# Example of an non-symmetrical Wilcoxon Rank Sum test statistic value

I have been given a homework in a subject called "Non-Parametric Statistics" and I'm a bit stuck with it. I would be very thankful if you could give me any advice or help, which would lead to a solution!

The task is about Wilcoxon Rank Sum Test, but in a case, where there are equal observations in the sample. In this case midranks are being used (e.g. if sample consists of 1, 3, 3, 5. Then the ranks would be 1, (2+3)/2 = 2,5, (2+3)/2 = 2,5, 4. As we see, the distribution of $$W_s^{*}$$ is symmetrical, because mean, mode and median all fall at the same point (which is 3 at the moment). And the formula for a Wilcoxon Rank Sum Test in this case is: $$W_{s}^{*} = \sum_{i=1}^{n} midrank(X_i)$$ ($$X$$ and $$Y$$ are observations from a united variations series.)

Bring an example, where the distribution of $$W_{s}^{*}$$ is NOT symmetrical under H0 hypothesis. (An example must have realistic subject - what is being examined and measured etc!)