Apprentice and trainee data are reported by the State and Territory Training Authorities to NCVER (National Centre for Vocational Education Research) on a quarterly basis, starting at the September quarter of 1994. The set of data submitted that quarter is referred to as Collection 1. The sets of data submitted in subsequent quarters are referred to as Collection 2, Collection 3 and so on. At the time of writing, the set of data being submitted is for the June 2009 quarter and is referred to as Collection 60. Of particular interest is the numbers of contracts of training that commence, complete, cancel/withdraw, re-commence, expire or suspend and the time at which these events occur (referred to as the "date of effect"). From these events, the number of contracts in training at a given time can be calculated. The purpose of this technical paper is to describe: (1) the way data accumulate over many collections; (2) how items derived from the data change as the data accumulates; (3) the endorsed estimation method (developed from the analysis of the above); (4) the formulae for calculating the required estimates; and (5) potential weaknesses in the method. Throughout the main text of this document data for New South Wales commencements and expired contracts are used as examples to illustrate the concepts being discussed. Supporting data is appended. A glossary is included. (Contains 4 tables and 8 figures.) [For the accompanying report, "Apprentices and Trainees: December Quarter, 2009", see ED510135.]