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In almost all random sampling schemes, we adopt different sampling designs with an objective of obtaining a better representative sample (optimal sample) for the population. Application of different randomization techniques were adopted for providing a supportive basis for this. Now the question arises, whether the final sample selected, on which all our efforts are utilized, from the population is an optimal sample or not? No where we are checking about the optimality of this sample, i.e., whether this sample is the best one or there exists any other sample which is more optimal than the selected one satisfying all the constraints. In all these procedures, we only assume but, nowhere we are establishing a guarantee about the achievement of such a representative sample. The present paper emphasizes on achieving an optimal sample by using variable neighborhood search (VNS) technique.

Data Mining and Data Warehousing are two most important techniques for pattern discovery and centralized data management in today’s technology. ELearning is one of the most significant applications of data mining. The main objective is to provide a proposal for a functional model and service architecture. The standards and system architecture are analyzed here. This paper gives importance to the integration of Web Services on the e-Learning application domain, because Web Service is the most advanced choice for distance education now. The process of e-Learning can be possible more effectively with the help of Web usage mining. More advanced tools are developed for online customer’s behaviour to increase sales, and profit, but no such tools are developed to understand learner’s behaviour in e-Learning. In this paper, some data mining techniques are discussed that could be used to enhance web-based learning environments.

In sample surveys ratio estimator has found extensive applications to obtain more precise estimators of the population ratio, population mean, and population total of the study variable in the presence of auxiliary information, when the study variable is positively correlated with the auxiliary variable. The theory underlying the ratio method of estimation is same whether we estimate the population ratio or population mean/population total, excepting the fact that in the latter case we assume the advance knowledge of the population mean or total of the auxiliary variable in question. In this paper we use the term ratio estimator for both the purposes. However, in spite of its simplicity the ratio estimator is accompanied by an unwelcome bias, although the bias decreases with increase in sample size and is negligible for large sample sizes. In small samples the bias may be substantial so as to downgrade its utility by affecting the reliability of the estimate. As pointed out by L.A. Goodman, H.O. Hartley, J. Am. Stat. Assoc. 53 (1958), 491 508, in sample surveys where we draw very small samples from a large number of strata in stratified random sampling with the ratio method of estimation in each stratum, the combined bias from all the strata may assume serious proportions, affecting the reliability of the estimate. This calls for devising techniques either at estimation stage or in the sampling scheme at the selection stage to reduce the bias or completely eliminating it to make it usable in practice. This has motivated many research workers like E.M.L. Beale, Ind. Organ. 31 (1962), 27 28 and M. Tin, J. Am. Stat. Assoc. 60 (1965), 294 307 among others to construct estimators at the estimation stage removing the bias of O(1/n), where n is the sample size, and thus reducing the bias to O (1/n 2). Such estimators are termed as Almost Unbiased ratio-type estimators found in literature. In this paper we have proposed a class of almost ratio type estimators following the techniques of E.