Skewness is a measure of how symmetrical or asymmetrical a data distribution is. A distribution is asymmetrical if its left and right sides are not mirror images. Skewness helps us understand the shape of the data and whether it deviates from a normal (bell-shaped) distribution.

Types of Skewness
- Zero Skew (Symmetrical Distribution):
 - The left and right sides of the peak are mirror images.
 - Examples: Normal distribution, uniform distribution, and some bimodal distributions.
 - Key point: In zero skew, the mean and median are approximately equal.
 - Right Skew (Positive Skew):
 - The right tail (the longer part of the curve) extends further than the left.
 - Common in data with extreme high values, such as income or sales data.
 - Key point: In right skew, the mean > median.
 - Left Skew (Negative Skew):
 - The left tail extends further than the right.
 - Common in data where most values are high with a few very low values, such as test scores.
 - Key point: In left skew, the mean < median.
 
How to Check Skewness
- Visual Check:
 - Plot a histogram to observe the shape of the distribution.
 - If the data is symmetrical, it has zero skew. If it leans right or left, it's skewed.
 - Mathematical Check:
 - Use Pearson’s median skewness formula
 
- A skewness close to 0 indicates symmetry, while higher positive or negative values show skew.
 
Handling Skewed Data
- Do Nothing:
 - Mild skewness often doesn't significantly affect statistical tests like linear regression.
 - Choose a Different Model:
 - Use models that don't assume normality, such as non-parametric tests or generalized linear models.
 - Transform the Data:
 - Apply a mathematical transformation to reduce skewness and make the distribution closer to normal.
 
Transformations for Skewness
Type of Skew  | Intensity  | Transformation  | 
Right  | Mild  | No transformation  | 
Moderate  | Square root  | |
Strong  | Natural logarithm  | |
Very strong  | Log base 10  | |
Left  | Mild  | No transformation  | 
Moderate  | Reflect*, then square root  | |
Strong  | Reflect*, then natural logarithm  | |
Very strong  | Reflect*, then log base 10  | 
Note: Reflection reverses the direction of the data. The reflection is calculated as K+1−xK + 1 - xK+1−x, where KKK is the largest observation.
Handling Skewed Data
- Do Nothing:
 - Mild skewness often doesn't significantly affect statistical tests like linear regression.
 - Choose a Different Model:
 - Use models that don't assume normality, such as non-parametric tests or generalized linear models.
 - Transform the Data:
 - Apply a mathematical transformation to reduce skewness and make the distribution closer to normal.
 
Transformations for Skewness
Type of Skew  | Intensity  | Transformation  | 
Right  | Mild  | No transformation  | 
Moderate  | Square root  | |
Strong  | Natural logarithm  | |
Very strong  | Log base 10  | |
Left  | Mild  | No transformation  | 
Moderate  | Reflect*, then square root  | |
Strong  | Reflect*, then natural logarithm  | |
Very strong  | Reflect*, then log base 10  | 
Note: Reflection reverses the direction of the data. The reflection is calculated as K+1−xK + 1 - xK+1−x, where KKK is the largest observation.