Statistics - Skewness

Statistics – Skewness

If dispersion measures quantity of variation, then the route of variation is measured by skewness. Probably the most generally used measure of skewness is Karl Pearson’s measure given by the image Skp. It’s a relative measure of skewness.

Method

SOkP=MeanModeStandardDeviationSKP=Imply−ModeStandardDeviation

When the distribution is symmetrical then the worth of coefficient of skewness is zero as a result of the imply, median and mode coincide. If the co-efficient of skewness is a optimistic worth then the distribution is positively skewed and when it’s a unfavorable worth, then the distribution is negatively skewed. When it comes to moments skewness is represented as follows:

β1=μ23μ22 Where μ3=(XX¯)3Nμ2=(XX¯)2Nβ1=μ32μ22 The place μ3=∑(X−X¯)3Nμ2=∑(X−X¯)2N

If the worth of μ3μ3 is zero it implies symmetrical distribution. The upper the worth of μ3μ3, the higher is the symmetry. Nevertheless μ3μ3 don’t inform us concerning the route of skewness.

Instance

Drawback Assertion:

Data collected on the typical power of scholars of an IT course in two schools is as follows:

Measure Faculty A Faculty B
Imply 150 145
Median 141 152
S.D 30 30

Can we conclude that the 2 distributions are related of their variation?

Resolution:

A take a look at the knowledge obtainable reveals that each the universities have equal dispersion of 30 college students. Nevertheless to determine if the 2 distributions are related or not a extra complete evaluation is required i.e. we have to work out a measure of skewness.

SOkP=MeanModeStandardDeviationSKP=Imply−ModeStandardDeviation

Worth of mode isn’t given however it may be calculated through the use of the next formulation:

Mode=3Median2MeanCollege A:Mode=3(141)2(150)=423300=123SOkP=15012330=2730=0.9College B:Mode=3(152)2(145)=456290Sokayp=(142166)30=(24)30=0.8