Here is something you almost never get in real life: a whole population you can see. All 400 commuters, every value known. Now take a random sample from it and watch what the sample mean does — it misses. Every single time.
The population — 400 commuters
short commutelong commutein your sample
Sample means pile up here
the 400 individual valuesyour sample means
Draw your first samplepress the button below
20
Samples drawn0
Latest x̄—
Latest miss—
Biggest miss—
Typical miss—
Within 1 typical miss—
Parameter goes with Population (μ, σ). Statistic goes with Sample (x̄, s). The parameter is one fixed number; the statistic is a number that reshuffles every time you sample.
Switch to "Population hidden." That is the honest picture of research: the grid goes dark, μ becomes a question mark, and you are left holding a single x̄ and an estimate of how far it probably strayed.