Skewness

The classic item gives you a mean, median, and mode and asks for the skew direction, so memorize the ordering: a positively skewed (right-tailed) distribution has mean > median > mode; reverse all three for negative skew. The tell is that the mean is dragged toward the long tail because it alone uses every observation’s magnitude, while the median depends only on rank/position. A second pattern asks for the sign of sample skewness—but watch the trap that a symmetric distribution can still be leptokurtic (fat-tailed), because skewness and kurtosis are independent.

Don’t confuse the two: skewness is the standardized third moment (asymmetry); kurtosis is the standardized fourth moment (tail thickness), so a symmetric fat-tailed series has zero skew but high positive excess kurtosis. The frequent error is assuming mean > median means the mean is the better center—it signals the opposite, that the median is more robust. (Mean > median > mode is an empirical rule for unimodal distributions, not an exact identity.) Hook: the mean chases the tail.