Sampling practice and theory

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 NEVER within the realm of practicality, or feasible with respect to cost and production.

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, a 100 ton lot is proposed to be sampled. The size of the sample to be taken depends upon the particle size of the material to be sampled, to have a 90% chance of being a reproducible sample.
Particle Diameter
In Inches 
Minimum Weight of Sample (pounds) 
0.04  0.0625 
0.08  0.5 
0.32  32 
0.64  256 
1.25  2048 
2.5   16348 
Sampling Theory In The Late 1800's

The table, above, is one of the early sampling studies that proposed to relate the particle size of the material being sampled to the sample size required for a representative sample. The basis for the lot to be sampled for this theory was a 100 tons of ore. 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.

For more information, continue to the Next Page, "Sampling, Page 2"

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