Mean

The exam rarely just asks you to add and divide — it tests which mean to use. The “tell” is the verb in the stem: averaging a sequence of prices paid per share (dollar-cost averaging) signals the harmonic mean; equal-weighting rates, ratios, or P/E multiples across a portfolio often does too (a value-weighted index average uses the weighted harmonic mean), while compounded growth over time signals geometric. A reliable check is the ordering harmonic ≤ geometric ≤ arithmetic, with equality only when all positive observations are identical — so the wrong choice usually lands too high. The weighted mean appears as expected return, where weights are portfolio allocations (or probabilities) that sum to one.

The classic trap is conflating center with spread: the mean feeds variance (every squared deviation is measured from it), but it is not itself a dispersion measure. A second trap is robustness — unlike the median, the arithmetic mean is pulled toward outliers and the skewed tail, which is exactly why mean-versus-median comparisons diagnose skew direction (mean > median signals right skew). Memory hook: harmonic for what you paid, geometric for what you earned.