Uncertainty in analyte mass for samples containing small numbers of particles

A sampling equation was derived that relates the standard deviation in anal yte mass to the number of particles in the sample, the fractions of the dif ferent types of particles in the mixture and the masses and analyte concent rations of the individual particles. The equation, which is applicable to s amples containing any number of particles, was verified by sampling and ana lysis of two cereal grain mixtures for manganese, potassium, chlorine and m agnesium, and by Monte Carlo computer simulation. Comparison of the samplin g precision of analyte mass with the analytical measurement precision was a lso studied, and it was shown that use of the equation allows the calculati on of the minimum number of particles required to hold the sampling relativ e standard deviation to that of the analytical measurement.