The measure of dispersion shows the scatterings of the data. It tells the variation of the data from one another and gives a clear idea about the distribution of the data. The measure of dispersion shows the homogeneity or the heterogeneity of the distribution of the observations.
Suppose you have four datasets of the same size and the mean is also same, say, m. In all the cases the sum of the observations will be the same. Here, the measure of central tendency is not giving a clear and complete idea about the distribution for the four given sets.
Characteristics of Measures of Dispersion
- A measure of dispersion should be rigidly defined
- It must be easy to calculate and understand
- Not affected much by the fluctuations of observations
- Based on all observations
Classification of Measures of Dispersion
The measure of dispersion is categorized as:
(i) An absolute measure of dispersion:
- The measures which express the scattering of observation in terms of distances i.e., range, quartile deviation.
- The measure which expresses the variations in terms of the average of deviations of observations like mean deviation and standard deviation.
(ii) A relative measure of dispersion:
We use a relative measure of dispersion for comparing distributions of two or more data set and for unit free comparison. They are the coefficient of range, the coefficient of mean deviation, the coefficient of quartile deviation, the coefficient of variation, and the coefficient of standard deviation.
Coefficient of Dispersion
Whenever we want to compare the variability of the two series which differ widely in their averages. Also, when the unit of measurement is different. We need to calculate the coefficients of dispersion along with the measure of dispersion. The coefficients of dispersion (C.D.) based on different measures of dispersion are
- Based on Range = (X max – X min) ⁄ (X max + X min).
- C.D. based on quartile deviation = (Q3 – Q1) ⁄ (Q3 + Q1).
- Based on mean deviation = Mean deviation/average from which it is calculated.
- For Standard deviation = S.D. ⁄ Mean
Coefficient of Variation
100 times the coefficient of dispersion based on standard deviation is the coefficient of variation (C.V.).
C.V. = 100 × (S.D. / Mean) = (σ/ȳ ) × 100.