A population has a mean of μ = 80 and a standard deviation of σ = 20. would a score of x = 70 be considered an extreme value (out in the tail) in this sample? if the standard deviation were σ = 5, would a score of x = 70 be considered an extreme value?

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Mathematics

Esteban Wade

9 January, 02:59

A population has a mean of μ = 80 and a standard deviation of σ = 20. would a score of x = 70 be considered an extreme value (out in the tail) in this sample? if the standard deviation were σ = 5, would a score of x = 70 be considered an extreme value?

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Messiah Hoffman · Answer 1

With a sigma of 20, a score of 70 is half a standard deviation below the mean 80, z=-1/2. I don't know if there's an official definition, but I consider values extreme if the absolute values their z scores is say 3 or more. So no, this is not extreme at all.

If the standard deviation is 5 instead of 20, then 70 is 2 standard deviations below the mean (z = - 2). I still wouldn't consider that an extreme value.