Gaussian statistics

Analyzing a number of observations, each subject to some experimental error, in an effort to obtain a more reliable answer from a multitude of measurements than can presumably be obtained from a single observation, is part of statistics. For example, while the age at which you, my dear reader, will die, is usually not well known in advance, the commercial providers of life insurance need only know the average life expectancy of your cohort (the group of persons of comparable age, gender, socioeconomic group, etc.) in order to compute a profitable premium, on the assumption that they will insure a large enough group so that the effects of early and late deaths will cancel each other out.

The underlying assumption in statistical analysis is that the experimental error is not merely repeated in each measurement, otherwise there would be no gain in multiple observations. For example, when the ‘pure’ chemical we use as a standard is contaminated (say, with water of crystallization), so that its purity is less than 100%, no amount of chemical calibration with that standard will show the existence of such a bias, even though all conclusions drawn from the measurements will contain consequent, determinate or systematic errors.