We consider the problem of estimating the distribution of carcass weights in a flock of animals from estimates made on a truncated sample. This arises when a farmer chooses the heaviest lambs for slaughter and then measurements are made by the meat processor. This enables a farmer to answer two questions: what proportion of the animals remaining exceed a nominated carcass weight, and/or what carcass weight is exceeded by a nominated proportion of the population? Estimates of these statistics and their uncertainties are derived and are exact if the animal weights are normally distributed. These calculations can be the basis of decisions about future feeding and drafting strategies, important for farmers producing animals on contracts for future delivery. An example is given based on 1000 lambs using a cut-off weight of 15.5 kg with mean of this upper group of 16 kg. Using a realistic estimate of a standard deviation (of the weighing scales) of 0.3 kg, this gives an estimated mean of 14.6± 0.04 kg, with a standard deviation of 0.94±0.044 kg, and that 75% of the lambs in the population exceed 13.9±0.07 kg. The proportion of lambs that exceed 14.5 kg is then between 51.3% and 55.7%.
Wake, G.C., Pleasants, A.B. (2003), Calculating animal performance from limited liveweight measurements of the population, Research Letters in the Information and Mathematical Sciences, 4, 173-180