Extractive summarization aims at selecting a set of indicative sentences from a source document as a summary that can express the major theme of the document. A general consensus on extractive summarization is that both relevance and coverage are critical issues to address. The existing methods designed to model coverage can be characterized by either reducing redundancy or increasing diversity in the summary. Maximal margin relevance (MMR) is a widely-cited method since it takes both relevance and redundancy into account when generating a summary for a given document. In addition to MMR, there is only a dearth of research concentrating on reducing redundancy or increasing diversity for the spoken document summarization task, as far as we are aware. Motivated by these observations, two major contributions are presented in this paper. First, in contrast to MMR, which considers coverage by reducing redundancy, we propose two novel coverage-based methods, which directly increase diversity. With the proposed methods, a set of representative sentences, which not only are relevant to the given document but also cover most of the important sub-themes of the document, can be selected automatically. Second, we make a step forward to plug in several document/sentence representation methods into the proposed framework to further enhance the summarization performance. A series of empirical evaluations demonstrate the effectiveness of our proposed methods.