Find standard error from mean and upper/lower quartile?

Hi folks,

I'm hoping there's a straightforward answer to this (that isn't "no") :tup:

For some data I know the mean, the upper and lower quartile figure, and also the number of observations on which it is based. I would like to know the standard error.

Is there a way of working this out? Even if only an estimation. I know Excel has the Solver function, but I don't really know how to use that or if it could even do it if I wanted it to.

Any ideas?



TS Contributor
Every standard error correspond to an estimator.
Which estimator are you referring to? The sample mean or sample quartile?

Or you want to estimate the standard deviation?


Ambassador to the humans
Also unless you're willing to make some sort of distributional assumption then most likely the answer will be no.
Apologies for the delayed reply - hope you're still around.

And apologies for the lack of information.

I'm actually trying to work out the standard deviation of a sample, not the error of a mean (oops). I'm trying to fit this to a gamma distribution.

Thanks for the help
Anyway, I think I cracked it using Solver. For anyone who might need to do it (despite it now seeming really simple:rolleyes:):

Set target cell: "GAMMAINV,.25,alpha,beta"...
...equal to my known lower quartile
By changing cell: "standard deviation" (blank)

Where, of course, my cells with "alpha" and "beta" are calculated using the estimated standard deviation and my known mean.

Thanks to those who offered help! :tup:


TS Contributor
So it looks like that you are given the mean and standard deviation of a gamma distribution, which in turns you can solve for the parameters \( \alpha, \beta \) in terms of these, just like the method-of-moments estimates. Then you can compute the corresponding quantile (estimates)?