One solution (using R) is to create extent objects of the bounding boxes you're interested in, and then crop() to that extent and use the cellStats() function to extract the mean, min, max, sd, etc. for that region. Here's what that looks like in code:
myraster = raster("PATH/TO/RASTER.tif")
extmat1 = matrix(data = c(-180,180,-50,0), nrow =...