Quantitative Methods for Business and Management

1 Business ManagementStudy ManualsDiploma inBusiness ManagementQUANTITATIVEMETHODS FORBUSINESS ANDMANAGEMENTThe Association of Business Executives5th Floor, CI Tower St Georges Square High Street New MaldenSurrey KT3 4TE United KingdomTel: + 44(0)20 8329 2930 Fax: + 44(0)20 8329 2945E-mail: Copyright, 2008 The Association of Business Executives (ABE) and RRC Business TrainingAll rights reservedNo part of this publication may be reproduced, stored in a retrieval system, or transmitted inany form, or by any means, electronic, electrostatic, mechanical, photocopied or otherwise,without the express permission in writing from The Association of Business in Business ManagementQUANTITATIVE Methods FOR Business ANDMANAGEMENTC ontentsUnitTitlePage1 Data and Data Collection1 Introduction2 Measurement Scales and Types of Data3 Collecting Primary Data5 Collecting Secondary Data102 SamplingProcedures13 Introduction14 Statistical Inference15 Sampling16 Sampling Methods18 Choice of Sampling Method233 Tabulating and Graphing Frequency Distributions25 Introduction26 Frequency Distributions27 Class Limits and ClassIntervals29 Cumulative and Relative Frequency Distributions32 Ways of Presenting Frequency Distributions34 Presenting Cumulative Frequency Distributions424 Measures of Location47 Introduction49 Use of Measures of Location49 Means50 Median56 Quantiles59 Mode62 Choice of Measure64 Appendix.

2 Functions, Equations and Graphs655 Measures of Dispersion71 Introduction72 Range73 Quartile Deviation74 Standard Deviation and Variance75 Coefficient of Variation79 Skewness80 UnitTitlePage6 Index Numbers83 Introduction84 Simple (Unweighted) Index Numbers84 Weighted index Numbers (Laspeyres and Paasche Indices)87 Fisher's Ideal Index89 Formulae90 Quantity or Volume Index Numbers91 Changing the Index Base Year94 Index Numbers in Practice957 Correlation103 Introduction104 Scatter Diagrams104 The Correlation Coefficient108 Rank Correlation1128 Linear Regression119 Introduction120 Regression Lines121 Useof Regression125 Connection Between Correlation and Regression126 Multiple Regression1269 Time Series Analysis129 Introduction130 Structure of a Time Series130 Calculation of Component Factors for the Additive Model135 Multiplicative Model143 Forecasting148 The Z Chart15010 Probability153 Introduction155 Two Laws of Probability156 Permutations159 Combinations162 Conditional Probability164 Sample Space165 Venn Diagrams16711 Binomial and Poisson Distributions183 Introduction184 The Binomial Distribution185 Applications of the

3 Binomial Distribution193 Mean and Standard Deviation of the Binomial Distribution195 The Poisson Distribution195 Application of the Poisson Distribution197 Poisson Approximation to a Binomial Distribution199 Application of Binomial and Poisson Distributions Control Charts202 Appendix: The Binomial Expansion210 UnitTitlePage12 The Normal Distribution213 Introduction214 The Normal Distribution214 Use of the Standard Normal Table219 General Normal Probabilities221 Use of Theoretical Distributions222 Appendix: Standard Normal Table Area under the Normal Curve22613 Significance Testing227 Introduction228 Introduction to Sampling Theory229 Confidence Intervals231 Hypothesis Tests233 Significance Levels240 Small Sample Tests24114 Chi-squared Tests247 Introduction248 Chi-squared as a Test of Independence248 Chi-squared as a Test of Goodness of Fit252 Appendix.

4 Area in the Right Tail of a Chi-squared ( 2) Distribution25715 Decision-making259 Introduction260 Decision-making Under Certainty260 Definitions261 Decision-making Under Uncertainty262 Decision-making Under Risk264 Complex Decisions26716 Applying Mathematical Relationships to Economic and BusinessProblems273 Using Linear Equations to Represent Demand and Supply Functions274 The Effects of a Sales Tax279 Breakeven Analysis280 Breakeven Charts282 The Algebraic Representation of Breakeven Analysis2871 ABE and RRCS tudy Unit 1 Data and Data Role of Quantitative Methods in Business and Scales and Types of Data3 Measurement Scales3 Variables and Primary Data5 Interviews5 Advantages of Interviewing6 Disadvantages of Interviewing6 Self-Completion Questionnaires7 Advantages of Self-Completion Questionnaires8 Disadvantages of Self-Completion Questionnaires9

5 Non-response Bias and Sampling Error9 Personal Secondary Data10 Scanning Published Data10 Internal Data Sources11 External Data Sources11 ONS Publications11 Annual Business Inquiry122 Data and Data Collection ABE and Role of Quantitative Methods in Business and ManagementQuantitative Methods play an important role both in Business research and in the practicalsolution of Business problems. Managers have to take decisions on a wide range of issues,such as: how much to produce what prices to charge how many staff to employ whether to invest in new capital equipment whether to fund a new marketing initiative whether to introduce a new range of products whether to employ an innovative method of all of these cases, it is clearly highly desirable to be able to compute the likely effects ofthe decisions on the company's costs, revenues and, most importantly, profits.

