# 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
Mo = Mode value
s = Standard deviation of the sample data

2. #### Pearson Median Skewness

`Skewness = `

where
Md = 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.

• 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.