Sphericity and roundness data of quartz grains (of varying size) of sieve fractions are empirically shown to be non-normally distributed. It is also demonstrated that log10 [ψ/(1−ψ)] and −log10(P) transformations, respectively, normalize the sphericity and roundness data, where ψ denotes the two-dimensional sphericity and P the roundness of the grains in a plane. Laboratory experiments on sampling quartz grains from a sieve fraction show that the cone-and-quartering method is preferable as it yields similar results to those of the more time-consuming random sampling procedure. Results of laboratory measurement errors on two-dimensional sphericity and roundness data are also presented. The frequency of sphericity and roundness data are noted on number basis.

For all parametric statistical studies of sphericity and roundness the sample statistics should, therefore, be calculated according to the above normalizing log functions. Suitable grade scales of sphericity and roundness data are proposed here basing on these log functions and the total range and the minimum range of the variates (sphericity and roundness).