Introduction
This topic covers the main descriptive measures that summarise where the centre of a numerical data set lies and how widely its values are spread around that centre. For each measure you should be able to define it, state how it is calculated, and give its advantages and disadvantages, especially with respect to outliers, skewed distributions and the type of data.
Measures of central tendency
A measure of central tendency is a single value that represents the typical or central value of a set of observations. The three classic measures are the mean, the median and the mode. Which one is appropriate depends on the level of measurement, the shape of the distribution and whether extreme values are present.
- Arithmetic mean: the sum of all values divided by the number of values; it is the balance point of the data.
- Median: the middle value when the data are ordered; for an even number of values it is the mean of the two central values.
- Mode: the most frequently occurring value (or category). A data set may have one mode, several modes or none.
The geometric mean is a special case worth knowing. It is appropriate for data that are multiplicative, such as antibody titres, growth factors or ratios, and it is always less than or equal to the arithmetic mean for positive data. Its limitation is that it cannot be used when values are zero or negative.