For a population containing n 902

Chapter #1:

Beginning of the End … Or the End of the

Beginning?

The past few years have been challenging for Good Tunes & More (GT&M), a

business that traces its roots to Good Tunes, a store that exclusively sold music

CDs and vinyl records.

GT&M first broadened its merchandise to include home entertainment

and computer systems (the “More”), and then undertook an expansion to take

advantage of prime locations left empty by bankrupt former competitors. Today,

GT&M finds itself at a crossroads. Hoped-for increases in revenues that have

failed to occur and declining profit margins due to the competitive pressures of

online sellers have led management to reconsider the future of the business.

While some investors in the business have argued for an orderly retreat,

closing

stores and limiting the variety of merchandise, GT&M CEO Emma Levia

has decided to “double down” and expand the business

by purchasing Whitney

Wireless, a successful three-store chain that sells smartphones

and other mobile

devices.

Levia foresees creating a brand new “A-to-Z” electronics retailer but

first must establish a fair and reasonable price for the privately held Whitney

Wireless.

To do so, she has asked a group of analysts to identify the data that

would be helpful in setting a price for the wireless business. As part of that

group, you quickly realize that you need the data that would help to verify the

contents of the wireless company’s basic financial statements.

You focus on data associated with the company’s profit and loss statement

and quickly realize the need for sales and expense-related

variables.

You begin to

think about what the data for

such variables would look

like and how to collect those

data. You realize that you are

starting to apply the DCOVA

framework to the objective

of helping Levia acquire

Whitney Wireless.

Chapter Defining and

1 Collecting Data

Tyler Olson/Shutterstock

contents

1.1 Defining Variables

1.2 Collecting Data

1.3 Types of Sampling Methods

1.4 Types of Survey Errors

Think About This: New Media

Surveys/Old Sampling Problems

Using Statistics: Beginning of

the End … Revisited

Chapter 1 Excel Guide

Chapter 1 Minitab Guide

Objectives

Understand issues that arise

when defining variables

How to define variables

How to collect data

Identify the different ways to

collect a sample

Understand the types of

survey errors

Business Statistics: A First Course, Seventh Edition, by David M. Levine, Kathryn A. Szabat, and David F. Stephan. Published by Pearson.

Copyright © 2016 by Pearson Education, Inc.

ISBN: 978-1-323-26258-0

1.1 Defining Variables 11

When Emma Levia decides to purchase Whitney Wireless, she has defined a new

goal or business objective for GT&M. Business objectives can arise from any

level of management and can be as varied as the following:

• A marketing analyst needs to assess the effectiveness of a new online advertising campaign.

• A pharmaceutical company needs to determine whether a new drug is more effective

than those currently in use.

• An operations manager wants to improve a manufacturing or service process.

• An auditor needs to review a company’s financial transactions to determine whether the

company is in compliance with generally accepted accounting principles.

Establishing an objective marks the end of a problem definition process. This end triggers

the new process of identifying the correct data to support the objective. In the GT&M scenario,

having decided to buy Whitney Wireless, Levia needs to identify the data that would be helpful

in setting a price for the wireless business. This process of identifying the correct data triggers

the start of applying the tasks of the DCOVA framework. In other words, the end of problem

definition marks the beginning of applying statistics to business decision making.

Identifying the correct data to support a business objective is a two-part job that requires

defining variables and collecting the data for those variables. These tasks are the first two tasks

of the DCOVA framework first defined in Section GS.1 and which can be restated here as:

• Define the variables that you want to study to solve a problem or meet an objective.

• Collect the data for those variables from appropriate sources.

This chapter discusses these two tasks which must always be done before the Organize, Visualize,

and Analyze tasks.

Defining variables at first may seem to be the simple process of making the list of things one

needs to help solve a problem or meet an objective. However, consider the GT&M scenario.

