Some Hints on Statistical Errors

There are many examples of random processes in physics. For example, if we pick a single card out of a pack of 52 cards we don't know which one we will find. All we can say is that there is a certain probability (one in 52) of getting a particular card (say, the jack of clubs). If we have 150 packs of cards and pick one card from each, how many jacks of clubs will we pick out? About three times on average. (150 times 1/52 is about equal to 3.) However, sometimes we will get only 2 jacks of clubs, sometimes 4 and sometimes other numbers. This is what we mean by statistical fluctuations.

Physicists need to be able to estimate the effect of statistical fluctuations on the measurements they make. If you have counted a certain number N of a particular type of event then the "statistical error" or "statistical uncertainty" on N is approximately given by the square root of N. So, for example, if you counted 49 events, the statistical uncertainty on your measurement would be the square root of 49, which is 7.

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Terry Wyatt. March 1997.