I have been doing it wrong my whole life. I realized it only very recently.
I used to look at the hump to determine the direction of skew for a distribution.
But hump represents the most frequent value in the distribution. It is not skewing the distribution.
If anything, that hump is trying its best to preserve the normal distribution despite the skewness.
The actual culprit here is the long tail. It consists of the outlier values that are skewing the distribution.
From now onwards, I will keep in mind to look at the tail instead of the hump to tell whether a distribution is left-skewed or right-skewed.
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