formulating questions and collecting data...will any of these sampling methods produce a random...

Chapter 14 Assignments • 255

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Lesson 14.1 Assignment

Name ________________________________________________________ Date _________________________

We Want to Hear from You!Formulating Questions and Collecting Data

1. In this assignment, you will design and conduct your own survey. After you have collected the

data, you will analyze it.

a. What type of data would you like to collect?

b. Formulate at least five questions you will ask each person you interview. List those questions.

c. Write a complete sentence describing who you will interview and why you chose these people.

d. Are you collecting data from a population or a sample? Explain your reasoning.

256 • Chapter 14 Assignments

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Lesson 14.1 Assignment page 2

e. Will you be conducting a survey or a census? Explain your reasoning.

f. Will the data you collect be statistics or parameters? Explain your reasoning.

g. Conduct your survey. Give three statistics or parameters that you collected from your sample

or population.

7718A_C2_Assign_CH14_255-276.indd 256 6/14/11 10:05 AM


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Name ________________________________________________________ Date _________________________

Dealing with Data: Selecting a SampleCollecting Data through Random Sampling

1. The manager of the Millcreek Mall wants to know the mean age of the people who shop at the mall

and the stores in which they typically shop. He hires Barker Market Research Company to collect

the data. Dennis works for the Barker Market Research Company and has been put in charge

of collecting data for the Millcreek Mall. Dennis decides to interview 100 people one Saturday

because it is the mall’s busiest shopping day.

a. What is the population for this situation?

b. What is the sample?

c. When Dennis calculates the mean age of the people who shop at the mall, will he be calculating

a parameter or a statistic? Explain your reasoning.

d. Describe three different ways Dennis can take a sample. Describe how any of these three

possible samples may cause the results of Dennis’s survey to inaccurately reflect the average

age of shoppers at the mall.


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2. Dennis is conducting a survey at the mall. He considers the following options for choosing

100 people to survey. Will any of these sampling methods produce a random sample?

Explain your reasoning.

a. Choose the first 100 people that come in the mall on Saturday.

b. Choose 100 shoppers at the bookstore in the mall.

c. Use a random number generator to determine which shoppers to interview as they

come into the mall.


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Name ________________________________________________________ Date _________________________

3. Dennis decides to use a random number generator to help him choose who to interview for a

survey of shoppers at the mall. He will interview 10 people each hour the mall is open. The mall

manager says that about 80 people come in the mall through the main doors each hour. He follows

the graphing calculator steps to randomly generate 10 numbers.

Step1: Press MATH and use the right arrow to highlight PRB.

Step2: Use the down arrow to highlight 5:randInt ( and press ENTER.

Step3: Enter (1, 80) and Press ENTER.

A number from 1 through 80 should appear.

Step4: Continue to press ENTER until the sample is chosen.

a. Dennis’s graphing calculator generated the following numbers: 77, 18, 30, 1, 75, 9, 44, 69,

79, 23. How does this list of numbers compare to the list of numbers that you would receive

if you followed the same steps to randomly generate 10 numbers?

b. Suppose that the first 10 people Dennis interviews are all going to shop at the bookstore.

Does this mean the sample is not random? Explain your reasoning.


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c. Dennis decides to use a random number table to choose the next 10 people to interview.

Explain how to choose 10 two-digit numbers between 1 and 80 from the random number table.

d. Begin on line 16 and record 10 two-digit numbers from the random number table.

Line 16 67642 05204 30697 44806 96989 68403 85621 45556 35434 09532

Line 17 64041 99011 14610 40273 09482 62864 01573 82274 81446 32477

Line 18 17048 94523 97444 59904 16936 39384 97551 09620 63932 03091

Line 19 93039 89416 52795 10631 09728 68202 20963 02477 55494 39563

Line 20 82244 34392 96607 17220 51984 10753 76272 50985 97593 34320

e. What does this list of numbers represent?


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Floor Plans and TilesRandom Sampling

The table shows the names and ages of the 44 Presidents of the United States.

