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Maximum of standard deviation when mean is fixed

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A set if numbers t1,...,tn has a mean of one and all numbers are non-negative.
Show that the standard deviation could be as large as √(n-1).

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Solution Summary

The expert finds the range of standard deviation when the mean is fixed.

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The mean = ( t1 + t2 + t3 + t4 .........tn) / n = 1.0

The standard deviation = square root (variance)

The variance can be calculated as the average of the squared difference from the mean.

Thus, variance = [(t1 - 1)^2 + (t2 - 1)^2 + (t3 - ...

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