Chapter 1
An Introduction to Business
Statistics
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

Chapter Outline
1.1 Populations and Samples
1.2 Selecting a Random Sample
1.3 Ratio, Interval, Ordinal, and Nominative
Scales of Measurement (Optional)
1.4 An Introduction to Survey Sampling
(Optional)
1.5 More About Data Acquisition and Survey
Sampling (Optional)
1-2

1.1 Populations and Samples
 Population: A set of existing units
(people, objects or events)
 Variable: Any characteristic of the population
 Census: An examination all of the population of measurements
 Sample: A subset of the units of a population
1-3

Quantitative Versus Qualitative
 Quantitative: Measurements that represent quantities
 Annual starting salary
 Gasoline mileage
 Qualitative: A descriptive category to which a population unit belongs: a descriptive attribute of a population unit
 A person’s gender is qualitative
 Make of automobile
1-4

Population of Measurements
 Measurement of the variable of interest for each and every population unit
 Sometimes referred to as an observation
 For example, annual starting salaries of all graduates from last year’s MBA program
 Census: The process of collecting the population of all measurements
 Sample: A subset of population units
1-5

Descriptive Statistics
 Descriptive Statistics: The science of describing the important aspects of a set of measurements
 Statistical Inference: The science of describing the important aspects a set of measurements
1-6

1.2 Selecting a Random Sample
 Random Sample: Selected so that, on each selection from the population, every unit remaining in the population on that selection has the same chance of being chosen
 Sample with replacement
 Sample without replacement
1-7

Approximately Random Samples
 In general, must make a list identifying each and every individual population unit
 This may not be possible
 Draw a “systematic” sample
 Randomly enter the population and systematically sample every k th unit
1-8

Finite and Infinite Populations
 Finite if it is of fixed and limited size
 Finite if it can be counted
 Infinite if it is unlimited
 Infinite if listing or counting every element is impossible
1-9

Sampling a Process
Inputs Process Outputs
1-10

Statistical Control
 To determine if a process is in control or not, sample the process often enough to detect unusual variations
 Issue: How often to sample?
 See Example 1.3, “The Car Mileage
Case: Estimating Mileage,” in the textbook
1-11

Figure 1.2
Runs Plot
1-12

Figure 1.3
Out of Control (Level Decreasing)
1-13

Figure 1.4
Out of Control (Variation Increasing)
1-14

1.3 Ratio, Interval, Ordinal, and
Nominative Scales of Measurement
(Optional)
 Nominative
 Ordinal
 Interval
 Ratio
1-15

Qualitative Variables
 Nominative: A qualitative variable for which there is no meaningful ordering, or ranking, of the categories
 Example: gender, car color
 Ordinal: A qualitative variable for which there is a meaningful ordering, or ranking, of the categories
 Example: teaching effectiveness
1-16

Interval Variable
 All of the characteristics of ordinal plus…
 Measurements are on a numerical scale with an arbitrary zero point
 The “zero” is assigned: it is nonphysical and not meaningful
 Zero does not mean the absence of the quantity that we are trying to measure
1-17

Interval Variable
Continued
 Can only meaningfully compare values by the interval between them


Cannot compare values by taking their ratios
“Interval” is the arithmetic difference between the values
 Example: temperature


0  F means “cold,” not “no heat”
60  F is not twice as warm as 30  F
1-18

Ratio Variable
 All the characteristics of interval plus…
 Measurements are on a numerical scale with a meaningful zero point
 Zero means “none” or “nothing”
 Values can be compared in terms of their interval and ratio
 $30 is $20 more than $10
 $0 means no money
1-19

Ratio Variable
Continued
 In business and finance, most quantitative variables are ratio variables, such as anything to do with money
 Examples: Earnings, profit, loss, age, distance, height, weight
1-20

1.4 An Introduction to Survey
Sampling
(Optional)
 Already know some sampling methods
 Also called sampling designs, they are:

Random sampling


Systematic sampling
Voluntary response sampling
 But there are other sample designs


Stratified random sampling
Multi-stage cluster sampling
1-21

Stratified Random Sample
 Divide the population into nonoverlapping groups, called strata, of similar units


Separately, select a random sample from each and every stratum
Combine the random samples from each stratum to make the full sample
 Appropriate when the population consists of two or more different groups
1-22

Multi-Stage Cluster Sampling
 Group a population into subpopulations
 Each cluster is a representative small-scale version of the population
 Pick a random sample of clusters
 A simple random sample is chosen from each chosen cluster
 Combine the random samples from each cluster to make the full sample
1-23

Combination
 It is sometimes a good idea to combine stratification with multistage cluster sampling
 For example, we wish to estimate the proportion of all registered voters who favor a presidential candidate
 Divide United States into regions
 Use these regions as strata
 Take a multi-stage cluster sample from each stratum
1-24

Systematic Sampling
 To systematically select replacement from a frame of divide N by n whole number n units without
N units, and round down to a
 Randomly select one unit within the first N/n interval
 Select every N/n th unit after that
1-25

1.5 More About Data Acquisition and
Survey Sampling
(Optional)
 Web searches…
 Cheap, fast
 Limited in type of information we are able to find
 Data collection agency
 Cost money
 Buy subscription or individual reports
1-26

Initiating a Study
 First, define the variable of interest, called a response variable
 Next, define other variables that may be related to the variable of interest and will be measured, called independent variables
 If we manipulate the independent variables, we have an experimental study
 If unable to control independent variables, the study is observational
1-27

Types of Survey Questions
 Dichotomous questions ask for a yes/no response
 Multiple choice questions give the respondent a list of of choices to select from
 Open-ended questions allow the respondent to answer in their own words
1-28

Errors Occurring in Surveys
 Random sampling should eliminate bias
 But even a random sample may not be representative because of:
 Sampling error
 Under-coverage
 Non-response
 Response bias
1-29