dispersion meaning

 -meaning-example-why

-significance

-methods oof studying variation

-range

-meerits &limitation

-uses

Introduction

► Various Measure of central value we have discussed. It gives us one single figure that represents data. epresents the entire

It is necessary to describe the Variability or Dispersion of the observation. In two or more distributions the central value may be the same but still there can be wide disparities in the formation of distribution.

Measure of dispersion help us in studying this important characteristic of a distribution.

Example

Since AM is the same in all three series, one is likely to conclude that these series are alike in nature. But a close examination shall reveal that distributions differ widely from one another.

In series A, each and every item is perfectly represented by the arithmetic mean or none of the items of series A deviates from arithmetic mean and hence there is no dispersion.

In series B, only one item is perfectly S represented by the AM and the other items vary but the variation is very small as compared to series C.

In series C, not a single item is represented by the AM and the items vary widely from one another. In series C dispersion is much greater as compared to series B.

4 The two curves in diagram (a)

represent two distribution with the same mean x^{\prime} but with different dispersions.

The two curves in (b) represent two distributions with the same dispersion but with unequal mean X1, X2'.

(C) represents two distributions with unequal dispersion.

Therefore the measure of central tendency are insufficient. They must be supported and supplemented with other measures. Like variability or spread or dispersion.

Significance Of Measuring Variation

1) To determine the Reliability of an Average. an Aver

2) To serve as a basis for the control of variability. S

3) To compare two or more series with regard to their variability.

4) To facilitate the use of other statistical Measures.

Methods Of Studying Variation

1. The Range

2. The Interquarile Range & the Quartile Deviation. cation.

3. The Mean Deviation or Average Deviation.

4. The Standard Deviation

5. The Lorenz Curve.

Of these the First Two namely the range and the quartile deviation are Positional Measures because they depend values at a particular position in the distribution. on the

The Other Two, the average deviation and the standard deviation, are called Calculation Measure of deviation because all of the values are employed in their calculation and the Last One is the Graphic Method.

1.Range

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► Range is the simplest method of studying dispersion.

► It is defined as the difference between the value of the smallest item and the value in the distribution. of the largest item included

► Range= L-S

4 L= Largest Item

▶ S= Smallest Item em

The relative measure corresponding to range, called the coefficient of range, is obtained by applying the following formula : L-S Coefficient of Range = L+S

Merits & Limitations

Merits and Limitations enumerated here. The merits and limitations of Range can be

Merits.

Amongst all the methods of studying dispersion range is the simplest to understand and the easiest to compute.

It takes minimum time to calculate the value of range. Hence, if one is interested in getting a quick rather than a very accurate picture of variability one may compute range.

Limitations.

Range is not based on each and every item of the distribution.

It is subject to fluctuations of considerable magnitude from sample to sample.

Range cannot tell us anything about the character of the distribution within the two extreme observations. For example, observe the follow- ing three series :

Series A    46      6       46      46       46      46     46    46  

Series B    6      10      6         6        46       46     46     46

Series C    6      6       15       25      30        32     40    46   

In all the three series range is the same. i.e.. (466) = 40. But it does not mean that the distributions are alike. The range takes no account of the form

of the distribution within the range. Range is, therefore, most unreliable as a guide to the dispersion of the value within a distribution.

(iv) Range cannot be computed in case of open-end distributions.

Uses

1) Quality Control- When statistical methods of quality control are used, control charts_are prepared and in preparing these charts range play a very important role.

2)Fluctuations in share price. ations in share

3) Weather Forecasting.