I am writing a systematic review and meta-analysis of the association of exposure to X with the outcome Y. I have identified ten studies that report on this subject. This will be a meta-analysis of the published literature, not of individual participant data. I want to report the overall mean age and standard deviation of all patients in all of the studies together. The studies all have different sample sizes. How should I do this?
(1) I imagine that I cannot just add up the reported mean values and divide by ten. This would give smaller studies an undue weight in contributing to the overall mean.
(2) I thought perhaps that I could just do a simple weighted average, using the sample size of each study as the weight. Is this appropriate? Can I also just do a weighted average of the reported standard deviations and ranges? If not, how would I compute those?
(3) Another thought I had was actually taking each of the ten reported mean weights along with their standard deviations and actually plugging them into a meta-analysis program to get a "pooled weight" with a fixed effects model. But perhaps this would be a strange approach?
Any advice on which technique to use? Is there another possibility that I'm not thinking of? Thanks!