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been developed, which derived graduation rules based on summation formulae (convolution of the series of observations with a chosen set of weights). Two such rules are the 15-point and 21-point rules of Spencer (1904). These graduation rules were carefully designed to have a quadratic-reproducing property: If the ungraduated values exactly follow a quadratic formula, then the graduated values equal the ungraduated values. This is an important property: a simple moving average, by contrast, cannot

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