In this paper a new quantizer called the set quantizer (SQ) is introduced. In quantization, the input space is partitioned into quantization regions. A single output point in a quantization region is used to represent all the inputs falling into that region. The SQ presented in this paper uses a collection, or a set (hence the name), of output points to represent the input points in a quantization region. The proposed quantizer was implemented and tested on Markov sources, memoryless sources and image data. Simulation results show that the SQ quantization algorithm based on the hidden Markov model performs better than minimum mean square error scalar quantizers when there is redundancy in the source data. However, the SQ algorithm based on the random sequence coding approach compares favourably with most existing quantizers for memoryless sources. We also present an application to image compression.