The values that a standard deviation s can possibly take are all non-negative real numbers
How to determine the values
The standard deviation of a distribution is the square root of the variance.
The standard deviation is represented by the following formula:
[tex]\sigma = \sqrt{\sigma^2[/tex]
For the above formula to have a usable value, then the following must be true
[tex]\sigma^2 \ge 0[/tex] ---- i.e. the variance must be at least 0.
So, we have:
[tex]\sigma \ge \sqrt{0[/tex]
Evaluate the square root
[tex]\sigma \ge 0[/tex]
Hence, the values that a standard deviation s can possibly take are all non-negative real numbers
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