Skewness and Kurtosis of Data

 1 Skewness

Skewness is a statistical numerical method to measure the asymmetry of the distribution or data set. It

tells about the position of the majority of data values in the distribution around the mean value.

There exist 3 types of skewness values on the basis of which the asymmetry of the graph is decided. These areas follow:

1.1 Positive Skew

If the coefficient of skewness is greater than 0 i.e. γ1 > 0, then the graph is said to be positively skewed

with the majority of data values less than mean. Most of the values are concentrated on the left side of the graph.

1.2 Zero Skewness or Symmetric

If the coefficient of skewness is equal to 0 or approximately close to 0 i.e. γ1 = 0, then the graph is said to be symmetric, and data is normally distributed.

1.3 Negatively skewed

If the coefficient of skewness is less than 0 i.e. γ1 < 0, then the graph is said to be negatively skewed with the majority of data values greater than the mean. Most of the values are concentrated on the right side of the graph.

2. Kurtosis

Kurtosis is a numerical method in statistics that measures the sharpness othe f the peak in the data

distribution. There exist 3 types of Kurtosis values on the basis of which sharpness of the peak is measured. These are as follows:

2.1 Platykurtic

If the coefficient of kurtosis is less than 3 i.e. γ2 < 3, then the data distribution is platykurtic. Being

platykurtic doesn’t mean that the graph is flat-topped.

2.2 Mesokurtic

If the coefficient of kurtosis is equal to 3 or approximately close to 3 i.e. γ2 = 3, then the data distribution is mesokurtic. For the normal distribution, the kurtosis value is approximately equal to 3.

Leptokurtic If the coefficient of kurtosis is greater than 3 i.e. γ1 > 3, then the data distribution is

leptokurtic and shows a sharp peak on the graph. # Statistical Designs