The median represents a convenient way to summarise a series of numbers to give a rough indication of a typical value. It is a summary statistic as it represents a summary of a set of data. There are other summary statistics which also represent a summary or ‘typical’ value of a series of values such as the average or arithmetic mean (or just ‘mean’), and this is more frequently used relative to the median. However, there are circumstances where the mean or average could be misleading or not represent a ‘typical’ value, and in these cases the median can be used instead of the average or mean.

The median can give a ‘better’ measure of a typical value (compared to the average or mean) when there the distribution (or set of values) are skewed. A skewed distribution has a small number of observations (or values) with very high or very low numerical value.

The median is the middle value when all the values are ordered from smallest to largest, and if there are two values in the ‘middle’ then the average of these two values are taken.

For instance, the median age of three people aged 30, 28 and 32 years is 30 years as 30 is the middle value when these are placed in order of magnitude (28, 30 and 32). In this case, the median is the same as the average or sum (which is the sum divided by the count, that is 90 divided by 3 to give the average of 30 years).

However, if there was another person aged 70 then the middle two values when placed in order would be 30 and 32 (with four values placed in order: 28, 30, 32 and 70) and the median would be the average of these two values ((30+32)/2) giving 31 years. The average or mean would be the sum (160) divided by the count (4) so would be the average would become 40 years. In this case, as there is one high value in relation to the other values, the average is skewed towards that higher value whereas the median is relatively unaffected by that single value. In this case, it could be argued that the median might represent a better ‘typical’ value compared to the average. Another summary statistic is the mode which can be an alternative, and can be used in certain circumstances. The mode is the most commonly occurring value.

The most frequently used measure of a ‘typical’ value is the average or mean, but house prices and income are often summarised using medians as there are often a small number of individual records with very high values which makes the median a more appropriate summary measure. The mode is generally not used, but useful for non-numerical data such as the most frequently occurring colour.