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.