Mean-versus-median skew inference
SAT glossary · Course Foundations
Definition
The tested one-line reading of shape: mean > median indicates right skew, mean < median indicates left skew, and mean ≈ median indicates symmetry. The mean is a balance point that follows the tail because extreme values enter it at full weight; the median only counts positions.
Mean-versus-median skew inference in plain English
There's a quick, reliable way to read the SHAPE of a lopsided (skewed) distribution just by comparing its mean and median: if the mean is bigger than the median, the data is 'right-skewed' (has a long tail stretching out to the right); if the mean is smaller than the median, it's 'left-skewed'; and if they're roughly equal, the distribution is symmetric. This works because the mean (the plain average) gets dragged around by extreme values — every single data point, even a wildly extreme one, pulls on the mean with its FULL weight. The median, on the other hand, only cares about which POSITION a value sits in, not how extreme it actually is, so it barely budges when an outlier shows up.
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