Median, expected value, correlation: these words turn up in the puzzle explanations and look dry. But each of them has its own trap for intuition. Here you can play with them in simulations and see when to use which number.
The middle value: line everyone up in order, and half are below it, half above.
A millionaire walks into a bar: the average income shoots up, the median barely moves.
The sum of all values divided by how many there are: what everyone would get if it were shared equally.
Almost everyone has more legs than average: the average is a little under two.
The average result you can expect if you repeat the same thing very many times.
A die's expected value is 3.5, yet no face shows 3.5.
A number from −1 to +1 showing how closely two quantities move together.
In summer both ice cream sales and drownings go up. Ice cream isn't to blame: the heat drives both.
A measure of spread: how far values typically stray from the mean. The standard deviation is its square root, in the same units.
Two towns with the same average temperature: one stays near +15 all year, the other swings from −20 to +50.
A bell-shaped distribution: most values sit near the mean, and the further away, the rarer.
Every ball on a Galton board falls at random, yet thousands of balls always build the same bell.
The more repetitions, the closer the share of an outcome gets to its true probability.
The share of heads creeps towards 50%, while the gap between heads and tails in coins usually grows.
The chance of an event given that something else is already known.
Almost all NBA players are tall, but almost all tall people are not NBA players.
Events are independent if knowing about one doesn't change the chances of the other.
After five heads in a row tails is no more likely: the coin remembers nothing.
How many times you multiply the base by itself to get a number: log₂ 8 = 3, because 2 · 2 · 2 = 8.
A sheet of paper folded in half 42 times would be thicker than the distance to the Moon.
A sample some people get into more easily than others, so it describes everyone badly.
In 1936 a magazine polled millions of Americans and still picked the wrong election winner.
How often chance alone would produce a gap at least as big as yours if there were really no difference.
When there is no effect at all, p below 0.05 turns up as often as p between 0.50 and 0.55.
A range around a measured number, built by a method that covers the true value in a chosen share of samples, such as 95%.
Of twenty honest 95% intervals, on average one misses the truth, and none of them knows whether it is the one.
The probability that a test notices a real effect of a given size. A power of 80% means the test misses one working effect in five.
A weak A/B test that does find an effect almost always exaggerates it: a real +10% shows up on the dashboard as +24%.
How far an average or a rate computed from a sample usually misses the truth: σ divided by the square root of the sample size.
Halving the error takes four times as much data.