Presidents of the United States

Number PresidentAge at

InaugurationNumber President

Age at Inauguration

1 George Washington 57 13 Millard

Fillmore 50

2 John Adams 61 14 Franklin Pierce 48

3 Thomas Jefferson 57 15 James

Buchanan 65

4 James Madison 57 16 Abraham

Lincoln 52

5 James Monroe 58 17 Andrew

Johnson 56

6 John Quincy Adams 57 18 Ulysses S.

Grant 46

7 Andrew Jackson 61 19 Rutherford B.

Hayes 54

8 Martin Van Buren 54 20 James A.

Garfield 49

9 William Henry Harrison 68 21 Chester A.

Arthur 51

10 John Tyler 51 22 Grover Cleveland 47

11 James K. Polk 49 23 Benjamin Harrison 55

12 Zachary Taylor 64 24 Grover Cleveland 55


Name ________________________________________________________ Date _________________________


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Presidents of the United States

Number PresidentAge at

InaugurationNumber President

Age at Inauguration

25 William McKinley 54 35 John F.

Kennedy 43

26 Theodore Roosevelt 42 36 Lyndon B.

Johnson 55

27 William Howard Taft 51 37 Richard Nixon 56

28 Woodrow Wilson 56 38 Gerald Ford 61

29 Warren G. Harding 55 39 Jimmy Carter 52

30 Calvin Coolidge 51 40 Ronald

Reagan 69

31 Herbert Hoover 54 41 George H.W. Bush 64

32 Franklin D. Roosevelt 51 42 Bill Clinton 46

33 Harry S. Truman 60 43 George W.

Bush 54

34 Dwight D. Eisenhower 62 44 Barack Obama 47


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Name ________________________________________________________ Date _________________________

1. You want to determine the mean age of the U.S. Presidents at their inaugurations. Instead of

calculating the mean using all 44 Presidents’ ages, you will take a sample.

a. What is the population for this situation?

b. Select 10 Presidents whose ages best represent the mean age of a U.S. President at

inauguration.

c. Record the ages of these Presidents.

d. Explain why you chose these Presidents.

e. Is this a random sample? Explain your reasoning.


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f. Calculate the mean age of the Presidents you selected. Round to the nearest year.

Show your work.

g. Record the mean age you calculated and the mean age your classmates calculated

on the line plot.

Mean Age of U.S. Presidents at Inauguration

40 45 50 55Age (in years)

60 65 70

h. Describe the distribution of the line plot in part (g).


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Name ________________________________________________________ Date _________________________

2. You decide to use another method to choose presidents.

a. Randomly select 10 Presidents using the random number generator on a calculator, a random

number table, or some other method. Record the ages of these Presidents.

b. Is this a random sample? Explain your reasoning.

c. Calculate the mean age of the Presidents you selected. Round to the nearest year.

Show your work.

d. Is the mean age of the 10 Presidents you selected a statistic or parameter?

Explain your reasoning.


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e. Record the mean age you calculated and the mean age your classmates calculated on

the line plot.

40 45 50 55Age (in years)

60 65 70

Mean Age of U.S. Presidents at Inauguration

f. Calculate the actual mean age at inauguration of all 44 Presidents. Round to the nearest year.

Plot this age with an M on the line plot in part (e).

g. Describe the distribution of the line plot in part (e).

3. Why is a random sample more desirable than a sample that is not chosen randomly?


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Name ________________________________________________________ Date _________________________

What Does the Data Mean?Using Samples, Centers, and Spreads to Describe Data

There are many different types of breakfast cereals, many of which contain sugar for sweetening.

The data in the table is a sample of the breakfast cereals that are on the market.

CerealGrams of Sugar

per Serving

Mean Number of Grams of Sugar

per Serving

Deviation From the Mean

Absolute Value of the Deviation From the Mean

Cocoa Rounds 13

Flakes of Corn 2

Frosty Flakes 11

Grape Nuggets 7

Golden Nuggets 10

Raisin Branola 9

Wheatleys 8

Multi-Grain O’s 6

All Branola 5

Munch Crunch 12

Branola Flakes 5

Corn Chrisps 3

O’s 1

Shredded Wheatleys 0

Fruity Circles 13

Mean Absolute Deviation


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1. Use the data in the table to answer the following questions.

a. What is the population?

b. What is the sample of cereals that will be used to estimate the average number of grams of

sugar in a typical serving of cereal?

c. Describe the parameter and the statistic for this problem.

d. Determine the mean number of grams of sugar per serving of the sample of cereals. Enter this

value into the 3rd column of the table.

e. Calculate the deviation from the mean for each of the breakfast cereals. Enter the values into

the 4th column of the table.

f. Calculate the absolute value of the deviation from the mean for each of the breakfast cereals.

