The analysis of the problems arising upon transition from nonparametric statistics of progress of the certain student to parametrical statistics of the description of progress of big selection of students is carried out. It is shown that a number of problems of limit transitions arises because of violation of the restrictions imposed on selection by the central limit theorem. In article it is proved that for application of limit transition from nonparametric statistics of certain students to parametrical statistics of the general selection of students it is necessary to allocate previously subgroups of the students answering to conditions of applicability of the limit theorem. It is offered to classify previously the received selections of students on the basis of lack of functional dependence of dispersion in the range from average progress. The algorithm providing additional check of selection on a normality of distribution of a random variable is described, concrete recommendations for transition conditions from nonparametric statistics to parametrical on the example of the analysis of average progress of students are formulated.