Why is it so uncommon to report confidence intervals for medians? Why is it so uncommon to find confidence intervals reported in papers from applied sciences? I work mostly on Computer Science, but often read papers from (Social) Psychology, Sociology and Urban planning. I cannot recall having seen a CI for the median reported. 
At the same time, while studying confidence intervals and the such, it became apparent to me that in all situations where the median is a better descriptor of one's data, this is the estimate that should be presented. 
Are there any theoretical reasons for why presenting CIs for the median is not common? 
 A: Your question touches on both the question of why confidence intervals are not used in these fields, and on the question of why the mean is used in preference to the median even when one would think the median is more appropriate. In psychology (and possibly sociology and urban planning too, but I'm a psychologist, so I have no real idea), no, there are no particularly good theoretical (that is, statistical) reasons for these things. Instead, it's a matter of the field having long ago fallen into a cargo-cult approach to data analysis in which p-values are the coin of the realm, means and standard deviations are thought to be accurate representations of entire vectors, and researchers imagine that significance tests tell them whether the sample effect is equal to the population effect. See these papers for some discussion and speculation about how we ended up here and why psychologists have resisted change.
Cohen, J. (1994). The earth is round (p < .05). American Psychologist, 49(12), 997–1003. doi:10.1037/0003-066X.49.12.997
Cumming, G. (2014). The new statistics: Why and how. Psychological Science, 25, 7–29. doi:10.1177/0956797613504966
A: I think it is because confidence intervals are more difficult to estimate for quantiles, such as the median, than for the mean. Here's an intro into the subject.
