You put a short-lived radioactive sample in front of a Geiger tube and count. It sounds simple — but this is the first experiment here in which nothing is broken and yet repeating the same measurement twice gives two different numbers. It is not instrument noise: decay itself is random.
Why this experiment is different
In the calliper you saw that averaging cannot repair a systematic error. Here you meet the other side of that coin: the error really is random. A count of N carries a relative error of 1/√N, and no amount of care shrinks it — only counting longer does. Because it falls as a square root, halving it costs four times the time.
But a genuine systematic is lying in wait too: the background. The detector counts even with no source present — cosmic rays, potassium in the walls, radon in the air. That constant is invisible early on, but in the tail, where the sample is nearly dead, it is most of what you measured. Leave it in and the curve settles onto a flat floor instead of continuing down, so the half-life comes out too long — always too long, never too short. The escape is the same one as in the calorimeter: go and measure it separately.
And a third lesson belonging to this page alone: not every point deserves an equal vote. A point built from a few thousand counts is far more trustworthy than one built from a few dozen, yet an ordinary least-squares fit takes both equally seriously. The page shows all three answers side by side so you can see for yourself how much the weighting is worth.
The Python section takes a completely different route: it never takes a logarithm. It maximises the Poisson likelihood on the raw counts, so the tail points that the semi-log method is forced to discard stay in the fit. It also prints how many points that method threw away.