What does it imply for standard deviation being more than twice the mean? Our data is timing data from event durations and so strictly positive. (Sometimes very small negatives show up due to clock resolution issues). We are accustomed to the following table (locally developed):
stdev / mean <= .5 : treat as normal distribution stdev / mean >= .5 <= .75 : usually normal but might be exponential stdev / mean >= .75 <= 2 : exponential / poisson stdev / mean >= 2 : outside inhibitors dominate
In this case we got a ratio of
10 7 and outside inhibitors (meaningless external variables) are eliminated.
What we're trying to do is get some kind of estimate on whether the fat-tail is going to kill the estimate of the mean. The default model is noise applied to a constant time from an effectively constant load distribution, which we reject and replace with an exponential model of load distribution when the stdev gets too large. Observationally, we know that breakers almost always appear in the exponential distributions due to variables we cannot account for.
And then this thing popped up. We eliminated all external variables and still it remains. Our theoretical model for this case says it should be bi-modal normal (that is, the weighted sum of two normals) but this doesn't look like it. If it weren't for the fact we're reasonably confident we've seen the largest datapoint at just over 8 standard deviations away from the mean I'd think we haven't reached the second hump of the bi-modal distribution yet. Incidentally we have the median which is 13 times smaller than the mean.
For the fast answer, the plot does not exist because the mean and standard deviation are dominated by single outliers separated by more than the mean's value. If I set my histogram based on the median, I lose the important part of the graph off the right. If I set my histogram based on the mean, I blow the left-most bar off the top of the graph and the right-hand is still indistinguishable from noise because no histogram bar on the right is > 1.