Standard deviation - Math Central

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Question from Ethan, a student:

Okay I have a question about standard deviation.
Can you tell me a five number set of data that will have a standard deviation of zero and how you know that?

Hi Ethan.

The closer the numbers in the data set are to one another, the smaller the standard deviation will be. How close do the numbers need to be in order for the standard deviation to drop all the way to zero?

Cheers,
Stephen La Rocque.

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