Whether to use mean or median to summarise the central tendency of length of time to perform a task I work for a commission-based company that gives accounts to employees for about a month and the employees try and resolve the account, if they are successful they get a commission, otherwise the account goes to another employee to try and resolve. 
We are running some reports to measure some performance characteristics for the company. We have years of data that we can analyze.
My question is:
What summary(median or mean) can best describe the central tendency of length of time to resolve an account per employee?
Almost every employee's median is greater than their mean, some are further apart than others. 
One thing that we are trying to find out is if we give an employee an account, how long should it take for him or her to resolve it. 
It seems to me that median is a better summary.
 A: You should use the median, not the mean. However, you'll need to use methods appropriate for time-to-event (survival) data that deal appropriately with censoring: if the account was handled to another employee without being resolved you know only that the time this employee would have taken to resolve it is greater than or equal to the observed time for which they handled the account, so the observed time is right-censored.
The appropriate method would be to construct the Kaplan–Meier estimator of the survival function. If you want a single number for each employee, you could use this method to obtain the median 'survival' time, which gives you the median time taken to resolve an account. You can also get confidence intervals for the median if you so wish. It's possible that the median may not be estimable for some employees though if they fail to resolve more than half the accounts before they are re-assigned, in which case you could consider switching to some other percentile that is estimable for all (or at least the great majority of) employees.
The Kaplan-Meier estimator isn't difficult -- it's perfectly possible, if somewhat tedious, to construct by hand, and straightforward to program. Confidence intervals are a bit more tricky, but are available in any decent statistical software package.
