Skewness and Kurtosis

Skewness looks at distortion of data in a specific direction, Kurtosis in both directions

Skewness refers to a distortion or asymmetry that deviates from the symmetrical bell curve, or normal distribution

• A negative skew indicates that the tail is on the left side of the distribution, which extends towards more negative values.
• A positive skew indicates that the tail is on the right side of the distribution, which extends towards more positive values.
• A value of zero indicates that there is no skewness in the distribution at all, meaning the distribution is perfectly symmetrical.

Python:

data = [88, 85, 82, 97, 67, 77, 74, 86, 81, 95, 77, 88, 85, 76, 81]

#calculate sample skewness
skew(data, bias=False)
0.032697

Kurtosis is a measure of the combined weight of a distribution’s tails relative to the center of the distribution.

• The kurtosis of a normal distribution is 3.
• If a given distribution has a kurtosis less than 3, it is said to be playkurtic, which means it tends to produce fewer and less extreme outliers than the normal distribution.
• If a given distribution has a kurtosis greater than 3, it is said to be leptokurtic, which means it tends to produce more outliers than the normal distribution.

Python:

data = [88, 85, 82, 97, 67, 77, 74, 86, 81, 95, 77, 88, 85, 76, 81]

#calculate sample kurtosis
kurtosis(data, bias=False)
0.118157