<P> The medcouple is a scale - invariant robust measure of skewness, with a breakdown point of 25% . It is the median of the values of the kernel function </P> <Dl> <Dd> h (x i, x j) = (x i − x m) − (x m − x j) x i − x j (\ displaystyle h (x_ (i), x_ (j)) = (\ frac ((x_ (i) - x_ (m)) - (x_ (m) - x_ (j))) (x_ (i) - x_ (j)))) </Dd> </Dl> <Dd> h (x i, x j) = (x i − x m) − (x m − x j) x i − x j (\ displaystyle h (x_ (i), x_ (j)) = (\ frac ((x_ (i) - x_ (m)) - (x_ (m) - x_ (j))) (x_ (i) - x_ (j)))) </Dd> <P> taken over all couples (x i, x j) (\ displaystyle (x_ (i), x_ (j))) such that x i ≥ x m ≥ x j (\ displaystyle x_ (i) \ geq x_ (m) \ geq x_ (j)), where x m (\ displaystyle x_ (m)) is the median of the sample (x 1, x 2,..., x n) (\ displaystyle \ (x_ (1), x_ (2), \ ldots, x_ (n) \)). It can be seen as the median of all possible quantile skewness measures . </P>

When a distribution is positively skewed standard deviation