Underline the scores that

appear more than .

Nine appears most frequently. The is .

Example 3

Employees at a store earned $275, $330, $290, $300, $350, $365, and $310during one week. What measure of central tendency or range would makethe salaries look the highest?

Find each measure of central tendency and range of the data set.

mean: �

�$2,

7220� � $

median: $275, $290, $300, $ , $330, $350, $365

Underline the value.

mode: There is mode.

range: $310 � $275 � $

The would make the salaries look the highest.

$275 � $330 � $290 � $300 � $350 � $365 � $310��7


Variability9-4

LESSON

Lesson Objectives

Find measures of variability

Vocabulary

variability (p. 476)

quartile (p. 476)

box-and-whisker plot (p. 477)

Additional Examples

Example 1

Find the first and third quartiles of each data set.

A. 15, 83, 75, 12, 19, 74, 21

21, the values.

first quartile:

third quartile:


Variability9-4

LESSON

The spread of values in a set of data.

Three values, one of which is the median, that divide a data set

into four equal parts.

A graph that displays the highest and lowest

quarters of data as whiskers, the middle two quarters of the data as a box, and

the median.

Lesson Objectives

Find measures of variability

Vocabulary

variability (p. 476)

quartile (p. 476)

box-and-whisker plot (p. 477)

Additional Examples

Example 1

Find the first and third quartiles of each data set.

A. 15, 83, 75, 12, 19, 74, 21

21, the values.

first quartile:

third quartile: 75

15

Order74, 75, 8312, 15, 19,


Displaying Data9-5

LESSON

Lesson Objectives

Display data in bar graphs, histograms, and line graphs

Vocabulary

double-bar graph (p. 485)

frequency table (p. 485)

histogram (p. 485)

double-line graph (p. 486)

Additional Examples

Example 1

Make a double-bar graph.

The following are the number of books read in one month by some boysand girls in Grade 8:

The frequencies are the of

the bars in the bar graph.

Use a different to represent

each gender.

00 1 2 3 4 5

1234

Freq

uenc

y

Books Read

Number of BooksRead by 8th-grade Students

Boys Girls

Books read 0 1 2 3 4 5

Boys 2 3 3 1 0 1

Girls 2 1 2 4 1 0



Example 2

Jimmy asked 12 children how much money they received from the toothfairy. Use the data to make a histogram.

0.35 2.00 0.75 2.50 1.50 3.00 0.25 1.00 1.00 3.50 0.50 3.00

First, make a table with intervals of $1.00.

Then make a

.

Example 3

Make a double-line graph of the given data.Use the graph to estimate the number of CDsand DVDs sold in 2003.

Create two sets of ordered pairs and plot them on a grid. Connect each set of points with different color lines

Then find the points on the graph thatcorrespond to 2003. The graph shows about

CDs sold and DVDs sold.

09 10 11 12 13

12345

Freq

uenc

y

DataDataSet 1

DataSet 2

01 2 3 4 5 6

123456

Freq

uenc

y

DataDataSet 1

DataSet 2

Year CDs sold DVDs sold

1998 3002 735

2000 3098 1057

2002 4685 3010

2004 5804 4047

The Music Shop CD and DVD Sales


9-6LESSON Misleading Graphs and Statistics

Lesson Objectives

Recognize misleading graphs and statistics

Additional Examples

Example 1

Explain why the graph is misleading.

The graph suggests that the stock will

continue to increase through , but

there’s no way to foresee the .

Example 2

Explain why each statistic is misleading.

A. Four out of five dentists surveyed preferred UltraClean toothpaste.

This statement does not give the size or state what

UltraClean toothpaste was with.

B. Shopping at Save-a-Lot can save you up to $100 a month!

The words save up to $100 mean that the you can save

is $100, but there is no that you will save that

amount.

Stock Value40

30

20

10

01990 2000 2010 2020


9-7LESSON Scatter Plots

Lesson Objectives

Create and interpret scatter plots

Vocabulary

scatter plot (p. 494)

correlation (p. 494)

line of best fit (p. 494)

Additional Examples

Example 1

Use the given data to make a scatter plot of the weight and height ofeach member of a basketball team.

The points on the scatter plot are ( ), ( ),

( ), ( ), and ( ).

71 170

68 160

70 175

73 180

74 190

Height (in.) Weight (lb)200

190

180

170

160

150

140

69 71Height (in.)

Wei

ght

(lb)

7370 72 7468



Example 2

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

A. the size of a jar of baby food and the number of jars of baby food a babywill eat

correlation: The food in each jar, the

number of jars of baby food a baby will eat.

B. the speed of a runner and the number of races she wins

correlation: The the runner, the

races she will win.

C. the size of a person and the number of fingers he has

correlation: The size of a person affect the number of fingers he has.

Example 3

Use the data to predict how much a worker will earn in tips in 10 hours.

According to the graph a worker who works 10 hours should earn about

$ .

30

25

20

15

10

5

4 8Hours

Tips

($)

126 102

Choosing the Best Representation of Data9-8

LESSON


Lesson Objectives

Select the best representation for a set of data

Additional Examples

Example 1

A. Which graph is a better display of the data on temperature?

Since the question asks about change in data over , the

is the better representation.

B. Which graph is a better display of the data on temperature?

Since the question asks about the relationship of two data sets, the

is the better representation.

1 2 3 4 5 8 126 107 119

x x x xxx x

Pric

e ($

)

Gallons

Gasoline Prices

1 3 5

50

1510

2520

3530

72 4 6 8 9 10 11 12

Tem

pera

ture

(F)

Time of Day

Temperature Measurements

8 12 4

400

5045

6055

7065

75

810 2 6

40 50 7060 80



Example 2

The Singer family keeps the budget shown below for their monthlyexpenses. Choose an appropriate data display and draw the graph. Whichtwo categories account for one-fifth of their budget?

1. Understand the Problem

You are looking for the best data display and the two categories thataccount for one-fifth of the budget.

2. Make a Plan

You need to compare each category to the whole. Find the percentage of

each category and make a graph.

3. Solve

Make a circle graph. To find which two categories account for one-fifth of

the budget, convert one-fifth to a percent. One-fifth equals %. The

two categories that add to 20% are or and

.

4. Look Back

Look at the table. Saving or auto plus entertainment equals $ , which is about 20% or one-fifth of the budget.

Groceries $400Utilities $330Mortgage $850Clothing $200Entertainment $100Auto $500Savings $500Misc. $120

lesson samples and surveys 9-1 - manchester high school · in a county survey, ... four out of five...

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