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Q: Is it possible for the mean and standard deviation to be equal?

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If all four numbers are the same, there is no standard deviation. The mean will be equal to all 4 numbers, resulting in a 0 standard deviation. Ex) 5,5,5,5

no the standard deviation is not equal to mean of absolute distance from the mean

it is possible to distribute standard deviation and mean but you dont have to understand how the mouse runs up the clock hicorky dickory dock.

Without more information, it isn't possible to determine the standard deviation from the mean alone.

The mean and variance are equal in the Poisson distribution. The mean and std deviation would be equal only for the case of mean = 1. See related link.

A standard deviation of zero means that all the data points are the same value.

Information is not sufficient to find mean deviation and standard deviation.

True.

One standard deviation

Mean 0, standard deviation 1.

Mean = 0 Standard Deviation = 1

Yes.

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