Note on Discrete Approximations

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Abstract
Suppose it is required to replace a continuous variate Z by an integer-valued approximation X in such a way that X retains as much information as possible. This problem is encountered, for example, in the field of educational measurement, where performance scores are often replaced by letter grades, which are then converted to grade points. Given certain reasonable assumptions, optimal integer-valued approximations to Z are calculated for k = 2,…, 15, where k is the number of values which X can take on.

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