Statistics >> Skewness
The absence of symmetry in a distribution is known as skewness. When a distribution is not symmetrical, it is called skewed or asymmetrical. The symmetry of a distribution shows' that at equal distances on either side of the centre, the frequencies are evenly distributed. We study skewness to have an idea about the shape of the curve which we can draw with the help of given frequency distribution.
In a symmetrical distribution
(i) Mean = Median = Mode
(ii) Q3 - Median = Median – Q1
(iii) The curve of the given data is symmetrical.
A distribution is said to be positively skewed if the longer tail lie towards the right side. Here mean> median> mode.
Again a distribution is said to be negatively skewed if the longer tail lie towards the left side. Here mean < median < mode.
Measures of skewness
The larger the distance between the mean and the mode, the greater is the skewness.
Skewness (Sk) = Mean - Mode
This measure is not suitable for comparison
1. Karl Pearson's co-efficient of skewness
It is given by
Sk = (Mean - Mode) / SD
If mode is not well defined we use the formula
Sk = .3(Mean - Mode) / SD
Here - 3 £ Sk £ 3.
In practice it is rarely obtained.
2. Bowley's co-efficient of skewness
This is based on quartiles and is given by
Sk = (Q3+Q1+2Q2) / Q3+Q1
Here -1 <= Sk <= 1
The co-efficient of skewness is a pure number and is zero for a symmetrical distribution.
3. Kelly's co-efficient of Skewness
Sk = (P90 + P10 + 2P50) / P90- P10
= (D9 + D1 - 2D5) / D9 - D1
Where Pi and Di denote ith percentile and decile respectively.
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