Skewness
It refers to the asymmetry or lack of symmetry in the shape of a frequency distribution. In other words, skewness describes the shape of a distribution. A distribution is said to be skewed‘ when the mean and the median fall at different points in the distribution, and the centre of gravity is shifted to one side or the other – to left or right.
Normal or Symmetrical Distribution : The spread of the frequencies is the same on both sides of the centre point of the curve. The curve drawn for such distribution is bellshaped. The value of Mean, Median and Mode are equal.
Asymmetrical or Skewed Distribution : A distribution which is not symmetrical is called a skewed distribution. It can be of two types
Positively Skewed Distribution :In the positively skewed distribution, the curve has a longer tail towards the right and the value of mean is maximum and that of mode least and the median lies in between.
Negatively Skewed Distribution : In negatively skewed distribution, it has a longer tail towards the left and the value of mode is maximum‘ and that of mean least, the median lies in between the two.
In order to ascertain whether a distribution is skewed or not the following tests are applied. Skewness is present if -
- If mean, median and mode are not equal.
- If the curve is not bell shaped.
- Quartiles are not equidistant from the median.
- If the sum of deviations from median and mode is not zero, and
If the sum of frequencies on the two sides of the mode are not equal, the distribution has skewness..
Bowley’s Measure or Quartiles Measure :
Bowley‘s measure of skewness is called second measure of skewness. This measure is useful in distributions where mode is ill-defined and can also be used in open end distributions
Coefficient of skewness \[J_q=\frac{Q_3+Q_1-2M}{Q_3-Q_1}\]
for \[ P=3.5\] \[ Q=1.5 \]\[M=2\]
skewness is \[ \frac{3.5+1.5-4}{3.5-1.5}=0.5\]
