Contribution to the Study of Grouped Observations |
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Authors: | N F Gjeddebæk |
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Institution: | A/S Ferrosan , Copenhagen |
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Abstract: | § 1. Introduction. a. Grouping. From a purely mathematical point of view practical observations are often more or less grouped, but in applied mathematics only fairly coarse groupings need be taken into account. The statures of the individuals in a population are commonly given as an example of grouped observations. A measurement of between x - ![/></span> unit and <i>x</i> + <span class=](/na101/home/literatum/publisher/tandf/journals/content/sact20/1949/sact20.v1949.i01/03461238.1949.10419768/production/images/medium/sact_a_10419768_o_ilf0001.gif) ![/></span> unit is referred to as <i>x</i> units, and in order to compensate for the inaccuracy of the estimates of the means and standard deviations calculated from such observations the use of certain corrections has been advised. The benefit hereof is, however, doubtful as usually grouping is comparatively fine and then it is not really disturbing. In the following an account will be given of some facts connected with far coarser grouping. As otherwise the subject would become too extensive, the exposition will here be confined to normally distributed observations. The problem of the “best estimates” of the mean and the standard deviation for the coarsely grouped normal observations will be solved in accordance with the principle of maximum likelihood.</td>
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