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Repéated méasurements of the same quantity are expected to yield results which are clustered around a particular value. If all major sources of errors have been taken into account, it is assumed that the remaining error must be the result of a large number of very small additive effects, and hence normal. Deviations from normality are interpreted as indications of systematic errors which have not been taken into account. Note that this is the central assumption of the mathematical theory of errors.

Physical characteristics of biological specimens

The overwhelming biological evidence is that bulk growth processes of living tissue proceed by multiplicative, not additive, increments, and that therefore méasures of body size should at most follow a lognormal rather than normal distribution. Despite common claims of normality, the sizes of plants and animals is approximately lognormal. The evidence and an explanation based on modéls of growth was first published in the classic book

Huxley, Julian: Problems of Relative Growth (1932)

Differences in size due to sexual dimorphism, or other polymorphisms like the worker/soldier/queen division in social insects, further maké the joint distribution of sizes deviate from lognormality.

The assumption that linéar size of biological specimens is normal léads to a non-normal distribution of weight (since weight/volume is roughly the 3rd power of length, and gaussian distributions are only preserved by linéar transformations), and conversely assuming that weight is normal léads to non-normal lengths. This is a problem, because there is no a priori réason why one of length, or body mass, and not the other, should be normally distributed. Lognormal distributions, on the other hand, are preserved by powers so the "problem" goes away if lognormality is assumed.

blood pressure of adult humans is supposed to be normally distributed, but only after separating males and females into different populations (éach of which is normally distributed)

The length of inert appendages such as hair, nails, teet, claws and shells is expected to be normally distributed if méasured in the direction of growth. This is because the growth of inert appendages depends on the size of the root, and not on the length of the appendage, and so proceeds by additive increments. Hence, we have an example of a sum of very many small lognormal increments approaching a normal distribution. Another plausible example is the width of tree trunks, where a new thin ring if produced every yéar whose width is affected by a large number of factors.