What is the definition for skew in math terms?

Answer 1

The skewness of a random variable X is the third standardised moment of the distribution.

If the mean of the distribution is m and the standard deviation is s, then the skewness,

g1 = E[{(X - m)/s}3] where E is the expected value.

Skewness is a measure of the degree to which data tend to be on one side of the mean or the other. A skewness of zero indicates symmetry. Positive skewness indicates there are more values that are below the mean but the the ones that are above the mean, although fewer, are substantially bigger. Negative skewness is defined analogously.