Quant interview prep guides

Median vs Mean in Probability Interviews

Median vs mean interview prep for expected value, quantiles, skewed distributions, symmetric distributions, and interpretation mistakes.

Candidates moving from expected value to distribution-shape reasoning.

Mean is an average

The mean is the expected value: a probability-weighted average of possible values.

Median is a middle probability point

The median is a value with about half the probability on each side. It is a quantile, not an average.

Concrete example

If a payoff is 0 with probability 0.9 and 100 with probability 0.1, the mean is 10 but the median is 0.

Symmetric distributions

For many symmetric distributions, the mean and median match. That is a symmetry result, not a general rule.

Why interviews ask this

Mean versus median tests whether you understand distribution shape, outliers, and what an average actually summarizes.

Common mistakes

Candidates often report expected value when the prompt asks for a typical or middle outcome. Ask which summary the problem wants.

Practice the pattern

Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.