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What are all the values that a standard deviation s can possibly take?
Any non-negative value.
What does a negative z-score mean?
z-score of a value=(that value minus the mean)/(standard deviation). So if a value has a negative z-score, then it is below the mean.
Is standard deviation an absolute value?
No. Standard deviation is not an absolute value. The standard deviation is often written as a single positive value (magnitude), but it is really a binomial, and it equals both the positive and negative of the given magnitude. For example, if you are told that for a population the SD is 5.0, it really means +5.0 and -5.0 from the population mean. It defines a region within the distribution, starting at the lower magnitude (-5.0) increasing to zero (the mean), and another region starting at zero (the mean) and increasing up to the upper magnitude (+5.0). Both regions together define the (continuous) region of standard deviation from the mean value.
Can standard deviation value be bigger than maximum and minimum value?
No standard deviation can not be bigger than maximum and minimum values.
Is variance square of standard deviation?
Yes, the variance of a data set is the square of the standard deviation (sigma) of the set. This means that the variance is always a positive number, even though the data might have a negative sigma value.
