Ecological fallacy:

Mathematical/Conceptual Fallacy

Definition	Example
When inferences about the nature of specific individuals are based solely upon aggregate statistics collected for the group to which those individuals belong.	Because the average German is taller than me, you won’t find a German who is shorter than me.
Also known as: distribution fallacy
Notes
Averages are useful when a higher resolution of the context would be cumbersome. However, there may be some contexts where an understanding of the actual distribution of the measurments is required.

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Case Study One

In a part of town with many nursing homes and nursery schools, the average age may be 35. It would be a mistake, however, to then expect to see many middle-age individuals in that part of town.

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Case Study Two

The average income of many countries is largely uninformative since there exists a large income gap between the rich and poor.

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^{Keep in mind that a fallacious argument does not entail an erroneous position.}

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