Measures of Dispersion
While central measures describe the central values
(mean, median, and mode) of a sample, the dispersion measures provide description of the data spread
in the sample of observations.
Range: The range of a set of observations (or sample) is the absolute value of the difference between
the largest and smallest values in the data set. It measures the size of the interval that encompasses all
of the data values.
It is based solely on two values, not on the entire data set. In addition, it cannot be defined for
open-ended distributions such as Normal distribution. The Range estimate would become less valuable when there are
extreme points present in the data set.
Quantiles: When we order the data, for example in ascending order, we may divide
the data into quarters, Q1, Q2, Q3, and Q4, known as quartiles.
The first Quartile (Q1) is that value where 25% of the values are smaller and 75% are larger. The second Quartile
(Q2) is that value where 50% of the values are smaller and 50% are larger. The third Quartile (Q3) is that value
where 75% of the values are smaller and 25% are larger.
Percentiles: Percentiles have a similar concept and therefore are related. For example, the 25th percentile
corresponds to the first quartile Q1. The advantage of percentiles is that they may be subdivided into 100 parts.
The percentiles and quartiles are most conveniently read from a cumulative distribution function.
Interquartiles Range: The interquartile range (IQR) describes the extent for which the middle 50% of the observations
scattered or dispersed. It is the distance between the first and the third quartiles (i.e., Q3 - Q1).
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