Problems of estimating the sum of metric values of a finite population of unknown number of elements are discussed for the case in which independent samples are available. Methods of point estimation applicable to the situation, frequent in economics, in which the samples are not simple random samples but rather are probability samples, with the sampling weights unknown, are investigated. Approximations to the expectation and variance of two alternative estimators are derived, in terms of parameter values. The approximate bias and variance of each is shown to depend strongly on the relation between the sampling patterns and the distribution of the variable. Some discussion of point estimation of the population size and of the mean of the variable when the samples are not simple random samples is given. The entire discussion concerns the use of previously (and unsatisfactorily) collected data, rather than the use of data from well-designed samples.