Most would quickly agree that yearly sales of Whitney Wireless would be part of the data

needed to meet Levia’s objective, but just placing “yearly sales” on a list could lead to confusion

and miscommunication: Does this variable refer to sales per year for the entire chain or

for individual stores? Does the variable refer to net or gross sales? Are the yearly sales values

expressed in number of units or as currency amounts such as U.S. dollar sales?

These questions illustrate that for each variable of interest that you identify you must supply

an operational definition, a universally accepted meaning that is clear to all associated

with an analysis. Operational definitions should also classify the variable, as explained in the

next section, and may include additional facts such as units of measures, allowed range of

values, and definitions of specific variable values, depending on how the variable is classified.

Classifying Variables by Type

When you operationally define a variable, you must classify the variable as being either categorical

or numerical. Categorical variables (also known as qualitative variables) take categories

as their values. Numerical variables (also known as quantitative variables) have values

that represent a counted or measured quantity. Classification also affects a variable’s operational

definition and getting the classification correct is important because certain statistical methods

can be applied correctly to one type or the other, while other methods may need a specific mix

of variable types.

Categorical variables can take the form of yes-and-no questions such as “Do you have a

Twitter account?” (in which yes and no form the variable’s two categories) or describe a trait

or characteristic that has many categories such as undergraduate class standing (which might

have the defined categories freshman, sophomore, junior, and senior). When defining a categorical

variable, the list of permissible category values must be included and each category

1.1 Defining Variables

Student Tip

Providing operational

definitions for concepts

is important, too, when

writing a textbook! The

end-of-chapter Key

Terms gives you an index

of operational definitions

and the most fundamental

definitions are

presented in boxes such

as the page 3 box that

defines variable and data.

Business Statistics: A First Course, Seventh Edition, by David M. Levine, Kathryn A. Szabat, and David F. Stephan. Published by Pearson.

Copyright © 2016 by Pearson Education, Inc.

ISBN: 978-1-323-26258-0

12 Chapter 1 Defining and Collecting Data

value should be defined, too, e.g., that a “freshman” is a student who has completed fewer

than 32 credit hours. Overlooking these requirements can lead to confusion and incorrect data

collection. In one famous example, when persons were asked by researchers to fill in a value

for the categorical variable sex, many answered yes and not male or female, the values that the

researchers intended. (Perhaps this is the reason that gender has replaced sex on many data collection

forms—gender’s operational definition is more self-apparent.)

The operational definitions of numerical variables are affected by whether the variable being

defined is discrete or continuous. Discrete variables such as “number of items purchased”

or “total amount paid” are numerical values that arise from a counting process. Continuous

variables such as “time spent on checkout line” or “distance from home to store” have numerical

values that arise from a measuring process and those values depend on the precision of the

measuring instrument used. For example, “time spent on checkout line” might be 2, 2.1, 2.14,

or 2.143 minutes, depending on the precision of the timing instrument being used. Units of

measures and the level of precision should be part of the operational definitions of continuous

variables, e.g., “tenths of a second” for “time spent on checkout line.” The definitions of any

numerical variable can include the allowed range of values, such as “must be greater than 0”

for “number of items purchased.”

When defining variables for survey collection (discussed in Section 1.2), thinking about

the responses you seek helps classify variables as Table 1.1 demonstrates. Thinking about how

a variable will be used to solve a problem or meet an objective can also be helpful when you

define a variable. The variable age might be a numerical (discrete) variable in some cases or

might be categorical with categories such as child, young adult, middle-aged, and retirement

aged in other contexts.

Problems for Section 1.1

Learning the Basics

1.1 Four different beverages are sold at a fast-food restaurant:

soft drinks, tea, coffee, and bottled water. Explain why the

type of beverage sold is an example of a categorical variable.

1.2 U.S. businesses are listed by size: small, medium, and large. Explain

why business size is an example of a categorical variable.

1.3 The time it takes to download a video from the Internet is

measured. Explain why the download time is a continuous

numerical variable.

