Why mean and median are similar for well distributed dataset?
I've read that when considering well distributed variables, median and mean tend to be similar, but can't figure out why mathematically this is the case.
Topic mean
Category Data Science
For a lognormal distribution this is definitely not the case!
Many real world processes have normal distributions, for which mean, median, and mode are all equal. This is due to the central limit theorem. However, there are also lots of real world processes that are thoroughly non-normal.
I'm not sure what a "well-distributed variable" is. Perhaps you could edit your question to provide a definition or a reference to what you were reading.
Many distributions that are commonly used for statistical modelling are symmetric and all symmetric distributions have the same mean and median (if the mean exists).
You can measure the extent to which a distribution is asymmetric by computing the non-parametric skew which uses the difference between the mean and median.
So a distribution where the mean and median are similar would have a low non-parametric skew. And a distribution where the mean and median are exactly the same would have a non-parametric skew of zero and be symmetric.
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