> If you need to reduce a distribution to a single number, the most informative number is going to be the mean.
No such rule of thumb is ever going to work, you always need to consider context.
In the case where disutility is non-linear with response time, especially if there is a cliff below which differences are irrelevant, an improvement in the response time to the worst decile may well be worth degraded performance for a majority of users. The most useful single statistic in that case could be, not mean, median, or mode, but the percentage of users who fall above the "unacceptable" delay threshold.
No such rule of thumb is ever going to work, you always need to consider context.
In the case where disutility is non-linear with response time, especially if there is a cliff below which differences are irrelevant, an improvement in the response time to the worst decile may well be worth degraded performance for a majority of users. The most useful single statistic in that case could be, not mean, median, or mode, but the percentage of users who fall above the "unacceptable" delay threshold.