As the foundations of modern science were being laid, the need for a model for the uncertainty in a measurement became apparent. Here we look at the development of the theory of measurement error and discover its consequences.

The problem may be expressed as follows: Repeated measurements of one and the same item, if they are not rounded off too much, will frequently yield a whole range of observed values. If we let X denote one of these observed values, then it is logical to think of X as having two components. Let Y denote the actual, but unknown, value of the item measured, and let E denote the measurement error associated with that observation Then X = Y + E, and we want to use our repeated measurements to find an estimate for Y in spite of the uncertainties introduced by the error terms E. As it turns out, the best estimate to use will depend on the properties of the distribution of the error terms E.

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