Applying the Concepts

SELF

Test

1.4 For each of the following variables, determine

whether the variable is categorical or numerical. If the

variable is numerical, determine whether the variable is discrete or

continuous.

a. Number of cellphones in the household

b. Monthly data usage (in MB)

c. Number of text messages exchanged per month

d. Voice usage per month (in minutes)

e. Whether the cellphone is used for email

1.5 The following information is collected

Question Responses Variable Type

Do you have a Facebook

profile?

❑ Yes ❑ No Categorical

How many text messages have

you sent in the past three days?

______ Numerical

(discrete)

How long did the mobile app

update take to download?

______ seconds Numerical

(continuous)

Problems for Section 1.1

Learning the Basics

1.1 Four different beverages are sold at a fast-food restaurant:

soft drinks, tea, coffee, and bottled water. Explain why the

type of beverage sold is an example of a categorical variable.

1.2 U.S. businesses are listed by size: small, medium, and large. Explain

why business size is an example of a categorical variable.

1.3 The time it takes to download a video from the Internet is

measured. Explain why the download time is a continuous

numerical variable.

Applying the Concepts

SELF

Test

1.4 For each of the following variables, determine

whether the variable is categorical or numerical. If the

variable is numerical, determine whether the variable is discrete or

continuous.

a. Number of cellphones in the household

b. Monthly data usage (in MB)

c. Number of text messages exchanged per month

d. Voice usage per month (in minutes)

e. Whether the cellphone is used for email

1.5 The following information is collected from students upon

exiting the campus bookstore during the first week of classes.

a. Amount of time spent shopping in the bookstore

b. Number of textbooks purchased

c. Academic major

d. Gender

Classify each of these variables as categorical or numerical. If the

variable is numerical, determine whether the variable is discrete or

continuous.

1.6 For each of the following variables, determine whether the

variable is categorical or numerical. If the variable is numerical,

determine whether the variable is discrete or continuous.

a. Name of Internet service provider

b. Time, in hours, spent surfing the Internet per week

c. Whether the individual uses a mobile phone to connect to the

Internet

d. Number of online purchases made in a month

e. Where the individual uses social networks to find sought-after

information

Learn More

Read the Short Takes for

Chapter 1 for more examples

of classifying variables

as either

categorical or numerical.

Ta ble 1 . 1

Identifying Types of

Variables

Question Responses Variable Type

Do you have a Facebook

profile?

❑ Yes ❑ No Categorical

How many text messages have

you sent in the past three days?

______ Numerical

(discrete)

How long did the mobile app

update take to download?

______ seconds Numerical

(continuous)

Business Statistics: A First Course, Seventh Edition, by David M. Levine, Kathryn A. Szabat, and David F. Stephan. Published by Pearson.

Copyright © 2016 by Pearson Education, Inc.

ISBN: 978-1-323-26258-0

1.2 Collecting Data 13

1.2 Collecting Data

After defining the variables that you want to study, you can proceed with the data collection

task. Collecting data is a critical task because if you collect data that are flawed by biases,

ambiguities, or other types of errors, the results you will get from using such data with even

the most sophisticated statistical methods will be suspect or in error. (For a famous example of

flawed data collection leading to incorrect results, read the Think About This essay on page 21.)

Data collection consists of identifying data sources, deciding whether the data you collect

will be from a population or a sample, cleaning your data, and sometimes recoding variables.

The rest of this section explains these aspects of data collection.

Data Sources

You collect data from either primary or secondary data sources. You are using a primary data

source if you collect your own data for analysis. You are using a secondary data source if the

data for your analysis have been collected by someone else.

You collect data by using any of the following:

• Data distributed by an organization or individual

• The outcomes of a designed experiment

• The responses from a survey

• The results of conducting an observational study

• Data collected by ongoing business activities

Market research companies and trade associations distribute data pertaining to specific industries

or markets. Investment services provide business and financial data on publicly listed

companies. Syndicated services such as The Nielsen Company provide consumer research data to

telecom and mobile media companies. Print and online media companies also distribute data that

they may have collected themselves or may be republishing from other sources.

