Hello,
I have a histogram and calculate standard deviation.
Can we determine minimum and maximum of possible SD?
Thanks
Hey life24.
You need to supply a distribution and set of constraints.
Remember that if sigma is greater [or equal] than zero then it can be anything finite which means there is no real maximum.
Is there any other information you want to supply?
You pretty much have to maximize the standard deviation function and that will depend on what the range of the distribution is along with the family of distributions that has a maximum standard deviation.
You will have to find a distribution where E[X^2] - E[X]^2 is maximized to answer this question.
You will have to find a function f(x) [probability distribution] where you maximize that function of the variance.
So you have the following constraints:
Integral f(x)dx = 1 and
E[X^2] - E[X]^2 = Integral x^2*f(x)dx - [Integral x*f(x)dx]^2 is maximum.