The article discusses the construction of statistical inference about the characteristics of the totality of data volume on the results of the analysis of its parts, volume and containing the anomalous objects. It is admitted that the information about may be missing. We give solutions of two tasks of constructing statistical inference for all objects: estimating the total number of abnormal objects, analysis measure of the deviation from the norm. In the scope of model of random sampling without replacement confidence interval for the total number of abnormal objects is constructed. For the hypergeometric distribution monotone properties of its distribution function on and unimodal probability distributions are proved. When information about is given as a range of possible values, it is suggested to choose from the set of confidence intervals, each of which corresponds to a definite value of , the one that has the greatest width, i.e. the best confidence interval for the worst case. To describe the properties of the measures deviations from the norm nonparametric bootstrap method is used. Discrete distribution defined on a set of distinct values from a set , the probability of occurrence of each of which is equal , is considered for the specific values for correspondingly. From this distribution can generate the bootstrap sample, and then build (analytically or by simulation) the distribution of any characteristics of the vector . The problems of efficient algorithms for hypergeometric distribution are discussed. The proposed solutions allow the implementation of the sampling sites both in the case of complete background information and partially available.