Skewness

What is skewness? Provide the definition and intuitive explanation.

Answer
\[ \text{Skewness}(X) \;=\; \frac{\mathbb{E}\big[(X-\mu)^3\big]}{\sigma^3}. \]

Skewness measures the asymmetry of a distribution w.r.t. its mean.

In general (not always) we have:

  • $\text{Skewness} > 0$: long right tail (right-skewed).

  • $\text{Skewness} < 0$: long left tail (left-skewed).

  • $\text{Skewness} = 0$: symmetric distribution (e.g. normal).

Notes and comments

Comment 1: A symmetric distribution has a skewness of $0$. However, a skewness of $0$ does not necessarily imply symmetry.

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