Enter the values into the 5th column of the table.


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g. Calculate the mean absolute deviation of the sample of breakfast cereals. Enter this value at the

bottom of the table.

2. Use the five number summary to analyze the data set and variability.

a. Determine the five number summary and the IQR for the sample set of breakfast cereal.

Minimum

Q1

Median

Q3

Maximum

IQR

b. Construct a box-and-whisker plot of the data in the table.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


Name ________________________________________________________ Date _________________________


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Name ________________________________________________________ Date _________________________

Taking a SurveyUsing Sample Size

Andrew Carnegie was a businessman and philanthropist who lived in the 19th and 20th centuries.

One of the things Carnegie is well known for is his contributions toward establishing public libraries

throughout the United States, as well as other English-speaking countries. Now, there are an estimated

9,214 public libraries in the 50 states and the District of Columbia. The table shows the number of

libraries by state.

Number StateNumber of

Public LibrariesNumber State

Number of Public Libraries

1 Alabama 208 22 Massachusetts 370

2 Alaska 87 23 Michigan 386

3 Arizona 83 24 Minnesota 139

4 Arkansas 48 25 Mississippi 50

5 California 181 26 Missouri 152

6 Colorado 115 27 Montana 80

7 Connecticut 195 28 Nebraska 271

8 Delaware 21 29 Nevada 22

9 District of Columbia 1 30 New Hampshire 230

10 Florida 79 31 New Jersey 303

11 Georgia 58 32 New Mexico 91

12 Hawaii 1 33 New York 753

13 Idaho 104 34 North Carolina 77

14 Illinois 623 35 North Dakota 80

15 Indiana 239 36 Ohio 251

16 Iowa 539 37 Oklahoma 113

17 Kansas 326 38 Oregon 128

18 Kentucky 116 39 Pennsylvania 457

19 Louisiana 67 40 Rhode Island 49

20 Maine 272 41 South Carolina 42

21 Maryland 24 42 South Dakota 123


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Number StateNumber of

Public LibrariesNumber State

Number of Public Libraries

43 Tennessee 187 48 Washington 66

44 Texas 562 49 West Virginia 97

45 Utah 70 50 Wisconsin 382

46 Vermont 183 51 Wyoming 23

47 Virginia 90

1. Your English teacher has asked you to write an article for the school paper about the importance

of public libraries. You take a sample of the data in the table and calculate the mean number of

libraries in that sample. You decide to randomly select five states from the list.

a. What is the sample size?

b. Take your sample using the Random Number Table at the end of Chapter 14. Begin on any line

and select five states for your sample. What states did you select?

c. Calculate the mean number of libraries in these states. Round to the nearest whole number.

Show your work.


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d. Record the mean number of libraries you calculated and the mean number of libraries your

classmates calculated on a line plot.

e. Describe the data that are graphed on the line plot.


Name ________________________________________________________ Date _________________________


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f. Estimate the mean number of libraries for all 50 states and the District of Columbia using the

line plot. Explain your reasoning.

2. After looking over your data, your teacher thinks that your sample is too small. He asks you to

select 10 states from the list.

a. What is the sample size?

b. Determine a new sample using the random number generator on a calculator or the Random

Number Table in your textbook. What 10 states did you select?

c. Calculate the mean number of libraries in these states. Round to the nearest whole number.

Show your work.


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Name ________________________________________________________ Date _________________________

d. Record the mean number of libraries you calculated and the mean number of libraries your

classmates calculated on a line plot.

e. Describe the data that are graphed on the line plot.

f. Estimate the mean number of libraries for all 50 states and the District of Columbia using the

line plot.


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g. Calculate the actual mean number of libraries. Round to the nearest whole number.

Show your work.

h. How does the sample size affect the results of a survey?

formulating questions and collecting data...will any of these sampling methods produce a random...

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