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Weight, size and shape relationships and their uses in the study of graded yield data

SUMMARY For many horticultural crops the distribution of weight over size grades is of more importance than the total weight. This paper shows how simply determined features of interrelationships of the weight, size and shape of an individual in the crop can be combined to provide estimates of various aspects of the distribution of crop weight over size grades. The two relationships required are (i) the probability density function of the grading variable for the crop; (ii) a function relating the weight of an individual to the corresponding value of the grading variable. The paper shows how each of these can be determined either from published data or by simple experiment. Examples using data on onions and carrots are given to illustrate this and also to show some of the more important practical applications of the methods. For example, they allow the results of grading with one set of size grades to be extrapolated to a different set of grades without recourse to further measurement or experimentation and this is illustrated using published data on carrots. Other possible uses are also discussed and outlined.