no it is not possible because you have to take the square of error that is (x-X)2. the square of any number is always positive
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Improved answer:
It is not possible to have a negative standard deviation because:
SD (standard deviation) is equal to the square of V (variance).
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No. Standard deviation is the square root of a non-negative number (the variance) and as such has to be at least zero. Please see the related links for a definition of standard deviation and some examples.
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.
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
When you don't have the population standard deviation, but do have the sample standard deviation. The Z score will be better to do as long as it is possible to do it.
The standard deviation is the standard deviation! Its calculation requires no assumption.