Statistics Assignment Help With Co-efficient Of Dispersion

Co-efficient of dispersion measure the variability of the two series which differ widely in their averages. The Co-efficient of dispersion denoted as C.D. the different measure of dispersion is as follows:

C.D based on range is

C.D based on quartile deviation is

C.D based on mean deviation is

Where v is the average from which the mean deviation is calculated
C.D based on standard deviation is

1.2.6 Co – efficient of variation:

The 100 times of the co – efficient of dispersion based upon standard deviation is called the co – efficient of variation (C.V.).

C.V. =

1.2.7 Skewness:

The skewness is about the shape of the bell shaped curve which is drawn with the given observations. Skewness is denoted as Sk. the measures of skewness are





Where M is the mean, Md is the median and Mo is the mode.

1.2.7 Co – efficient of Skewness:

The relative measure called the co efficient of skewness.

Karl Pearson’s co efficient of skewness is



Where M is the mean, Mo is the mode and σ is the standard deviation of the distribution.

If the mode is ill – defined, then using the relation



The skewness is positive if M> Mo or M> Md

The skewness is negative if M< Mo or M< Md

1.2.8 Kurtosis:

Kurtosis is defined as the ‘Convexity of curve’ by Professor Karl Pearson. It explains about the peakedness of the curve. It is measured by the co – efficient β2 or its derivation γ2 given by,

The normal curve or the Mesokurtic curve have β2 = 3 that is γ2 = 0.

The Platykurtic curve has β2 < 3 that is γ2 < 0.

The Leptokurtic curve has β2 > 3 that is γ2 > 0.

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