Skewness and Kurtosis in Statistics

A brief tutorial about skewness and kurtosis in Statistics

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Most commonly a distribution is described by its mean and variance which are the first and second moments respectively. Another less common measures are the skewness (third moment) and the the kurtosis (fourth moment). Today, we will try to give a brief explanation of these measures and we will show how we can calculate them in R.

Skewness

The skewness is a measure of the asymmetry of the probability distribution assuming a unimodal distribution and is given by the third standardized moment.

We can say that the skewness indicates how much our underlying distribution deviates from the normal distribution since the normal distribution has skewness 0. Generally, we have three types of skewness.

• Symmetrical: When the skewness is close to 0 and the mean is almost the same as the median
• Negative skew: When the left tail of the histogram of the distribution is longer and the majority of the…