6 Similarly, it isimportant in Business research to be able to use data from samples to estimate parametersrelating to the population as a whole (for example, to predict the effect of introducing a newproduct on sales throughout the UK from a survey conducted in a few selected regions).These sorts of Business problems require the application of statistical Methods such as: time-series analysis and forecasting correlation and regression analysis estimation and significance testing decision-making under conditions of risk and uncertainty break-even Methods in turn require an understanding of a range of summary statistics andconcepts of probability. These topics therefore form the backbone of this of the Quantitative Methods mentioned above come under the general heading ofstatistics. The term "statistics" of course is often used to refer simply to a set of data so, forexample, we can refer to a country's unemployment statistics (which might be presented in atable or chart showing the country's unemployment rates each year for the last few years,and might be broken down by gender, age, region and/or industrial sector, etc.)

7 However,we can also use the term "Statistics" (preferably with a capital letter) to refer to the academicdiscipline concerned with thecollection, description, analysis and interpretation of numericaldata. As such, the subject of Statistics may be divided into two main categories:(a)Descriptive StatisticsThis is mainly concerned with collecting and summarising data, and presenting theresults in appropriate tables and charts. For example, companies collect andsummarise their financial data in tables (and occasionally charts) in their annualreports, but there is no attempt to go "beyond the data".Data and Data Collection3 ABE and RRC(b)Statistical InferenceThis is concerned with analysing data and then interpreting the results (attempting togo "beyond the data"). The main way in which this is done is by collecting data from asample andthen using the sample results to infer conclusions about the example, prior to general elections in the UK and many other countries,statisticians conduct opinion polls in which samples of potential voters are asked whichpolitical party they intend to vote for.

8 The sample proportions are then used to predictthe voting intentions of the entire course, before any descriptive statistics can be calculated or any statistical inferencesmade, appropriate data has to be will start the course, therefore, by seeinghow we collect data. This study unit looks at the various types of data, the main sources ofdata and some of the numerous Methods available to collect SCALES AND TYPES OF DATAM easurementScalesQuantitative Methods use Quantitative data which consists of measurements of variouskinds. Quantitative data may be measured in one of four measurement scales, and it isimportant to be aware of the measurement scale that applies to your data beforecommencing any data description or analysis. The fourmeasurement scales are:(a)Nominal ScaleThe nominal scale uses numbers simply to identify members of a group or example, in a questionnaire, respondents may be asked whether they aremale orfemale and the responses may be given number codes (say 0 for males and 1 forfemales).

9 Similarly, companies may be asked to indicate their ownership form andagain the responses may be given number codes (say 1 for public limited companies,2 forprivate limited companies, 3 for mutual organizations, etc.). In these cases, thenumbers simply indicate the group to which the respondents belong and have nofurther arithmetic meaning.(b)Ordinal ScaleThe ordinal scale uses numbers to rank responses according to some criterion, buthas no unit of measurement. In this scale, numbers are used to represent "more than"or "less than" measurements, such as preferences or rankings. For example, it iscommon in questionnaires to ask respondents to indicate how much they agree with agiven statement and their responses can be given number codes (say 1 for "DisagreeStrongly", 2 for "Disagree", 3 for "Neutral", 4 for "Agree" and 5 for "Agree Strongly").

10 This time, in addition to indicating to which category a respondent belongs, thenumbers measure the degree of agreement with the statement and tell us whether onerespondent agrees more or less than another respondent. However, since the ordinalscale has no units of measurement, wecannotsay that the differencebetween 1 and 2( between disagreeing strongly and just disagreeing) is the same as the differencebetween 4 and 5 ( between agreeing and agreeing strongly).(c)Interval ScaleThe interval scale has a constant unit of measurement, but an arbitrary zero examples of interval scales are the Fahrenheit and Celsius temperature these scales have different zero points ( 0 degrees F is not the same as 0degrees C), it is not possible to form meaningful ratios. For example, although we cansay that 30 degrees C (86 degrees F) is hotter than 15 degrees C (59 degrees F), wecannotsay that it is twice as hot (as it clearly isn't in the Fahrenheit scale).