Is it appropriate to report the mean, standard deviation and coefficient of variation for binary measurements? I am reading an article where the authors reported the mean, standard deviation, coefficient of variation, minimum and maximum values for binary measurements/variables. In the summary table the authors also give a summary for other continuous variables. I am wondering whether this is appropriate and if not, what is the appropriate way to report the data structure/summary statistics for binary measurements.
 A: It's overkill, but may be justified for presentation reasons.
Usually, the total number $N$ of measurements is known. If we then know the number $N_1$ of "1" entries, we can calculate all the other summaries you describe. Conversely, if we know $N$ and the mean $m$, then we can calculate $N_1 = mN$, so if we know $N$, then $m$ contains exactly the same information as $N_1$. We can also calculate $N_1$ from $N$ and the coefficient of variation (as long as this is not zero).
Also, the minimum and the maximum only tell us whether there were any "0" and "1" entries at all, so this is usually very uninteresting to report.
So, the most appropriate report for binary variables would be simply the number of "0" and "1" entries.
However, the summary may be part of a table that also reports on other, non-binary variables. For these, the KPIs you list make more sense. So it makes sense to also report the binary variables in the same format, rather than create an additional table for the binary variables, or only report binary variables in the text, where the reader would need to hunt for them.
A: Like Stephan Kolassa says, I would go with a simple table of entries and the percentages.
The mean can be useful in getting a sense of proportion. I argue standard deviation (and thus coefficient of variation) is not useful because it's not as easy to interpret versus simply listing the counts and giving percentages.  For data distributed approximately with a Normal distribution, it is easy to visualize what a given SD value looks like, but not so much for binary variables. Standard deviation measures the spread of variables from the mean, but for binary variables the data are fixed to 0/1, and thus how the distance to the mean factors into the SD calculation is not intuitive.
