Primitive substances in asteroid and meteorite materials represent a record of early solar system evolution. To allow the study of these materials, they must be collected and transferred to the laboratory. Collection during sample return missions requires an assessment of the size of samples needed. Meteorite falls or finds must be subdivided into appropriate subsamples for analysis by successive generations of scientists. It is essential, therefore, to determine a representative mass or volume at which the collected or allocated sample is representative of the whole. For the first time, we have used a Bayesian statistical approach and a selected meteorite sample, Murchison, to identify a recommended smallest sample mass that can be used without interferences from sampling bias. Enhancing background knowledge to inform sample selection and analysis is an effective means of increasing the probability of obtaining a positive scientific outcome. The influence of the subdivision mechanism when preparing samples for distribution has also been examined. Assuming a similar size distribution of fragments to that of the Murchison meteorite, cubes can be similarly representative as fragments, but at orders of magnitude smaller sizes. We find that: (1) at all defined probabilities (90%, 95%, and 99%), nanometer-sized particles (where the axes of a three-dimensional sample are less that a nanometer in length) are never representative of the whole; (2) at the intermediate and highest defined probabilities (95% and 99%), micrometer-sized particles are never representative of the whole; and (3) for micrometer-sized samples, the only sample that is representative of the whole is a cube and then only at a 90% probability. The difference between cubes and fragments becomes less important as sample size increases and any >0.5 mm-sized sample will be representative of the whole with a probability of 99.9%. The results provide guidance for sample return mission planners and curators or advisory boards that must distribute valuable samples for analysis.