Distributions of Final Digits in Data

Usually, all the values in a variate (e.g. the plot yields in a field experiment) are recorded to the same degree of precision (e.g. to the nearest ,uth of a kilogram), and that degree of precision is often such that the final digits in the values ought to have a uniform distribution. In practice, however, the expected uniformity can be seriously disturbed. This paper discusses the main causes of such disturbances, and shows how a cause can often be deduced from the pattern of a disturbance. Patterns arising from the reading of scales are considered, instances are examined of different degrees of precision being mixed within a variate, and some final-digit distributions arising from arithmetical rounding are tabulated. Then follow three short detective stories in which explanations are found for seeming oddities in sets of real data. The fields of application touched on throughout the paper include agricultural experimentation, analytical chemistry, anthropometry, beer sales, electrical component manufacture, geography, medical records, meteorology, micrometry, and population statistics.