Wednesday, July 7, 2010

Skewness-Lack of symmetry in frequency distribution

Meaning of Skewness:

The term skewness means lack of symmetry in a frequency distribution. Skewness denotes the degree of departure of a distribution from symmetry and reveals the direction of scatterness of the items. It gives us an idea about the shape of the frequency curve. When a distribution is not symmetrical , It is called a skewed distribution. Skewness tells us about the asymmetry of the frequency distribution.

Definition of Skewness:

  1. Skewness is the degree of asymmetry or departure from symmetry of a distribution --------  M. R. Speigal.
  2. When a series is not symmetrical , it is said to be asymmetrical or skewed-------------Croxten and Cowden.
  3. By skewness of a frequency distribution , we mean degree of its departure from symmetry----------Simpson and kafka.

Skewness and frequency Distribution:

  1.  Symmetrical Distribution:
    In a symmetrical distribution or symmetrical curve , skewness is not present. The values of mean , median and mode coincide i.e. Mean=Meadian=Mode. The spread of the frequencies is the same on both sides of the central point curve.
  2. Skewed Distribution:
    A distribution which is not symmetrical is called skewed distribution or asymmetrical distribution . 
    A skewed distribution may be either positively skewed or negatively skewed.
    1. Positively skewed: If the longer tail of the frequency curve of distribution lies to the right of the central point, it is called a positively skewed distribution.In Positively skewed distribution , the  value of the  mean will be greater than median and median will be greater than mode.
    2. Negatively skewed.: If the longer tail of the frequency curve of the distribution lies to the left of the central point , it is called a negatively skewed distribution. In the negatively skewed distribution , the value of the mean will be less then median be less than mode.
    Formula for calculating Skewness is given in below fig.


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