Simple summaries of centre and spread

The simplest summary statistics that describe centre and spread are based on the five-number summary (and box plot).

Centre
The median is the simplest measure of centre. Half the data are more than it, and half less.
Spread
The range (maximum - minimum) and interquartile range (upper quartile - lower quartile) are two different summary statistics that describe the spread of values in a data set.
 

Distance perception (side-effect of drug)

The diagram below describes a similar context to the examples on the previous page. An experiment is conducted with a control group of 30 subjects (who get no drug) and another group of 30 subjects who are given a new drug whose side-effects may affect distance perception.

Each subject is told to stand 3 metres from a wall and the actual distance from the wall is exactly measured.

Use the two sliders to adjust the centre and spread of distances for those getting the new drug.

Observe that the differences between the medians and inter-quartile ranges of the two drugs concisely summarise:


Usefulness of summary statistics

Although a single measure of centre and one of spread provide only limited information about the shape of a distribution of values, they do often give a suprisingly accurate impression of the distribution.

Given the median and interquartile range, it is possible to sketch a bell-shaped histogram that matches these values. Such a 'guess' is often close to the actual distribution of values.