# Range and Quartile

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Introduction

The extent to which the numerical data in any distribution differs from each other is known as dispersion. Objectives of measuring dispersion are: to test the reliability of an average, to serve as a basis for control of variability, etc.

The properties of an ideal measure of dispersion are: it is not affected by fluctuation of samples, stable and definite, rigidly defined, capable of further algebraic treatment, not affected by extreme terms, etc.

Dispersion can be measured in two ways:

Absolute Measure

Relative Measure

Absolute measures are range, inter-quartile range, quartile deviation, mean deviation and standard deviation. Relative measures comprise coefficient of range, coefficient of quartile deviation, coefficient of mean deviation and coefficient of standard deviation.

For measuring the dispersion from the spread of values we use range and interquartile range and quartile deviation. Range is the difference between the largest and the smallest value of the distribution. Range can be calculated in all the three types of series individual series, discrete series and continuous series. The relative measurement of coefficient of range is calculated by dividing the difference between the largest and the smallest values by the sum of the largest and the smallest value. The interquartile range is calculated as the difference between the 3rd quartile and the 1st quartile of the distribution and the quartile deviation is the average of the difference of the 3rd quartile and 1st quartile. The coefficient of quartile deviation is calculated by dividing the difference between 3rd quartile and 1st quartile by the sum of the two. There are various merits and demerits associated with range and quartile.

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