Combining statistics from two distributions

[mclovin]

Is it possible to combine statistics from two distributions for the same parameter. For example I have one distribution for X from population A and a second distribution for X from population B. I want to assume all data is from the same population. I have calculated UTLs(Upper tolerance limits) for each population but need a single, combined utl for a combined population. The catch is I don't have the original data, only the calculated statistics.

 

[mfb]

How is that upper tolerance limit defined?
If you have some data about the distribution of the expected parameter (like mean+standard deviation and the assumption of a Gaussian distribution), you can combine both.

 

[mclovin]

According to the summary stats it is a normal distribution and the UTL is the 95% Upper tolrance Limit. i have the range of values and the artithmetic mean. No std dev.

 

[mfb]

In that case, the standard deviation is just ~1/2 of the distance between mean and UTL. You can combine both values with a weighted average (the formula should be somewhere at wikipedia or on other pages. The weights are just the inverse variances.).

 

[mclovin]

Thank you. I will follow up on this.