  An allometric height-mass exponent $\gamma$ gives an approximative power-law
relation $< M> \propto H^\gamma$ between the average mass $< M>$ and the height
$H$, for a sample of individuals. The individuals in the present study are
humans but could be any biological organism. The sampling can be for a specific
age of the individuals or for an age-interval. The body-mass index (BMI) is
often used for practical purposes when characterizing humans and it is based on
the allometric exponent $\gamma=2$. It is here shown that the actual value of
$\gamma$ is to large extent determined by the degree of correlation between
mass and height within the sample studied: no correlation between mass and
height means $\gamma=0$, whereas if there was a precise relation between mass
and height such that all individuals had the same shape and density then
$\gamma=3$. The connection is demonstrated by showing that the value of
$\gamma$ can be obtained directly from three numbers characterizing the spreads
of the relevant random Gaussian statistical distributions: the spread of the
height and mass distributions together with the spread of the mass distribution
for the average height. Possible implications for allometric relations in
general are discussed.