The outcomes of a designed experiment are a second data source. For example, a consumer

electronics company might conduct an experiment that compares the sales of mobile

electronics merchandise for different store locations. Note that developing a proper experimental

design is mostly beyond the scope of this book, but Chapter 10 discusses some of the

fundamental experimental design concepts.

Survey responses represent a third type of data source. People being surveyed are asked

questions about their beliefs, attitudes, behaviors, and other characteristics. For example,

people could be asked which store location for mobile electronics merchandise is preferable.

(Such a survey could lead to data that differ from the data collected from the outcomes of the

1.7 For each of the following variables, determine whether the

variable is categorical or numerical. If the variable is numerical,

determine whether the variable is discrete or continuous.

a. Amount of money spent on clothing in the past month

b. Favorite department store

c. Most likely time period during which shopping for clothing

takes place (weekday, weeknight, or weekend)

d. Number of pairs of shoes owned

1.8 Suppose the following information is collected from Robert

Keeler on his application for a home mortgage loan at the Metro

County Savings and Loan Association.

a. Monthly payments: $2,227

b. Number of jobs in past 10 years: 1

c. Annual family income: $96,000

d. Marital status: Married

Classify each of the responses by type of data.

1.9 One of the variables most often included in surveys is income.

Sometimes the question is phrased “What is your income

(in thousands of dollars)?” In other surveys, the respondent is

asked to “Select the circle corresponding to your income level”

and is given a number of income ranges to choose from.

a. In the first format, explain why income might be considered

either discrete or continuous.

b. Which of these two formats would you prefer to use if you

were conducting a survey? Why?

1.10 If two students score a 90 on the same examination,

what arguments could be used to show that the underlying

variable—test score—is continuous?

1.11 The director of market research at a large department store

chain wanted to conduct a survey throughout a metropolitan area

to determine the amount of time working women spend shopping

for clothing in a typical month.

a. Indicate the type of data the director might want to collect.

b. Develop a first draft of the questionnaire needed in (a) by writing

three categorical questions and three numerical questions

that you feel would be appropriate for this survey

One of the variables most often included in surveys is income.

Sometimes the question is phrased “What is your income

1.2 Collecting Data

After defining the variables that you want to study, you can proceed with the data collection

task. Collecting data is a critical task because if you collect data that are flawed by biases,

ambiguities, or other types of errors, the results you will get from using such data with even

the most sophisticated statistical methods will be suspect or in error. (For a famous example of

flawed data collection leading to incorrect results, read the Think About This essay on page 21.)

Data collection consists of identifying data sources, deciding whether the data you collect

will be from a population or a sample, cleaning your data, and sometimes recoding variables.

The rest of this section explains these aspects of data collection.

Data Sources

You collect data from either primary or secondary data sources. You are using a primary data

source if you collect your own data for analysis. You are using a secondary data source if the

data for your analysis have been collected by someone else.

You collect data by using any of the following:

• Data distributed by an organization or individual

• The outcomes of a designed experiment

• The responses from a survey

• The results of conducting an observational study

• Data collected by ongoing business activities

Market research companies and trade associations distribute data pertaining to specific industries

or markets. Investment services provide business and financial data on publicly listed

companies. Syndicated services such as The Nielsen Company provide consumer research data to

telecom and mobile media companies. Print and online media companies also distribute data that

they may have collected themselves or may be republishing from other sources.

The outcomes of a designed experiment are a second data source. For example, a consumer

electronics company might conduct an experiment that compares the sales of mobile

electronics merchandise for different store locations. Note that developing a proper experimental

design is mostly beyond the scope of this book, but Chapter 10 discusses some of the

fundamental experimental design concepts.

