# Find standard error from mean and upper/lower quartile?

#### sampson87

##### New Member
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?

Thanks,
Chris

#### BGM

##### 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?

#### Dason

Also unless you're willing to make some sort of distributional assumption then most likely the answer will be no.

#### sampson87

##### New Member
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

#### sampson87

##### New Member
Anyway, I think I cracked it using Solver. For anyone who might need to do it (despite it now seeming really simple):

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:

#### BGM

##### 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)?