Central Measures

Central Measures describe the "central" values of a collected sample. For an ungrouped set of data these measures are: the mean, the median, and the mode. The mean is not always an adequate measure to descibe the central value. The mode is a useful measure for certain datasets.

The mode is the most frequently occurring value in a set of observations. Why use the mode? The classic example is the shirt/shoe manufacturer who wants to decide what sizes to introduce. The manufacturing company may have to accept two sets of sizes: one set for men; and one set for women. In this case we say the data are bimodal. Sets of observations with more than two modes are referred to as multimodal.

Note that the mode is not a helpful measure of location, because there can be more than one mode or even no mode. When the mean and the median are known, it is possible to estimate the mode for the unimodal distribution using the other two averages as follows:

Mode 3*(median)2*(mean)

This estimate is applicable to both grouped and ungrouped data sets.

Whenever, more than one mode exist, then the population from which the sample came is a mixture of more than one population. However, note that a Uniform distribution has uncountable number of modes having equal density value; therefore it is considered as a homogeneous population.

Back: The Median

Next: Mean, Median, or Mode?