Week 3 Measures of location and dispersion

Introduction

Every day we are surrounded by information, often in the form of numbers. Sometimes these figures can seem trivial, such as the claim that Britain drinks 100 million cups of tea per day on average, or that your fingernails grow 3.5 millimetres per month. However, these numbers often reflect – and possibly affect – your daily life.

Figure 1

Perhaps you have already looked up today’s weather using an app or logged your daily step count using a fitness tracker. Getting data from a measurement or an observation is rarely the end of the story. Imagine going to the doctors and being told your blood pressure was ‘110 over 70’. What would your next question be?

Usually, we want to know if numbers are big, small, typical, or sufficient. You might go on to ask questions about how those numbers are changing: ‘is my blood pressure higher or lower than it was before?’

An average can be thought of as a value (or sometimes values) that best represents a set of data. Different averages can best serve for different purposes. However, an average alone may not give a good representation of the whole data set, so it is common to also investigate how spread out the data is, for instance from the minimum value to the maximumas is indicated by the range.

Averages are examples of measures of location – they tell us something about a particular place in the data. The range is an example of a measure of dispersion – telling us how spread out the data is.