What do you mean by Dispersion? Give the meaning of Absolute Measure and Relative Measure with example || What is the method of measuring Dispersion. Write the formula for calculating combined S.D.

Measures of Dispersion

Q1. What do you mean by Dispersion? Give the meaning of Absolute Measure and Relative Measure for example.

Dispersion could be a lie of the extent to that the individual item varies from a central worth. Dispersion is employed in 2 senses,

I.          Distinction between the acute things of the series and

II.        Average deviation of things from the mean.

a)     Absolute Measure: The figure showing the limit or magnitude of dispersion is understood as an absolute live and it's shown within the same unit as; those of the first information, example measures of dispersion within the age of scholars, their height, weight etc.

b)     Relative Measure: For comparative study the regarding absolute live is split by the corresponding mean or another characteristic worth to get a quantitative relation or proportion, that is understood because the relative live.

Q.2 Explain the various methods for measuring Dispersion. Also give their merits and demerits?

Following are the important methods of studying dispersion –

(1)  Numerical Methods:

a) Methods of limits

i) Range

ii) Inter-quartile range

iii) Percentile Range

           b) Methods of average deviation:

           i) Quartile Deviation

           ii) Mean Deviation

           iii) Standard Deviation

           (2) Graphic Method - Lorenz Curve:

Range:

The distinction between price {the worth} of the littlest item and the value of the most important item of the series is named RANGE.

Range = Largest item – Smallest item

Merits of Range:

-         Simple and easy to be computed.

-  It takes minimum time to calculate.

-     Not necessary to understand all the values, solely the smallest and largest price is needed.

-     Helpful in internal control of the product.

Demerits of Range: -

-     Not supported all the things.

-     Subject to fluctuation/uncertain live.

-     Cannot be computed just in case of open-end distributions.

-   As it's not supported all the values it's not thought about as an honest or acceptable live

ii) Inter-Quartile Range: -

      Inter-quartile vary represents the distinction between the third mark and therefore the 1st mark. it's conjointly called the RANGE of middle five hundredth values.

àInter-quartile range = Q3 – Q1

Merits: -

-     It is simple to calculate.

-     Can be measured in open finish distributions.

-     It is least laid low with the uncertainty of the acute values.

Demerits:

-     It doesn't represent all the values.

-     It is an unsure live.

-     It is incredibly a lot tormented by sampling fluctuations.

iii) Percentile Range:

-It is the distinction between the values of the ninetieth and tenth score. it's supported the centre eightieth things of the series.

Percentile Range = P90 – P10

Merits and Demerits:

-         Its use is restricted. Percentile range has virtually similar merits and demerits as those of the interquartile range.

Percentile Range = P90 – P10

iv) Quartile Deviation / Semi – Interquartile Range:

-         Quartile Deviation provides the typical quantity by that the 2 quartiles dissent from the median. Quartile deviation is the associate degree absolute measure of dispersion.

It is calculated by using the formula –

Merits:

-     It is straightforward to calculate and perceive.

-     It encompasses a special utility in measuring variation in open finish distributions.

-     QD isn't plagued by the presence of utmost values.

Demerits:

-     It is extremely abundant plagued by sampling fluctuations.

-     It doesn't offer a thought of the formulation of the series.

-     It isn't capable of any pure mathematics treatment.

v) Mean Deviation:

Mean Deviation is additionally called average deviation or the first measure of dispersion. It's the common distinction between the things in an exceeding distribution and therefore the median mean or mode of that series.

Computation of Mean Deviation:

Merits: 

- It's easy to know and straightforward to cypher.

- supported every item of the information.

- Least laid low with the acute values.

- It is computed from an average, mean, median or mode.

Demerits:

- Signs square {measure} neglected thus mathematically it's incorrect and not a big measure.

- can't be compared if mean deviations completely different {of various} series square measure supported different averages.

vi) Standard Deviation (σ):

Standard Deviation was introduced by Karl Pearson in 1823. It's the foremost necessary and widely used measure of learning dispersion because it is free from those defects from that the sooner strategies suffer and satisfies most of the properties of an honest measure of dispersion.

Standard Deviation is the root of the common of the sq. deviations from the arithmetic mean of a distribution.

Co-efficient of ordinary Deviation:

Standard deviation is an associate absolute measure. Once a comparison of variability in 2 or a lot of series is needed, a relative measure of ordinary deviation is computed that is named coefficient of standard deviation.

Computation of Standard Deviation:

Coefficient of variation: Coefficient of variation is used for the comparative study of stability or homogeneity in more than 2 or more series.

Merits: 

- Supported all the things.

- Well-defined and definite measure of dispersion.

- Least stricken by sample fluctuations.

- Appropriate for algebraical treatment.

Demerits:

- Standard Deviation is relatively troublesome to calculate.

- A lot of importance is given to the acute values.

   vii) Graphical Method - Lorenz Curve:

This curve was devised by Dr Max O‘Lorenz. He used this method to indicate a difference in wealth and financial gain of a bunch of individuals. It's a straightforward, attractive, and effective measure of dispersion, nevertheless, it's not scientific since it doesn't give a figure to measure dispersion.          

Merits:

-         Easy to know from the graph.

-         Comparison is often drained 2 or a lot of series.

-         Attractive & effective.

-         Concentration or density of frequency are often better-known from the curve.

 Demerits:

- It's not a numerical measure; thus, it's not definite as a mathematical measure.

- Drawing of curves needs longer and labour.

Q.3 What is the method of measuring Dispersion. Write the formula for calculating combined S.D.

Standard Deviation is the best methodology of mensuration dispersion as deviations taken from mean and algebraical signs don't seem to be neglected and it's algebraically correct.

      The formula for calculating combined Standard Deviation: