Sampling practice and theory - Updated Aug 2, 2014 -

Sampling, What Does It Entail?
& How To Obtain Representative Samples

Sampling is defined as taking a small portion of a whole mass that accurately represents the whole mass.

Very simple to define, however obtaining a representative sample is anything but simple. Mathematicians will say sampling is expressible as a series of mathematical equations. Such as, for sampling "X" pounds of material, one would take "y" increments of samples, each weighing "z" pounds. Then these equations are interfaced with statistics with probability which derive numbers and sizes of samples to take for a given probability of it accurately representing the whole lot. This might work fine for a fairly homogeneous substance, with relatively the same particle size. However, this rarely represents what one would sample in "the real world " of mining and mineral processing.

I have read many theories of sampling and found one similarity among them, the amount and frequency that is recommended for obtaining representative samples is not often within the realm of practicality, or feasible with respect to cost and production. Those that are, have done their field work, in addition to their mathematical exercises.

Since this site is primarily concerned with mining and mining issues, the sampling discussed here will be relative to mining, sampling of ores and processed products from mills, processing plants and mines. One problem faced by mining activities is the material to be sampled was formed in the earth hundreds of million years ago, and it is variable, depending upon the existing conditions at the time it was formed and the occurrences in the millions of years since. Precious metal ores are extremely variable, since the mineralization can be local, widely dispersed with a pattern or without any pattern. Other types of ores can vary less in composition, but almost no ore is homogenous.

Therefore, a knowledge of the material to be sampled must be factored into any sampling equation, for it to be accurate or workable. In the table, below, is a basic sampling equation that relates particle size to the amount of sample to be taken, with constants derrived for varions types of ore bodies. The values for "M" are the sample size required in pounds. Tha values of k are the constant derrived for differing ore bodies, in this example gold. The values of "n" are a probability factor that attempts to associate the probability that any grain is the grain of value, in this case gold. The values of "d" are the diameter of the largest particle of ore to be sampled. I have found that it can be useful in sampling, when used by pesonnel that understand the ore, and sampling,

The table, above, relates the particle size of the material being sampled to the sample size required for a representative sample. As one can see, the finer the material being sampled, the smaller the size of sample required. Taken into account is the statistical fact that the finer particles have many more individual particles per pound than do the coarser particles and that since ore is made up of many different materials, the finer particles are much more likely to contain all of the individual elements of the whole sample.

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