How should I quote errors when measurements are asymetrically clustered? Suppose five people measure the length of a stick and report the following values
4.90cm 4.92cm 4.93cm 4.94cm 4.94cm

In high school science we are told that in cases like this we should report the average as 4.92cm +/- 0.02cm because the range of results is 0.04cm and we halve that.
Suppose the measurements were instead this
4.89cm 4.89cm 4.90cm 4.91cm 4.99cm

Here the average is 4.92cm but what about the error? If I quote the error as +/-0.05cm then that would suggest, not knowing the details, that 4.87cm is a plausible value and that 4.99cm is not.
Should we just swallow that or is it more appropriate to report the average and errors differently?
 A: The way you quote your result should reflect your understanding of the underlying distribution. If you believe your data is normally distributed (for this you can do the Anderson-Darling normality test, for example), then taking the standard deviation and reporting mean $\pm$ standard deviation is acceptable.
If you have reason to believe that the data is not normally distributed (this usually happens when there is a single factor dominating your error - for example the time from the start of an exponential decay until the moment that you take your measurement) you might want to change this. You can report the median and range, median and 95% confidence interval, first and third quartile, ... 
The key concept here is this: when you write down your "result", you attempt to communicate what you learnt about your process to the person reading it. If the way you represent your data does not reflect your knowledge, you failed. If it does, you succeeded.
For the example you gave, the p value of the A-D test of 0.02: that means we reject the hypothesis that this is normally distributed data, and either conclude that 4.99 is an outlier, or that the process has some strange asymmetry. Without good reasons you cannot simply throw out an inconvenient value.
I would probably report this as 
median ($\pm$ range) = 4.90 (+0.09 -0.02) cm
A: The most accepted way to do so is use the standard deviation, and there are several reasons for it. 
But to put it simply, whenever you are measuring a magnitude that "ideally" should have only one value, it is expected that the measurements will behave as a gaussian distribution. That is, the probability of getting a certain value decreases with this mentioned shape the further you go from the mean value. This means that the standard deviation will provide a range around the mean value that will contain the "real" value you want to measure with a 68% certainty. 
