Measures of skewness

 As we described the importance and use of skewness in last post,Now  we are going to see the different formula's derived famous mathematicians and statistician.These measures are easy to calculate and have commenting capacity.We will see two methods elucidated by karl pearson and prof. Bowley.

I) Pearson's coefficient of Skewness
    Karl Pearson developed two methods for finding skewness in sample,by using mode and second one is by median
1) Pearson's coefficient of skewness using mode-

Interpretation of calculation done by using formula
If Sk<0 - negatively skewed
If Sk=0 - symmetric
If Sk>0 - positively skewed.
Let us consider following example 
A sample with mean 15 ,mode 14 and standard deviation 2..
Sk=(15-14)/2=1/2=0.5
Sk>0 .
Hence the curve of given sample is positively skewed

 2) Pearson's coefficient of skewness using median:
Example:
A sample with mean 20 ,median 22 and standard deviation 3.
Sk=3×((20-22)/3)=-6/3=-2
Here Sk<0.
Hence the curve of given sample is negatively skewed.
Pearson's coefficient of skewness lies  between -3 to +3.

II) Bowley's coefficient of skewness.


Let us take one example-
A distribution with first quartile 12 ,second quartile 14 and third quartile 17.
Bowley skewness=(17+12-28)/5
  =1/5=0.2
Here Sk>0 .
Hence the curve of distribution is positively skewed.
If Sk =0,then distribution said to be symmetric (no skewness).
If Sk >0,then distribution is positively skewed.
If Sk<0,then distribution is negatively skewed.
We use Bowley Coefficient When classes are open-end classes and mode not defined,and data have extreme observations in it.
The Bowley's coefficient of skewness lies between -1 to +1.
Thanks for reading...

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