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New BMI (exponent of 2.5)

A study found that the best exponent E for predicting the fat percent would be between 2 and 2.5 in m a s s / h e i g h t E {\displaystyle mass/height^{E}}.

An exponent of 5/2 or 2.5 was proposed by Quetelet in the 19 century:

In general, we do not err much when we assume that during development the squares of the weight at different ages are as the fifth powers of the height

This exponent of 2.5 is used in a revised formula for Body Mass Index, proposed by Nick Trefethen, Professor of numerical analysis at the University of Oxford, which minimizes the distortions for shorter and taller individuals resulting from the use of an exponent of 2 in the traditional BMI formula:

The scaling factor of 1.3 was determined to make the proposed new BMI formula align with the traditional BMI formula for adults of average height, while the exponent of 2.5 is a compromise between the exponent of 2 in the traditional formula for BMI and the exponent of 3 that would be expected for the scaling of weight (which at constant density would theoretically scale with volume, i.e., as the cube of the height) with height. In Trefethen's analysis, an exponent of 2.5 was found to fit empirical data more closely with less distortion than either an exponent of 2 or 3.