Measures of Central Tendency — Arithmetic Mean and Median

When economic data consists of many individual observations (e.g. the incomes of a group of households, or the prices charged by different shops for the same good), a measure of central tendency summarises the whole data set with a single representative value.

The Arithmetic Mean is the sum of all observations divided by the number of observations:

where $\sum X$ is the sum of all observed values and $N$ is the number of observations. The mean uses every value in the data set, but is sensitive to extreme (very high or very low) values, which can pull it away from where most of the data actually lies.

The Median is the value that lies exactly in the MIDDLE of the data when all observations are arranged in ascending (or descending) order — for an ODD number of observations, it is the single middle value; for an EVEN number, it is the average of the two middle values. Because it depends only on the POSITION of values, not their exact magnitude, the median is NOT affected by extreme values the way the mean is, making it a more reliable summary measure when a data set contains a few unusually large or small observations (e.g. a data set of incomes with one very high outlier income). …