# MEASURES OF DISPERSION IN STATISTICS FREE NOTES

## MEASURES OF DISPERSION IN STATISTICS

### RELATIVE MEASURES OF DISPERSION

Relative measures of dispersion is needed to make the absolute measures of dispersion comparable. The relative measures are calculated by dividing the absolute measures of dispersion by a measure of central tendency i.e. Mean, Median or Mode. The following are the relative measures of dispersion.

• Coefficient of range
• Coefficient of Quartile Deviation
• Coefficient of mean deviation
• Coefficient of standard deviation
• Coefficient of variation.

#### COEFFICIENT OF RANGE:

The relative measure corresponding to the range is called as Coefficient of Range. It is calculated as follows:

(HV-LV)/ (HV +LV)

Whereas, HV = Highest Value and LV= Lowest Value

Coefficient of Range is also known as Coefficient of Scatterness.

#### COEFFICIENT OF QUARTILE DEVIATION:

The relative measure of Quartile deviation is Coefficient of Quartile deviation. It is calculated as follows:

Coefficient of Quartile Deviation= (Q3-Q1)/ (Q3+Q1)

Coefficient of quartile deviation is studied to compare the degree of variation in the series.

#### COEFFICIENT OF MEAN DEVIATION

The coefficient of mean deviation is calculated with the objective of comparison. The coefficient of mean deviation is calculated by dividing the mean deviation by the average used. The formulae to calculated mean deviation are as follows:

#### COEFFICIENT OF STANDARD DEVIATION

In order to compare the variability in two or more series, relative measure of standard deviation is calculated. It is called “Coefficient of Standard Deviation”, which is calculated by dividing standard deviation (σ) by the mean of the data. Symbolically

#### COEFFICIENT OF VARIATION

Coefficient of variation or coefficient of variability is a relative measure of dispersion. It has been developed by Karl Pearson. The coefficient of variation is used in such problems where we want to compare the variability of two or more than two series. A group which has more variability as compared to the other or has more coefficient of variation, the consistency would be less and vice versa.

Higher C.V. Lower consistency, reliability, uniformity.

Lower C.V. Higher consistency, reliability, uniformity

According to Prof. Karl Pearson, “coefficient of variation is the percentage variation in mean, standard deviation being considered as the total variation in the mean.”

If we wish to compare the variability of distributions, we have to compute coefficient of variation,