Calculate variance from summary data

grandMean <- function(meanX, nX){
   return(sum(meanX*nX)/sum(nX))
}

grandSTD <- function(meanX, stdX, nX){
   gmean <- grandMean(meanX, nX)
   ssr <- sum((nX-1)*stdX*stdX) + sum(nX*meanX*meanX)
   ssm <- 2*sum(nX*meanX)*gmean
   ssg <- sum(nX)*gmean*gmean
   return(sqrt((ssr-ssm+ssg)/(sum(nX)-1)))
}