Say you have an apparently independent random process and you sample a hundred or so values from it. From those, you could get an estimate of the population statistics, the mean, deviation, skew, and such. Now, on the n+1th observation, you wind up with something at 5 sigma.
If the population is correctly characterized by the first hundred observations, then that data point is highly unlikely and not likely to be repeated.
If the population is not independent, or is in the process of changing, then it's possible that the population statistics are invalid.
If the population is correctly characterized by the first hundred observations, then that data point is highly unlikely and not likely to be repeated.
If the population is not independent, or is in the process of changing, then it's possible that the population statistics are invalid.