Survey responses represent a third type of data source. People being surveyed are asked

questions about their beliefs, attitudes, behaviors, and other characteristics. For example,

people could be asked which store location for mobile electronics merchandise is preferable.

(Such a survey could lead to data that differ from the data collected from the outcomes of the

1.7 For each of the following variables, determine whether the

variable is categorical or numerical. If the variable is numerical,

determine whether the variable is discrete or continuous.

a. Amount of money spent on clothing in the past month

b. Favorite department store

c. Most likely time period during which shopping for clothing

takes place (weekday, weeknight, or weekend)

d. Number of pairs of shoes owned

1.8 Suppose the following information is collected from Robert

Keeler on his application for a home mortgage loan at the Metro

County Savings and Loan Association.

a. Monthly payments: $2,227

b. Number of jobs in past 10 years: 1

c. Annual family income: $96,000

d. Marital status: Married

Classify each of the responses by type of data.

1.9 One of the variables most often included in surveys is income.

Sometimes the question is phrased “What is your income

(in thousands of dollars)?” In other surveys, the respondent is

asked to “Select the circle corresponding to your income level”

and is given a number of income ranges to choose from.

a. In the first format, explain why income might be considered

either discrete or continuous.

b. Which of these two formats would you prefer to use if you

were conducting a survey? Why?

1.10 If two students score a 90 on the same examination,

what arguments could be used to show that the underlying

variable—test score—is continuous?

1.11 The director of market research at a large department store

chain wanted to conduct a survey throughout a metropolitan area

to determine the amount of time working women spend shopping

for clothing in a typical month.

a. Indicate the type of data the director might want to collect.

b. Develop a first draft of the questionnaire needed in (a) by writing

three categorical questions and three numerical questions

that you feel would be appropriate for this survey.

Business Statistics: A First Course, Seventh Edition, by David M. Levine, Kathryn A. Szabat, and David F. Stephan. Published by Pearson.

Copyright © 2016 by Pearson Education, Inc.

ISBN: 978-1-323-26258-0

14 Chapter 1 Defining and Collecting Data

designed experiment of the previous paragraph.) Surveys can be affected by any of the four

types of errors that are discussed in Section 1.4.

Observational study results are a fourth data source. A researcher collects data by directly

observing a behavior, usually in a natural or neutral setting. Observational studies are a common

tool for data collection in business. For example, market researchers use focus groups

to elicit unstructured responses to open-ended questions posed by a moderator to a target audience.

Observational studies are also commonly used to enhance teamwork or improve the

quality of products and services.

Data collected by ongoing business activities are a fifth data source. Such data can be

collected from operational and transactional systems that exist in both physical “bricks-andmortar”

and online settings but can also be gathered from secondary sources such as third-party

social media networks and online apps and website services that collect tracking and usage data.

For example, a bank might analyze a decade’s worth of financial transaction data to identify

patterns of fraud, and a marketer might use tracking data to determine the effectiveness of a

website.

Sources for big data (see Section GS.3) tend to be a mix of primary and secondary sources

of this last type. For example, a retailer interested in increasing sales might mine Facebook

and

Twitter accounts to identify sentiment about certain products or to pinpoint top influencers and

then match those data to its own data collected during customer transactions.

Populations and Samples

You collect your data from either a population or a sample. A population consists of all the

items or individuals about which you want to reach conclusions. All the GT&M sales transactions

for a specific year, all the full-time students enrolled in a college, and all the registered

voters in Ohio are examples of populations. In Chapter 3, you will learn that when you analyze

data from a population you compute parameters.

A sample is a portion of a population selected for analysis. The results of analyzing a

sample are used to estimate characteristics of the entire population. From the three examples

of populations just given, you could select a sample of 200 GT&M sales transactions randomly

selected by an auditor for study, a sample of 50 full-time students selected for a marketing

study, and a sample of 500 registered voters in Ohio contacted via telephone for a political

poll. In each of these examples, the transactions or people in the sample represent a portion of

the items or individuals that make up the population. In Chapter 3, you will learn that when

you analyze data from a sample you compute statistics .

