Title: Measures of central tendency
Course: UGQuants (SSPS) > Section: Univariate Analysis

Measures of central tendency

Measures of central tendency are very simple summaries or ‘models’ of data that can be applied to just one variable and represent its complexity through a single number. You will doubtless be familiar with the term ‘average’ through its use in everyday life. Though it is often overused to the point of banality (how, for example, might we characterise ‘the average university student’?) the notion of an average is an attempt to reduce great complexity to a more simple and intelligible representation. When we talk of ‘central tendency’, essentially what we are referring to is equivalent to the everyday understanding of ‘average’.

But, an important first step in understanding central tendency is that there are different measures of central tendency (different ways of representing the ‘average’, if you like). Which of these different measures we can legitimately use depends on the type of variable we are dealing with, and more specifically its level of measurement. We will introduce three measures of central tendency: the mean, the median and the mode. Watch the short video of an experiment demonstrating the three terms.

Video: Measures of central tendency and jelly babies

The basic rule is that for variables at the highest levels of measurement (ratio and interval), all three measures of central tendency may be used. For variables at the ordinal level, only median and mode may be used. And for variables at the nominal level, only the mode may be used. This is summarised in the table below, and the reasons for this will become clearer as each measure is explained. It is also important to note that these different measures have significance not only with respect to how we attempt to summarise or ‘model’ data for one variable, but also in relation to techniques for examining the relationships between variables.

Which measures of central tendency may legitimately be used for variables at different levels of measurement?

 | Measures of central tendency
Levels of measurement | Create Infographics