Social media posts provide a compelling, yet challenging source of data of diverse perspectives from many socially salient groups. Automatic text summarization algorithms make this data accessible at scale by compressing large collections of documents into short summaries that preserve salient information from the source text. In this work, we take a complementary approach to analyzing and improving the quality of summaries generated from social media data in terms of their ability to represent salient as well as diverse perspectives. We introduce a novel dataset, DivSumm, of dialect diverse tweets and human-written extractive and abstractive summaries. Then, we study the extent of dialect diversity reflected in human-written reference summaries as well as system-generated summaries. The results of our extensive experiments suggest that humans annotate fairly well-balanced dialect diverse summaries, and that cluster-based pre-processing approaches seem beneficial in improving the overall quality of the system-generated summaries without loss in diversity.