# Schaum's Easy Outline of Business Statistics

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SCHAUMS Easy OUTLINES

BUSINESSSTATISTICS

LD7479.i-viii 12/24/02 11:46 AM Page i

Other Books in SchaumsEasy Outlines Series Include:

Schaums Easy Outline: CalculusSchaums Easy Outline: College AlgebraSchaums Easy Outline: College MathematicsSchaums Easy Outline: Differential EquationsSchaums Easy Outline: Discrete MathematicsSchaums Easy Outline: Elementary AlgebraSchaums Easy Outline: GeometrySchaums Easy Outline: Linear AlgebraSchaums Easy Outline: Mathematical Handbook

of Formulas and TablesSchaums Easy Outline: PrecalculusSchaums Easy Outline: Probability and StatisticsSchaums Easy Outline: StatisticsSchaums Easy Outline: TrigonometrySchaums Easy Outline: Principles of AccountingSchaums Easy Outline: Principles of EconomicsSchaums Easy Outline: BiologySchaums Easy Outline: BiochemistrySchaums Easy Outline: Molecular and Cell BiologySchaums Easy Outline: College ChemistrySchaums Easy Outline: GeneticsSchaums Easy Outline: Human Anatomy

and PhysiologySchaums Easy Outline: Organic ChemistrySchaums Easy Outline: Applied PhysicsSchaums Easy Outline: PhysicsSchaums Easy Outline: Programming with C++Schaums Easy Outline: Programming with JavaSchaums Easy Outline: Basic ElectricitySchaums Easy Outline: ElectromagneticsSchaums Easy Outline: Introduction to PsychologySchaums Easy Outline: FrenchSchaums Easy Outline: German Schaums Easy Outline: SpanishSchaums Easy Outline: Writing and Grammar

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SCHAUMS Easy OUTLINES

BUSINESS STATISTICS

B a s e d o n S c h a u m s

Out l ine o f Theory and Problems o f

Bus iness S ta t i s t ics , Third Edi t ion

b y L e o n a r d J . K a z m i e r , Ph.D.

A b r i d g e m e n t E d i t o r s

D a n i e l L . F u l k s , Ph.D.and

Michael K. Staton

S C H A U M S O U T L I N E S E R I E SM c G R AW - H I L L

New York Chicago San Francisco Lisbon London Madrid

Mexico City Milan New Delhi San Juan

Seoul Singapore Sydney Toronto

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Copyright 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in theUnited States of America. Except as permitted under the United States Copyright Act of 1976, no partof this publication may be reproduced or distributed in any form or by any means, or stored in a data-base or retrieval system, without the prior written permission of the publisher.

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Contents

v

Chapter 1 Analyzing Business Data 1Chapter 2 Statistical Presentations

and Graphical Displays 7Chapter 3 Describing Business Data:

Measures of Location 18Chapter 4 Describing Business Data:

Measures of Dispersion 26Chapter 5 Probability 37Chapter 6 Probability Distributions

for Discrete Random Variables:Binomial, Hypergeometric, and Poisson 46

Chapter 7 Probability Distributions for Continuous Random Variables:Normal and Exponential 54

Chapter 8 Sampling Distributions and Confidence Intervals for the Mean 60

Chapter 9 Other Confidence Intervals 72Chapter 10 Testing Hypotheses Concerning

the Value of the Population Mean 80Chapter 11 Testing Other Hypotheses 94Chapter 12 The Chi-Square Test for the

Analysis of Qualitative Data 106Chapter 13 Analysis of Variance 113

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Chapter 14 Linear Regression and CorrelationAnalysis 124

Chapter 15 Multiple Regression and Correlation 135Chapter 16 Time Series Analysis and Business

Forecasting 143Chapter 17 Decision Analysis: Payoff Tables

and Decision Trees 155Chapter 18 Statistical Process Control 162Appendices 168Index 173

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SCHAUMS Easy OUTLINES

BUSINESSSTATISTICS

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Chapter 1

AnalyzingBusiness Data

In This Chapter:

Definition of Business Statistics Descriptive and Inferential Statistics Types of Applications in Business Discrete and Continuous Variables Obtaining Data through Direct

Observation vs. Surveys Methods of Random Sampling Other Sampling Methods Solved Problems

Definition of Business Statistics

Statistics refers to the body of techniques used for collecting, organizing,analyzing, and interpreting data. The data may be quantitative, with val-ues expressed numerically, or they may be qualitative, with characteris-tics such as consumer preferences being tabulated. Statistics are used inbusiness to help make better decisions by understanding the sources ofvariation and by uncovering patterns and relationships in business data.

1

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Descriptive and Inferential Statistics

Descriptive statistics include the techniques that are used to summarizeand describe numerical data for the purpose of easier interpretation.These methods can either be graphical or involve computational analy-sis.

