It turns out that much of this performance data is log-normally distributed[1].    Log-normal distributions tend to have a hockey stick shape where most of the values are close to zero, but occasionally very large values appear[3].  Taking the mean of a log-normal distributions tend to be sensitive to outliers like the ones you describe.  

A solution to this problem is to generate a geometric mean[2] instead.  One convenient thing about log-normal data is that if you log() it, it becomes normal[4] -- and not sensitive to outliers in the usual way.  Also convenient, geometric means are super easy to generate.  All you need to do is this: (1) pass all of the data through log() (2) pass the same data through mean() (or avg() -- whatever) (3) pass the result through exp().  The best thing about this is that you can do it in MySQL.

For example:

SELECT

  country,

  mean(timings) AS regular_mean,

  exp(log(mean(timings)) AS geomteric_mean

FROM log.WhateverSchemaYouveGot

GROUP BY country