I know this might be a little ropey, statistically, but this is my problem.

I have a lot of range data, that is to say the minimum, maximum and sample size of a variable. For some of these data I also have a mean, but not many. I want to compare these ranges to each other to quantify the variability of each range, and also to compare the means. I have a good reason to assume that the distribution is symmetrical around the mean, and that the data will have a gaussian distribution. For this reason I am thinking I can justify using the mid-point of the distribution as a proxy for the mean, when it is absent.

What I want to do is reconstruct a distribution for each range, and then use that to provide a standard deviation or standard error for that distribution. The only information I have is the (expected) max and min, and the mid-point as a proxy for the mean.

In this way I hope to be able to calculate weighted means for each group, and also to work out coefficient of variation for each group as well, based on the range data I have and my assumptions (of a symmetrical and normal distribution).

I plan to use R to do this, so any code help would be appreciated as well.