Interpreting the results of the Dunn test I've seen some answers that come close to what I'm asking but not quite. I've run a Kruskall-Wallis test that rejected the null hypothesis. Now, I've run the Dunn test, but I'm wondering if I am interpreting it correctly. My results follow:

As you can see, the pairwise comparison was significant for all comparisons in the Dunn test. My question here regards the ranking. From what I gather, this outcome means that the White rate was significantly higher than the rest of the race's rates (looking at the Rank Sum column of the KW test). Is that a misinterpretation of the rank sum? 
 A: For this test, the null hypothesis for each pairwise comparison is that the probability of observing a random rate in the first group that is larger than a random rate in the second group equals one half. Here you reject that for all pairs of races, though you might want to use some sort of multiple comparison adjustment. On its own, I don't think this says anything about different means in the populations.
If you can assume that rate is continuous and the distributions for all groups are identical except for a shift in centrality, then this test can be interpreted as a test of median differences. Similarly, you will need additional, stronger, assumptions about the distribution to say something about the mean.   
Also, you probably want to show code itself, and not just the output when you ask questions. At the very least, you should mention that you are using a user-written command that was published in the Stata Journal, dunntest. This will make your question both easier to answer and will make it more useful for posterity.
