Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

Mode of a Distribution

The mode is the value which occurs most frequently in a data set. The mode is only of interest for large data sets, as in small samples the mode strongly depends on random variations of the data. The term "mode" is contained in the expressions "unimodal", "bimodal", and "multimodal". Distributions showing only a single peak are called unimodal, bimodal distributions show two peaks in their frequency diagrams.

The relative position of the mode, the median, and the mean provides an indication of the skewness of a distribution. Click on the figure above to see an example of differently skewed distributions.

The calculation of the mode D of classed data with equal bin widths (as in histograms) can be done according to the following equation:

with
kthe index of the bin containing the greatest number of objects
xuklower border of the bin containing the greatest number of objects
bbin width
fkfrequency of the k-th class
fk-1, fk+1frequencies of the neighboring bins

Last Update: 2012-10-08