# Mean and variance of grouped data, e.g.,
# VarID	Count
# 33	2
# 34	5
# ..	...
# Callig:
# source(sThisFileName)
# resOut <- StatsGroupedData(Chest, Number)
# for(i in 1:length(resOut)) {print(resOut[i])}
StatsGroupedData <- function(VarVecID, Count) {
  sum = 0
  sum2 = 0
  sum3 = 0
  sum4 = 0
  N = 0
  NumRow = length(VarVecID)
  oCumulP <- vector(mode="numeric",length=NumRow)
  eQ <- vector(mode="numeric",length=NumRow)
  for (i in 1:NumRow) {
    tmpVal = as.numeric(VarVecID[i]) * Count[i]
    sum = sum + tmpVal
    tmpVal = tmpVal * VarVecID[i]
    sum2 = sum2 + tmpVal
    tmpVal = tmpVal * VarVecID[i]
    sum3 = sum3 + tmpVal
    tmpVal = tmpVal * VarVecID[i]
    sum4 = sum4 + tmpVal
    N = N+Count[i]
    oCumulP[i] = N
  }
  Mean=sum/N
  tmpVal=Mean*Mean
  Var = (sum2 - tmpVal*N)/(N-1)
  SD = sqrt(Var)
  CV = 100*SD/Mean
  SE = sqrt(Var/N)
  CL95 = qt(0.975,N-1)*SE
  Skewness = sum3 - Mean*(3*sum2 - tmpVal*2*N)
  Skewness = Skewness/((N-1)*Var*SD)
#  Kurtosis = sum4 - Mean*(4*sum3 - 6*Mean*sum2 + 4*Mean^2*sum - Mean^3)
#  Kurtosis = sum4 - Mean*(4*sum3 - Mean*(6*sum2 - 4*sum*Mean + Mean^2))
#  Kurtosis = sum4 - Mean*(4*sum3 - Mean*(6*sum2 - Mean*(4*sum - N*Mean)))
  Kurtosis = sum4 - Mean*(4*sum3 - Mean*(6*sum2-3*N*tmpVal))
  Kurtosis = Kurtosis / (N-1)/(Var*Var) - 3

  for(i in 1:NumRow) { 
    p = oCumulP[i]/N
    eQ[i] = qnorm(p,Mean,SD)
  }
  plot(eQ,VarVecID,xlab="Observed Quantile",ylab="Expected Quantile")
  outVec <- c(Mean,Var,SD,CV,CL95,Skewness,Kurtosis)
  names(outVec) <- c("Mean","Var","SD","CV","CL95","Skewness","Kurtosis")
  return(outVec)
}