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For inherently random phenomena that involve counting individual events or occurrences, we measure only a single number N. This kind of measurement is relevant to counting the number of radioactive decays in a specific time interval from a sample of material. It is also relevant to counting the number of Lutherans in a random sample of the population. The (absolute) uncertainty of such a single measurement, N, is estimated as the square root of N. As example, if we measure 50 radioactive decays in 1 second we should present the result as 50±7 decays per second. (The quoted uncertainty indicates that a subsequent measurement performed identically could easily result in numbers dif- fering by 7 from 50.)

I can see that for "random" or acausal (stochastic) phenomena, the "absolute" uncertainty in a measurement is equal to the square root of that quantity of measurements. What is that about? I think I understand square roots and squaring just fine, and am looking for a little help in explanation.