# Statistics

**Topics:**Random variable, Probability distribution, Arithmetic mean

**Pages:**819 (62332 words)

**Published:**April 19, 2014

Rational Decision Making

Only study guide for

DSC2602

University of South Africa

Pretoria

c 2010 University of South Africa

All rights reserved.

Printed and published by the

University of South Africa,

Muckleneuk, Pretoria.

DSC2602/1/2011

Cover: Eastern Transvaal, Lowveld (1928) J. H. Pierneef

J. H. Pierneef is one of South Africa’s best known artists. Permission for the use of this work was kindly granted

by the Schweickerdt family.

The tree structure is a recurring theme in various branches

of the decision sciences.

Preface

Everyday life is full of decisions. What should I wear today? What should I eat? Should I buy the red or blue shirt? Should I buy a speciﬁc house or buy a piece of land? What is the shortest route from my house to work? . . . And many more.

Some of these decisions can be made without thinking or by guesswork. Some can be solved by reasoning or emotions. Some are a bit more diﬃcult and may need additional information. People have been using mathematical tools to aid decision making for decades. During World War II many techniques were developed to assists the military in decision making. These developments were so successful that after World War II many companies used similar techniques in managerial decision making and planning.

The decision making task of modern management is more demanding and more important than ever. Many organisations employ operations research or management science personnel or consultants to apply the principles of scientiﬁc management to problems and decision making. In this module we focus on a number of useful models and techniques that can be used in the decision making process. Two important themes run through the study guide: data analysis and decision making techniques.

Firstly we look at data analysis. This approach starts with data that are manipulated or processed into information that is valuable to decision making. The processing and manipulation of raw data into meaningful information are the heart of data analysis. Data analysis includes data description, data inference, the search for relationships in data and dealing with uncertainty which in turn includes measuring uncertainty and modelling uncertainty explicitly. In addition to data analysis, other decision making techniques are discussed. These techniques include decision analysis, project scheduling and network models. Chapter 1 illustrates a number of ways to summarise the information in data sets, also known as descriptive statistics. It includes graphical and tabular summaries, as well as summary measures such as means, medians and standard deviations.

Uncertainty is a key aspect of most business problems. To deal with uncertainty, we need a basic understanding of probability. Chapter 2 covers basic rules of probability and in Chapter 3 we discuss the important concept of probability distributions in some generality. In Chapter 4 we discuss statistical inference (estimation), where the basic problem is to estimate one or more characteristics of a population. Since it is too expensive to obtain the population information, we instead select a sample from the population and then use the information in the sample to infer the characteristics of the population.

In Chapter 5 we look at the topic of regression analysis which is used to study relationships between variables.

In Chapter 6 we study another type of decision making called decision analysis where costs and proﬁts are considered to be important. The problem is not whether to accept or reject a statement but to select the best alternative from a list of several possible decisions. Usually no statistical data are available. Decision analysis is the study of how people make decisions, particularly when faced with imperfect information or uncertainty.

Chapter 7 deals with project management. Project management consists of planning projects, acquiring resources, scheduling activities...

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