Remedial investigations often are biased toward sampling “hot spots”, or the areas of a site that are suspected to be most contaminated. This bias may be needed to characterize the contamination on site, but it can distort exposure estimates. We explored the problem of “hot spot” sampling by constructing a hypothetical site with a single contaminant source randomly located within the site domain. We prescribed two different spatial distributions for the source, which were integrated to provide exact measures of the average concentration over the site. Actual averages were compared to “empirical” averages constructed by sampling the contamination field on an evenly spaced grid and calculating the arithmetic mean of the samples. Empirical estimates either underestimate or overestimate the true site average concentration. We investigated the pattern of errors introduced by finite sampling schemes, and found the interaction between the relative extent of the source and the sampling density was particularly important. The smallest errors introduced by gridded sampling occurred when the domain was extensively sampled and the source was spread over a large portion of the site. One of two results occurred at the other extreme, in which a relatively small source was placed in a sparsely sampled network: either the source was not detected and the average concentration greatly underestimated, or the source coincided with a sampling point and the site-average concentration was greatly overestimated. On average, empirical sampling on evenly spaced grids overestimated the actual site average concentration. Even larger overestimates occurred when the upper 95th percentile confidence limit of the empirical means were compared to the actual average concentrations. Depending on the contaminant distribution and sampling density, overestimates ranged from (on average) 7% to more than 200%. An investigation of purposive sampling of “hot spots” was conducted by placing additional samples in the proximity of the maximum concentration detected on the regular grid. The additional samples tend to increase the empirical averages, and consequently increase the degree of overestimation of the true site average concentrations. The results emphasize the critical importance of the pattern of contamination and the conservative bias of purposive sampling plans.