Expected value — where it appears
Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.
The words "on average" are not a number
Quicksort is Θ(n log n) on average. Six hundred runs at n = 512 give a distribution with a mean of 4,945 comparisons, a median of 4,908, and a worst case 32% above the mean. The average is a summary of that picture, it is the least interesting thing in it, and it is almost always the only thing reported.
A distribution computed rather than sampled
Quicksort with a random pivot makes a random number of comparisons, and every plate on this site reports one draw from that distribution. The distribution itself can be computed exactly — every pivot, every split, weighed — and on sixty-four elements its mean is 360.706 and its standard deviation 36.741. A hundred real runs average 365.98; two thousand average 360.74. The exact answer says how many runs a sample needs, and it is fewer as the input grows.
What a planner pays to find out what to pay
Insurance against a row estimate is set from the error's median and spread, and a running system knows neither — it has to fit them from executed queries. Fitted from one query the divisor costs 1.263 times the better plan against 1.215 for a planner that never insures at all, so learning is worse than not learning until about sixteen queries have run. The tail, though, is bought immediately: one observation already holds the worst case to 24.7 against 36.6.
Named alongside it
The objects these essays reach for when they reach for this one.
DistributionSamplingComparison countQuicksortAverage caseBreak-evenCardinality estimationClosed formConcentrationCost modelDesign parameterGuarantee