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MAS1403 Quantitative Methods for Business Management Semester 1, 2013—2014 Lecturer: Dr. Daniel Henderson School of Mathematics & Statistics
Chapter 1 Collecting and Presenting Data 1.1 Introduction Data are the key to many important management decisions. Is a new product selling well? Do potential customers like the new advertising campaign? Should we launch a new product? These are all questions that can be answered with data. We begin this course with some basic methods of collecting, representing and describing data. In this first lecture we will look at the different kinds of data that exist, how we might obtain these data, and basic methods for presenting them. 1.1.1 Examples Car Maintenance If we were buying a new car, it would be useful to know how much it was going to cost to run it over the next three years. Obviously, we cannot predict this exactly as each individual car and each user will be slightly different. Collecting data from people who have bought similar cars will give us some idea of the distribution of costs over the population of car buyers, which in turn provides us with information regarding the likely cost of running the car. Sizing Clothes Most clothing now comes in essentially standard sizes, but from where do these standards come? By sampling from the general population as a whole, standards can be set around the most common sizes. We cannot say that an individual is exactly a standard size. However, we can say that they will probably fall within a range either side of a standard. 1.1.2 Definitions The quantities measured in a study are called random variables and a particular outcome is called an observation . A collection of observations is the data . The collection of all possible outcomes is the population . If we were interested in the height of people doing management courses at Newcastle, that would be our random variable; a particular person’s height would be the observation and if we 1
CHAPTER 1. COLLECTING AND PRESENTING DATA 2 measured everyone doing MAS1403, those would be our data, which would form a sample from the population of all students registered within the School of Management. In practice it is difficult to observe whole populations, unless we are interested in a very limited population, e.g. the students taking MAS1403. In reality we usually observe a subset of the population; we will come back to sampling later in Section 1.2. Variables are one of two types, qualitative or quantitative . Qualitative variables have non– numerical outcomes. They are usually categorical . Examples of qualitative variables include: sex of a person or animal, colour of a car, mode of transport and football team supported. Quan- titative variables have numerical outcomes with a natural ordering. Examples include: people’s height, time to failure of a component and number of defective components in a batch.