
Typically aggregate statistics like mean, median and standard deviations from mean are not detailed enough. Furthermore, they can be misleading! See figure where the mean of the data is 5.3 but the we can clearly see from the histogram that a bimodal distribution is in play. There isn't even a single data point close to the mean. Granted this particular example is contrived but it is not far from the typical situation in the real world. One example is if reads to a device were hitting the device cache only about 1/2 the time.

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Another example....
A 'stock' example: Out of 100 people in the village, 1 person earns $1m and all others earn $1.