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Lecture 4 ECON10005 Quantitative Methods 1
Data Reduction: Optimal Descriptive Statistics Data Reduction Optimal Descriptive Statistics
Introduction Distance: Pythagoras is Your Friend Finding the Centre of a Data Set Some Properties of Means Means and Spread Some Alternatives to Standard Deviation A Word About Units

Reading for today’s lecture: Textbook (SSK): Section 5.1 – 5.2 (but not the Introduction). Ignore distinctions between populations and samples. Might also look at Wikipedia entries on Average (especially section on Etymology), Absolute Deviations, Mean Absolute Deviations, and Median Absolute Deviations.

What Have We Learned?

Optimal Descriptive Statistics: Introduction
In the previous lecture we explored order statistics, including minimum, maximum, range, quantiles, and the interquartile range. They seem like sensible things to think about, but are otherwise ad hoc. Question: are they the ‘best’ ways of thinking about these ideas. Pro: they are robust statistics, not unduly sensitive to odd data points. (We will see other statistics that are not very robust at all.) Con: order statistics have a problem with a lack of uniqueness of definition (although this becomes less important in practice as the size of the data set becomes large).

Optimal Descriptive Statistics: Introduction (Continued)

There is no statistic that is ‘perfect’ for all possible uses. However, we can design statistics that have particular strengths. Our aim today is to think about
1. what strengths we might like a statistic to have, and 2. how we might achieve that goal.

Optimal Descriptive Statistics: Introduction (Continued)
To begin we will think about the simple problem of finding the middle (or location or centre) of a data set. Clearly the median is one such measure, as it is a number that splits an ordered data set in to two equally-sized subsets. But is that the best we can do? Another possibility is the mode, which is the most frequently occurring value...

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