can you report both a mean and a median for same variable I have a variable that is not normally distributed.  The two groups are statistically significantly different using a non-parametric test.  However, they do not "look" different when reporting the medians (1 vs 1 in each group with diff confidence intervals).  So in the same paper can I also report the mean along with the standard deviation because the two groups look different that way - but "legally" I would be doing the stats based on the median and in the methods state that for non-normal variables I used mann-whitney).
so perhaps saying groups 1 and 2 had medians of 1 (CI range) and the means were 3.1 (SD) vs 2.7 (SD) respectively"
A similar question: can I state both the mean and median in the text of the paper and then graphically display the means along with the SEM or SD error bars?
 A: This might depend on your field, but in econometrics it is quite common to report summary statistics on your data. And these statistics are often not used in tests. If it is informative to the reader and does not create confusion, I don't see anything wrong with it.
A: The test you used is a non-parametric test, an alternative to a t-test for normal samples. So, you only compared if a random value from group A had the same probability to be on group B. So, if you found statistical difference it will be expected that you report the means and SDs, yes. Since you are working with non-parametric data you cuould try to compare two density plots with lines highlighting the means. I would usually plot them together with some trasnparency, so the distributions and means are easily compared.
A: The mean and the SD are generally a must, you are comparing the means with your test. 
The median will give you an idea about the distribution of the samples without the need of a density plot. In a Normal curve, the mean and media will be the same, or almost identical at least. As your distribution skews the mean and the median will separate. o, in summary, depending on what you want to show with your results.
A: There are two points worth making here.
The test you used, the Mann-Whitney test, does not compare medians it compares stochastic equality. What you observed, equality of sample medians while the test reaches some arbitrary level of statistical significance can occur easily. There is a nice graph in this Q&A Why is the Mann–Whitney U test significant when the medians are equal? which illustrates perfectly what happens. So if a journal referee complains just tell them what happens.
As far as reporting means and medians alongside one another this is absolutely fine and is often done in journal articles. If you think it helps the reader to understand your data-set then go ahead. After all the goal is to inform the reader.
A: You can and should report anything that is relevant.  
In my work, there have been times where this meant I needed to report the mean, median, standard deviation, skewness, and kurtosis. Other things to consider might be correlation between two variables, autocorrelation for a time-series, or a variety of visual plots that show what summary statistics cannot. 
Report what's important to serve your purpose. 
