Why would the median be used to summarize ordinal data instead of the mode? I am working with ordinal data (produced from Likert-types scales). I am of the understanding that results should be presented as a mode, which makes sense to me. However, when working in SPSS and utilising the Kruskal Wallis test, results are presented as a median (or mean rank).
I am therefore a little confused as to how best to present this data.  
 A: Much of this is discussed in our classic thread on the topic: What are good basic statistics to use for ordinal data? 
The classical thinking on the topic is that data can instantiate one of a set of levels of measurement (nominal, ordinal, interval, and ratio).  While I think this theory is generally overblown, the standard recommendation is to use means to represent the central tendency of continuous (interval or ratio) data, medians to represent ordinal data, and the mode (potentially) to represent nominal data.  The reason to choose the median is that it carries more information about the distribution than the mode and it is unambiguously acceptable for ordinal data (e.g., using the mean could be controversial, see: Calculate mean of ordinal variable).  In truth, the mode is rarely ever used in my experience.  
A: One of the inherent problems of nonparametric statistics is that they, by definition, don't provide inferences about population parameters. Although it is theoretically possible to make up a situation in which comparing means on an ordinal scale would be misleading, such situations are very rare in the real world. I would recommend comparing means using ANOVA. See this article for more information: http://link.springer.com/article/10.1007/s10459-010-9222-y
