Optimization models for degrouping population data.

In certain countries population data are available in grouped form only, usually as quinquennial age groups plus a large open-ended range for the elderly. However, official statistics call for data by individual age since many statistical operations, such as the calculation of demographic indicators, require the use of ungrouped population data. In this paper a number of mathematical models are proposed which, starting from population data given in age groups, enable these ranges to be degrouped into age-specific population values without leaving a fractional part. Unlike other existing procedures for disaggregating demographic data, ours makes it possible to process several years' data simultaneously in a coherent way, and provides accurate results longitudinally as well as transversally. This procedure is also shown to be helpful in dealing with degrouped population data affected by noise, such as those affected by the age-heaping phenomenon.