Inferential statistics include those tech-niques by which decisions about a statisticalpopulation or process are made based onlyon a sample having been observed. Becausesuch decisions are made under conditions ofuncertainty, the use of probability conceptsis required. Whereas the measured charac-teristics of a sample are called sample sta-tistics, the measured characteristics of a sta-tistical population are called populationparameters. The procedure by which the characteristics of all the mem-bers of a defined population are measured is called a census. When sta-tistical inference is used in process control, the sampling is concernedparticularly with uncovering and controlling the sources of variation inthe quality of the output.

Types of Applications in Business

The methods of classical statistics were developed for the analysis ofsample data, and for the purpose of inference about the population fromwhich the sample was selected. There is explicit exclusion of personaljudgments about the data, and there is an implicit assumption that sam-pling is done from a static population. The methods of decision analysisfocus on incorporating managerial judgments into statistical analysis.The methods of statistical process control are used with the premise thatthe output of a process may not be stable. Rather, the process may be dy-namic, with assignable causes associated with variation in the quality ofthe output over time.

Discrete and Continuous Variables

Adiscrete variable can have observed values only at isolated points alonga scale of values. In business statistics, such data typically occur through

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the process of counting; hence, the values generally are expressed as in-tegers. A continuous variable can assume a value at any fractional pointalong a specified interval of values.

You Need to Know

Continuous data are generated by the process ofmeasuring.

Obtaining Data through Direct Observation vs. Surveys

One way data can be obtained is by direct observation. This is the basisfor the actions that are taken in statistical process control, in which sam-ples of output are systemically assessed. Another form of direct observa-tion is a statistical experiment, in which there is overt control over someor all of the factors that may influence the variable being studied, so thatpossible causes can be identified.

In some situations it is not possible to collect data directly but, rather,the information has to be obtained from individual respondents. A statis-tical survey is the process of collecting data by asking individuals to pro-vide the data. The data may be obtained through such methods as per-sonal interviews, telephone interviews, or written questionnaires.

Methods of Random Sampling

Random sampling is a type of sampling in which every item in a popula-tion of interest, or target population, has a known, and usually equal,chance of being chosen for inclusion in the sample. Having such a sam-ple ensures that the sample items are chosen without bias and providesthe statistical basis for determining the confidence that can be associatedwith the inferences. A random sample is also called a probability sample,or scientific sample. The four principal methods of random sampling arethe simple, systematic, stratified, and cluster sampling methods.

A simple random sample is one in which items are chosen individu-

CHAPTER 1: Analyzing Business Data 3

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ally from the target population on the basis of chance.Such chance selection is similar to the random draw-ing of numbers in a lottery. However, in statisticalsampling a table of random numbers or a randomnumber generator computer program generally isused to identify the numbered items in the populationthat are to be selected for the sample.

A systematic sample is a random sample in which the items are se-lected from the population at a uniform interval of a listed order, such aschoosing every tenth account receivable for the sample. The first accountof the ten accounts to be included in the sample would be chosen ran-domly (perhaps by reference to a table of random numbers). A particularconcern with systematic sampling is the existence of any periodic, orcyclical, factor in the population listing that could lead to a systematic er-ror in the sample results.

In stratified sampling the items in the population are first classifiedinto separate subgroups, or strata, by the researcher on the basis of one ormore important characteristics. Then a simple random or systematic sam-ple is taken separately from each stratum. Such a sampling plan can beused to ensure proportionate representation of various population sub-groups in the sample. Further, the required sample size to achieve a giv-en level of precision typically is smaller than it is with random sampling,thereby reducing sampling cost.

Cluster sampling is a type of random sampling in which the popula-tion items occur naturally in subgroups. Entire subgroups, or clusters, arethen randomly sampled.

Other Sampling Methods

Although a nonrandom sample can turn out to be representative of thepopulation, there is difficulty in assuming beforehand that it will be un-biased, or in expressing statistically the confidence that can be associat-ed with inferences from such a sample.

A judgment sample is one in which an individual selects the items tobe included in the sample. The extent to which such a sample is repre-sentative of the population then depends on the judgment of that individ-ual and cannot be statistically assessed.

A convenience sample includes the most easily accessible measure-ments, or observations, as is implied by the word convenience.

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A strict random sample is not usually feasible in statistical processcontrol, since only readily available items or transactions can easily beinspected. In order to capture changes that are taking place in the qualityof process output, small samples are taken at regular intervals of time.Such a sampling scheme is called the method of rational subgroups. Suchsample data are treated as if random samples were taken at each point intime, with the understanding that one should be alert to any known rea-sons why such a sampling scheme could lead to biased results.

Remember

The four principal methods of ran-dom sampling are the simple, sys-tematic, stratified, and cluster sam-pling methods.

Solved Problems

Solved Problem 1.1 Indicate which of the following terms or operationsare concerned with a sample or sampling (S), and which are concernedwith a population (P): (a) group measures called parameters, (b) use ofinferential statistics, (c) taking a census, (d) judging the quality of an in-coming shipment of fruit by inspecting several crates of the large num-ber included in the shipment.

Solution: (a) P, (b) S, (c) P, (d) S...

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