**Learning Objective:**

**What is Skewness?****What are measures of Skewness?****What does Kurtosis relate to?****How to measure Kurtosis?**

**Concept:**

**Skewness relates to asymmetry of a frequency distribution.****Skewness can be of two types.****If there is a positive tail in a frequency distribution, it is termed as postive skewness.****If there is a negative tail in a frequency distribution, is it termed as negative skeness.****Measures of Skewness can be Absolute or Relative.****Absolute measure of skewness cannot compare series with different units. It is not widely used.****Relative measure of skewness are of 4 types.**

**Karl Pearson's Coefficeint of Skewness based on Mean, Median, Mode and Standard Deviation.****Bowley's Coefficient of Skewness based on Quartiles.****Kelly's Coefficient of Skewenss based on upper and lower Deciles and Median.****Pearsonian's Coefficient of Skewness based on central Moments.**

**If the value of above 4 relative measures of skewness is 0, the distribution is symmetric.****If the value of above 4 relative measures of skewness is greater then 0, the distribution is positively skewed.****If the value of above 4 relative measures of skewness is less then 0, the distribution is negatively skewed.****In symmetric distribution, x̄ (Mean) = Median = Mode****In positive skewness, x̄ (Mean) > Median > Mode****In negative skewness, x̄ (Mean) < Median < Mode****Kurtosis relates to bulginess, peakedness, tailedness of a frequency distribution.****Leptokurtic frequency distribution is narrow with sharp peak and extended tails.****Mesokurtic frequency distribution is normal with less sharp peak and not much extended tails.****Platykurtic frequency distribution is like platypus without sharp peak and very less extended tails.****Kurtosis is measured with Pearsonian's Coefficient of Kurtosis which is based on central moments.****If γ₂ > 0, the frequency distribution is Leptokutic.****If γ₂ = 0, the frequency distribution is Mesokurtic.****If γ₂ < 0, the frequency distribution is Platukurtic.**

**Formulas:**

**Absolute Measure of Skewness = Sₖ = Mean - Mode****Karl Pearson's Coefficient of Skewness = [Mean - Mode] / Standard Deviation****Karl Pearson's Coefficient of Skewness = 3 x [Mean - Median] / Standard Deviation****Bowley's Coefficient of Skewness = [Q₃ + Q₁ - 2Q₂] / [Q₃ - Q₁]****Kelly's Coefficient of Skewness = [D₉ - D₁ - 2Q₂] / [D₉ - D₁]**