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Is there any difference between normal person and average person? Can I use these interchangeably?

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    In general, normal is subjective, while average is more objective (even quantifiable). – user13141 Oct 23 '11 at 13:44
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Normal has societal connotations and can vary according to perception, experience, culture, politics and period of history, whilst average usually refers to the results of statistical measurements related to groups of people.

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It depends very much on the context. Normal can have a variety of meanings, as can average. If you're talking about test scores for example, or anything involving quantities, you'll want to use average and not normal. However, if you're talking about behavior, they're pretty much interchangeable.

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An "average" person is a normal person BY DEFINITION.

"Normal" means "close to" average (in statistics), but plus or minus. It is this "plus or minus" part that allows "normal" to be NOT average. Even so, it would mean that the deviation from average is a "normal" or usual amount, and not "way out."

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In the world of medical writing, asymptomatic is sometimes used instead of normal. The idea is that referring to people as normal implies that other people are abnormal. Healthy was used in the same way, but that implies unhealthy, which eventually became a pejorative.

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