You collect data from a sample when any of the following applies:

• Selecting a sample is less time consuming than selecting every item in the population.

• Selecting a sample is less costly than selecting every item in the population.

• Analyzing a sample is less cumbersome and more practical than analyzing the entire

population.

Structured Versus Unstructured Data

The data you collect may be formatted in a variety of ways, some of which add to the data

collection task. For example, suppose that you wanted to collect electronic financial data

about a sample of companies. That data might exist as tables of data, the contents of standardized

documents such as fill-in-the-blank surveys, a continuous stream of data such as a

stock ticker, or text messages or emails delivered from email systems or social media websites.

Some of these forms, such as a set of text messages have very little or no repeating

structure, are examples of unstructured data. Although unstructured data forms can form a

part of a big data collection,

collecting data in unstructured forms for the statistical methods

discussed in this book requires conversion of the data to a structured form. For example,

after collecting text messages,

you could convert their contents to a structured form by defining

a set of variables that might include a numerical variable that counts the number of

words in the message and various categorical variables that help classify the content of the

message.

Learn More

Read the Short Takes

for Chapter 1 for a further

discussion about data

sources.

Student Tip

To help remember the

difference between a

sample and a population,

think of a pie. The

entire pie represents the

population, and the pie

slice that you select is

the sample.

Business Statistics: A First Course, Seventh Edition, by David M. Levine, Kathryn A. Szabat, and David F. Stephan. Published by Pearson.

Copyright © 2016 by Pearson Education, Inc.

ISBN: 978-1-323-26258-0

1.2 Collecting Data 15

Electronic Formats and Encodings

The same form of data can exist in more than one electronic format, with some formats more

immediately usable than others. For example, a table of data might exist as a scanned image

or as data in a worksheet file. The worksheet data could be immediately used in a statistical

analysis, but the scanned image would need to be first converted to worksheet data using a

character-scanning program that can recognize numbers in an image.

Data can also be encoded in more than one way, as you may have learned in an information

systems course. Different encodings may affect the recorded precision of values for

continuous variables and lead to values more imprecise or values that convey a false sense of

precision, such as a time measurement that gets encoded in ten-thousandths of a second when

the original measurement was only in tenths of a second. This changed precision can violate

the operational definition of a continuous variable and sometimes affect results calculated.

Data Cleaning

Whatever ways you choose to collect data, you may find irregularities in the values you collect

such as undefined or impossible values. For a categorical variable, an undefined value would

be a value that does not represent one of the categories defined for the variable. For a numerical

variable, an impossible value would be a value that falls outside a defined range of possible

values for the variable. For a numerical variable without a defined range of possible values,

you might also find outliers, values that seem excessively different from most of the rest of the

values. Such values may or may not be errors, but they demand a second review.

Values that are missing are another type of irregularity. A missing value is a value that was

not able to be collected (and therefore not available to be analyzed). For example, you would

record a nonresponse to a survey question as a missing value. You can represent missing values

in Minitab by using an asterisk value for a numerical variable or by using a blank value for a

categorical variable, and such values will be properly excluded from analysis. The more limited

Excel has no special values that represent a missing value. When using Excel, you must

find and then exclude missing values manually.

When you spot an irregularity in the data you have collected, you may have to “clean” the

data. Although a full discussion of data cleaning is beyond the scope of this book (see reference

8), you can learn more about the ways you can use Excel or Minitab for data cleaning in

the Short Takes for Chapter 1.

Recoding Variables

After you have collected data, you may discover that you need to reconsider the categories that

you have defined for a categorical variable or that you need to transform a numerical variable

into a categorical variable by assigning the individual numeric data values to one of several

groups. In either case, you can define a recoded variable that supplements or replaces the

original variable in your analysis.