L04: Representing & Benchmarking

Lecture Notes, Powerpoint Slides, and Data Set/EXCEL sheet are attached at bottom

Lecture 4: Representing & Benchmarking:

Measures Of Central Tendency

Quran 17:85 AND THEY will ask thee about [the nature of] divine inspiration. Say: "This inspiration [comes] at my Sustainer's behest; and [you cannot understand its nature, O men, since] you have been granted very little of [real] knowledge."

Limitations on our ability to understand lead us to try to understand complex data sets by summarizing them with a few numbers. The simplest summaries are just one number – these try to represent the entire data set by just one number. For example, on most issues, there is a range of opinions. Instead of exploring the whole range, we might say that most people have the following opinion. This gives us one opinion which is supposed to represent the whole population. Similarly, we might say that the typical family in Pakistan consists of six members, or that the average income of Pakistani people is PKR 3000 per month.

We use such over-simplified representations because our minds cannot cope with the data in its full diversity. We need to simplify in order to understand. For example, in economic theory, it is very frequently assumed that the whole economy consists of a single person – this allows economists to solve the equations required to make calculations demanded by models of economic theory. This assumption is solely due to limitations on our computational abilities: we cannot solve models with hundreds of thousands of equations, one for each person. At the same time, the single consumer model is so unrealistic that Nobel prize winning economist Robert Solow blamed it for the failure of economists to foresee the global financial crisis of 2007-2008.

Our goal in this chapter is to learn the most common methods used to summarize the data by one number, and also the strengths and weaknesses of such methods. At the same time, we must always be aware that one number summaries always hide more about the data than they reveal, and that they can be manipulated in many different ways for rhetorical purposes. There are three main measures of central tendency which are commonly used: the mean, median and mode. We first explain what they are and how they are calculated. Then we will compare and evaluate them by discussing their properties, strengths, weaknesses.

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