# Combining statistics from two distributions

1. Mar 1, 2013

### 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.

2. Mar 1, 2013

### Staff: Mentor

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.

3. Mar 1, 2013

### 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.

4. Mar 1, 2013

### Staff: Mentor

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.).

5. Mar 1, 2013

### mclovin

Thank you. I will follow up on this.