The full story on uncertainties in particle size analysis is somewhat complex. Gy dealt with the stats issue in terms of particle numbers and the correlation between terms on the cumulative size distribution. However, when sampling in an unbiased from a lot, there are what can be called ‘coarse’ particles and ‘fines’. The split between these comes somewhere about 4 to 8 mm. When sizing a sample that contains coarse particles, the uncertainty in the number of particles in a size fraction relates to Poisson particle numbers quite closely, so there is a 1 on root N SD fore the amount in the size fraction. This is also true for instrumental analysis like the Malvern sizer where individual particles are observed. But when sieving, the amounts in the finer fractions is affected more by the sieving method and practice than by particle numbers. In such a case, uncertainties in the mass in the finer fractions must be established by sieving of nominally identical subsamples. So, it ain’t that easy.

The fundamental points to consider are:
• What is the required or desired standard error (SE) in the measurement?

The standard error of the mean is proportional to 1/√n where n is the number of particles.
If 1% standard error (or FSE, Fundamental Sampling Error) is required than 10,000 particles will be required in the appropriate part of the distribution.

For 10% FSE, then 100 random particles.
• Is a bulk size (‘as is’/with agglomerates) required or is a dispersed (primary) size desired?

This is the answer to the question “What is the purpose of taking the measurement?

• What is the top end (largest size) and the polydispersity (width/spread) of the particle size distribution?
• What is the mass of sample used in the experiment?

The corollary is that we need to be careful if we’re using a technique like electron microscopy for a particle size distribution determination – indeed at the sizes you mention the minimum masses required are in the order of kg for a 1% accurate PSD.

However, for mineralogy and guides to subsequent processing then some form of electron microscopy with elemental determination is essential. The nugget effect is particularly relevant to taking samples for ore processing and for grade determination.