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Methods of graduation of a series of observations by means of moving averages were discussed by Sheppard (1914), and subsequently by Sherriff (1920) and a number of other writers. These methods based on least squares or weighted least squares solutions differ from actuarial or summation methods. Thompson (1947) has proposed that the method of moving averages be considered a ‘basic’ one in the estimation of the median effective dose (LD50) of bioassay data. On the basis of an empirical study of the data of Topley and Wilson he recommended in particular the use of a three-term moving average. In a recent paper, Finney (1950) has discussed the efficiency of Thompson's moving average method generally.