Instrument 4 · the central limit theorem
Why averages behave
Take almost any population — lopsided, lumpy, nothing like a bell — and average n of it. The averages pile into a bell anyway. Their spread shrinks as one over the square root of n, which is why four times the data buys you only twice the precision.
The thing you are measuring
Averages of 25 at a time
the population the averages the normal curve they converge to
The same statement, with the numbers in it
σ is the spread of one measurement; √n is what averaging buys you.
The square root is the tax: to halve the error you must quadruple the sample.
Fine tune
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