# standard error of mean

#### muddy

##### New Member
If I have a single data point and take that point as an estimate of the mean of the population, how would I estimate the standard error of the mean?

#### JohnM

##### TS Contributor
The standard error of the mean is the population standard deviation divided by the square root of the sample size, so you don't have enough information to estimate it.

#### muddy

##### New Member
JohnM said:
The standard error of the mean is the population standard deviation divided by the square root of the sample size, so you don't have enough information to estimate it.
Thanks John,

I agree that it cant be done with the estimate equation.

I was really fishing for alternative approaches (bootstrap methods, chi squared approximation, etc)

Actually I have one other peice of information ... the parent population is exponentially distributed ... therefore the standard deviation is equal to the mean. So would this mean that the standard error is equal to the mean?

Any ideas?

#### JohnM

##### TS Contributor
I would highly doubt any method that purports to allow estimation of anything remotely resembling a standard deviation, variance, or mean, with just one data point....a bunch of junk, IMHO.

Yes, you could then infer the standard deviation, but not the standard error of the mean would still be s/sqrt(n) - I guess in this case you could hazard a guess by using s and picking a hypothetical sample size....

#### muddy

##### New Member
John,

Thanks for all the help ... maybe I should just state what I am really after:

Given an observation time period T
and a number of events N

I can calculate Mean Time Between Events as M' = T/N

What I need now is a confidence (C) that the true M is above some Mlower

The function I am trying to find is:

Mlower = f(M',T,N,C)

Ive seen a few papers claiming to estimate this even for N=0 (an observation period with no events) with the Chi Squared distirbution:

Mlower = 2*T/ CHIINV(C,N+2)

Ive played around with some bootstrap simulations that seem so far to not support this.

any thoughts on this approach?