Measures of Dispersion / Variation
Central tendency measures do not reveal the variability present in the data. Dispersion is the scattered ness of the data series around it average. Dispersion provides insights into how data points differ from each other and from the average. Dispersion is the extent to which values in a distribution differ from the average of the distribution.
Concept of Measures of variation:
n Example 1. Weight (in kg) of 5 new born babies from two different hospitals on a particular day are as follows :
Hospital A : 2.5 , 2.5, 2.5, 2.5, 2.5
Hospital B : 3.0, 2.5, 2.5, 2.5, 2.5
Verify that the two Hospitals birth weight of babies
have the same total, mean, median and Mode.
As shown in above table for Hospital A and Hospital B new born babies birth weights Total, mean, median and mode are same, but for Hospital A, all the five new born babies birth weights are identical whereas For Hospital B, some babies birth weights were differ so Hospital B new born babies birth weight were having variability whereas Hospital A was not having any variability because all new born babies birth weights were identical.
Properties of Good Measures of Dispersion:
- It should be easy to understand and calculate.
- It should be rigidly defined.
- It should be based on all observations.
- It should be least affected by sampling fluctuation.
- It should be capable of further algebraic treatment.
- It should be least affected by extreme values.
Important Measures of Dispersion
Following are five important measures of dispersion which are commonly used.
I. Range
II. Inter Quartile Range
III. Mean Deviation
IV. Standard Deviation
V. Variance
