Title: The Mode
Course: UGQuants (SSPS) > Section: Univariate Analysis

The Mode

The mode can be used as a measure of central tendency with variables at any level of measurement. The mode is perhaps the most straightforward of all measures of central tendency: it is simply the most common value for a given variable, i.e., the value that is taken by the highest number of cases.

Whether or not the mode offers a useful measure of central tendency often depends on the number of possible values we have for the variable in question. For ratio variables that have a large number of possible values – e.g. income – the mode is rarely a useful ‘summary’ of the data because it is likely to represent only a very small number of cases which may not reflect the ‘average’ case very well at all. On the other hand, some ratio variables have quite a limited range of possible values and in these instances the mode is more useful – e.g. in the 2011 Census the modal number of children in households in England & Wales was zero (that is, more household contained no dependent children than contained any other number).

But we tend to highlight the mode more often for nominal and ordinal level variables, which by their nature tend to have only a limited range of possible values. Of course the mode is especially important for nominal variables, because it is the only legitimate measure of central tendency for such data: we cannot use the mean because nominal values have no numerical significance, and we cannot use the median, because they are not rank ordered.

However, like the other measures of central tendency the mode usually gives only an incomplete summary of our data and thus excludes a lot of detail. Even for nominal variables, the modal category might only account for a minority of cases and thus tells us nothing about how the majority of cases are distributed. For that reason we often highlight the mode only as part of a frequency table showing the full distribution of values for all cases.

The following are some examples of modal values:

Also note that it is possible to have more than one mode for any variable. When two distinct values are equally common, and more common than any other values, we say our data for that variable has a ‘bimodal’ distribution. We might also say this when two values do not represent an equally high proportion of cases, but are clearly much more common than any of the other possible values for a variable.