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.).
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
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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