# Averaging on skewed distribution

I have to compose a feature which summarizes the blocks area of different sections of cities. (A block is defined as the space contained by streets).

I could compute the arithmetic average of areas, but the data is often very skewed in the sections. I could compute the arithmetic average of log(areas), which transform the data to a more normal distribution, but the problem is that the data is skewed differently section by section. How would you create this feature?

• Have you tried to using the Z scale instead? – eliasah Oct 2 '15 at 5:58

You could use the median. That protects against the "Bill Gates walks into a bar, making everyone there a millionaire, on average" effect. It's used with wage distributions for exactly the reason that they tend to be very skewed.

Alternatively you could consider the distribution of the blocks areas per section and use the most popular value (the top peak of the distribution).

If it is possible to meanifully cluster the distribution curves, you may even define the feature as a factor - the nearest centroid of the cluster of distribution curves.