Histogram techniques are widely used in commercial database management systems for an estimation of query results. Recently, they have been also used in approximately, processing database queries, especially aggregation queries. Existing research results in this area have been mainly focused on constructing a histogram to approximately represent, as accurate as possible on an intuitive base, the original data frequencies. We propose a novel histogram construction method aiming to minimize the average approximate aggregation errors; and we have developed an efficient algorithm to construct near optimal histograms to achieve this goal. Our experiment results showed that the new histogram construction techniques lead to more accurate results than those by existing histogram techniques, and also out-perform the existing wavelet techniques.