I know the formula for pooled variance is 
if the mean for all samples are equivalent and I know that if I want to combine the sigma of two samples with different mu, then the formula is 
, but what would I do if I wanted something like the second formula with more samples? I'm working with 51 samples. I suppose I could use the second formula to combine 2 samples at a time until I got all 51, so I'd do the same thing 50 times, but that sounds terribly cumbersome and while that's work I'd be willing to do, I would strongly rather not if there happens to be an easier way to do this.
I also have access to LibreOffice Calc, which should relieve me of some of the workload.
To summarize, I have the mus and sigmas of 51 different samples and need to find the sigmas of all of the samples combined in the most efficient manner possible.
Well, Charles Zaiontz answered my question! ^_^
http://www.real-statistics.com/descriptive-statistics/measures-variability/measures-variability-detailed/#comment-848425