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I have a maximum and a minimum, can I calculate the theoretical lower quartile, median and upper quartile based on only this for a normal distribution?
I think you'll need the standard deviation for your distribution as well.
No, of course not. How on earth do you know how much of an outlier your max and min are?
as above, you ned the standard deviation.
ok, what if i can assume a standard normal distribution with a variance of 1?
it's ok, I've worked it out
I can use the =NORMSINV() formula in Excel
to randomly sample from a Normal
= NORMINV(RAND(),mean,stdev)
to calc P(X<=x)
=NORMDIST(x,mean,stdev,TRUE)
to calc a value of x given a prob.
= NORMINV(p, mean, stdev)
where p is the area to the left of the unknown x value
The Normal dist is unbounded so has no min or max, theoretically speaking
replace NORMINV with NORMSINV
and NORMDIST with NORMSDIST
if you want standard normal, rather than the original data