Measures of Asymmetry
1. Measures of Asymmetry – introduction

Instruction

We already know the measures of location (such as the mean, median or mode) and variation (quartiles, variance, or standard deviation). There are also ways to measure the asymmetry of a dataset. Up to this point, we only used terms like "skewed left" or "skewed right". We can do better than that and use quantitative measures like skewness and kurtosis.

We can easily give an example of datasets that have the same standard deviation, but look completely different due to asymmetry.

Both of the histograms have the same standard deviation of 1.57, but the first histogram is skewed left, while the second is skewed right. It would be nice to have a measure that captures this difference. Also see the histograms below:

Notice that while both histograms are skewed left, one is somehow "more skewed" than the other. We are about to explore the measures that can reflect this observation.