Skewness and Kurtosis:-

Skewness is a measurement of the symmetry of a distribution.

• It describes how much a distribution differs from a normal distribution, either to the left or to the right.
• The skewness value can be either positive, negative or zero.
• Note that a perfect normal distribution would have a skewness of zero because the mean equals the median.
• The way to analyze a skewed graph is to see where the mean lies in relation to the median.

There are two types of Skewness :-

1. Positive Skewness
2. Negative Skewness

“A positive skew ocurs if the data is piled up to the left, which leaves the tail pointing to the right.”

If mean>median>mode then, it is called positive skewness.

fig:1

“A negative skew occurs if the data is piled up to the right, which leaves the tail pointing to the left.”

If mean<median<mode then, it is called negative skewness.

fig:2

• Relationship between mean and median under different skewness:-

This figure(fig:3) shows the relationship b/w mean and median. You can see that when mode is maximum and mean is minimum than shows neagative skewed. Similarly, when mean is maximum and mode is minimum than shows positive skewed.

“when mean=median=mode i.e. skewness is zero then graph shows the normal distribution.”

fig:3

Comparison mean median mode for skewness:-

• Skewness is inversely proportional to standard deviation(S.D.) i.e. if S.D. is maximum then skewness will minimum and Similarly opposite this condition.

fig:4

Kurtosis:-

• Kurtosis measures whether your dataset is heavy-tailed or light-tailed compared to a normal distribution.
• Data sets with high kurtosis have heavy tails and more outliers and data sets with low kurtosis tend to have light tails and fewer outliers.

fig:5

• A normal distribution is called mesokurtic and has kurtosis of 3.0.
• A platykurtic distribution has negative kurtosis and tails are very thin compared to the normal distribution.
• Leptokurtic distributions have kurtosis greater than 3 and the fat tails mean that the distribution produces more extreme values and that it has a relatively small standard deviation.

fig:6

How to Remove Skewness:-

There are six method available for removing skewness-

• Normalization
• The Sigmoid
• Log
• Cube Root
• The Hyperbolic Tangent
• Percentile Linearization