Skewness and Kurtosis

Skewness

A measurement of the symmetry of the probability distribution of a random variable.

 

A distribution is skewed if one end of its tail is longer than the other.

 

A positive skew is displayed if the majority of values are on the left of the distribution with a long tail on the right, also known as a right-skewed distribution because the outlier values are on the right. For example amount of rainfall per day because lots of days are without any rainfall at all but some outlier days have large amounts of rainfall.

 

A negative skew occurs if the longer end is on the right, with values mainly at the higher end of the scale. A normal distribution has no skew at all, with skewness = 0.

 

When the skewness is low the mean and median will not be very far apart. When measuring central tendency, any skew above 1 or under -1 suggests the data is too skewed for the mean to be the best measurement and instead the median is a better indicator of typical value.

 

The SKEW function can be used to measure skewness in Excel.

 

 

Kurtosis

The sharpness of the peak of a frequency distribution curve. Kurtosis helps describe the shape of a probability distribution of a random variable, measuring the “tailedness” of the data. There are different interpretations of how to measure kurtosis from a population but the purpose is to understand whether the distribution is tall and narrow or short and flat.

 

The KURT function measures kurtosis in Excel.