Skewness

What is Skewness in Statistics?

Skewness measures the deviation of a probability distribution from the normal distribution which is a probability distribution without any skewness.

It measures the asymmetry in the distribution. Asymmetrical distribution is one which is not identical on the left and right sides.

Types of Skewness

There are three types of skewness in the data: positive, negative or no skewness. Normal Distribution is used as a reference to determine the types of distribution.

Positive Skewness

• The probability distribution which has its tail on the right side.
• The data is mostly concentrated on the left side.
• Mean>Median>Mode
  
• Q3-Q2>Q2-Q1
  

Negative Skewness

• The probability distribution which has its tail on the left side.
• The data is mostly concentrated on the right side.
• Mean<Median<Mode
  
• Q3-Q2<Q2-Q1
  

Zero Skewness

• The probability distribution which is symmetrical on both the left and right sides.
• The data is equally distributed on both sides.
• Mean=Median=Mode
  
• Q3-Q2=Q2-Q1
  

How to Calculate Skewness?

There are two methods to calculate skewness:

1. Pearson Mode Skewness

   Skewness =

   where
   X = Mean value
   M_o = Mode value
   s = Standard deviation of the sample data
   

2. Pearson Median Skewness
   

   Skewness = 

   where
   M_d = Median value

The direction of skewness is given by the sign and the value of the coefficient compares the sample distribution with a normal distribution. The larger the value, the larger the distribution differs from a normal distribution. A value of zero means no skewness at all.

How to Handle Skewness in Data

Skewness in the data can be handled and skewed data can be converted to normally distributed data by using the below transformation method:

• Power Transformation
• Log Transformation
• Exponential Transformation

How is Skewness Important to Statistics?

• Linear Model assumes that the distribution of independent variables and the dependent variables is the same. Skewness can be used to find distribution.
• Skewness tells us about the direction of outliers.

Disadvantages of Skewness

• The skewness doesn’t tell us about the number of outliers but it tells only about the direction.

Difference between Skewness and Kurtosis

• Both Skewness and Kurtosis are an important measures of the shape of the distribution
• Skewness measures the asymmetry in the data.
• Kurtosis measures the heaviness of the distribution tail relative to normal distribution.