Dispersion: Properties, Uses and Types of Dispersion

Properties or Features of a good Measure of Dispersion:

1. In should be capable of treating it by Algebraic or Statistical techniques.

2. It should be easy to calculate i.e. by simple methods.

3. It should be easy to understand i.e. Even a layman must understand about its message or what it demonstrates.

4. It must not be affected by different samples or fluctuation of sampling. Every sample should give same type of information.

5. The quality and quantity of each term must affect it. As in median, last value may be 15 or 15000 in the series 3, 5, 7, 9, 15 (15000); does not effect at all.

Uses or Objects of Dispersion:

1. To use other Statistical Methods: After getting value of dispersion we can proceed to other techniques such as to locate Co-relation or lines of Regression (Regression Analysis).

2. To Compare Variability: We are in the general habit of comparison, may it be income, weight, height or temperature. To achieve the required degree of result one tries to compare the variability in the data.

3. To test Reliability of Average: If the total of differences between the central value and the given value is smaller, the uniformity is less i.e. it means that this sum should be minimum for the reliability of the average.

4. To establish trends in Time Series: In time series we remove, cyclical, seasonal or random fluctuations, which we form after studying central values.

5. To Control the Undesired Variability:

Types of Measures of Dispersion:

A. Absolute and Relative Measures:

Absolute measures of Dispersion are expressed in same units in which original data is presented but these measures cannot be used to compare the variations between the two series. Relative measures are not expressed in units but it is a pure number. It is the ratio of absolute dispersion to an appropriate average such as co-efficient of Standard Deviation or Co-efficient of Mean Deviation.

B. Methods of Measuring Dispersion:

Following methods are used to calculate dispersion:

(i) Algebraic methods:

(1) Methods of limits:

(a) The Range

(b) The Inter-quartile Range

(c) The Percentile Rang

(2) Methods of moments:

(a) The first moment of dispersion or mean deviation.

(b) The second moment of dispersion or standard deviation.

(ii) Graphic Method:

Lorenz curve