In statistics, skewness and kurtosis are two ways to measure the shape of a distribution.
Skewness is a measure of the asymmetry of a distribution. This value can be positive or negative.
- 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.
Kurtosis is a measure of whether or not a distribution is heavy-tailed or light-tailed relative to a normal 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.
This tutorial explains how to calculate both the skewness and kurtosis of a given dataset in Google Sheets.
Example: Skewness & Kurtosis in Google Sheets
Suppose we have the following dataset:
To calculate the skewness and kurtosis of this dataset, we can use the SKEW() and KURT() functions with the following syntax:
- SKEW(Array of values)
- KURT(Array of values)
It’s important to note that either function will return the error #DIV/0! in the following two scenarios:
- If there are fewer than three data points.
- If the sample standard deviation is zero.
The image below shows how to use these functions for our particular dataset:
The skewness turns out to be -0.18490 and the kurtosis turns out to be 0.34624.
Additional Resource: Skewness & Kurtosis Calculator
You can also calculate the skewness for a given dataset using the Statology Skewness and Kurtosis Calculator, which automatically calculates both the skewness and kurtosis for a given dataset.