Saturday, September 5, 2015

left skew~left side outliers~mean pulled left

Label - math intuitive

[[FRM]] book has the most intuitive explanation for me - negative (or left) skew means outliers in the left region.

Now, intuitively, moving outliers further out won't affect median at all, but pulls mean (i.e. the balance point) to the left. Therefore, compared to a symmetrical distribution, mean is now on the LEFT of median. With bad outliers, mean is pulled far to the left.

Intuitively, remember mean point is the point to balance the probability "mass".

In finance, if we look at the signed returns we tend to find many negative outliers (far more than positive outliers). Therefore the distribution of returns shows a left skew.

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