void errors()
{
 Double_t points[4] = {2.3,1.2,4.3,5.5};
 Double_t weights[4] = {10.1,12.4,11.5,16.5};

 TProfile *profile = new TProfile("","",1,0,1);
 for(Int_t i=0;i<4;i++)
 {
  profile->Fill(0.5,points[i],weights[i]);
 }
 
 // print mean and statistical error from profile:
 cout<<"Profile calculation:"<<endl;
 cout<<"mean  = "<<profile->GetBinContent(1)<<endl;
 cout<<"error = "<<profile->GetBinError(1)<<endl;
 
 // manual calculation of mean:
 Double_t mean = 0.;
 Double_t sumOfWeights = 0.; // sum w
 Double_t sumOfSquaredWeights = 0.; // sum w*w
 for(Int_t i=0;i<4;i++)
 {
  sumOfWeights += weights[i];
  sumOfSquaredWeights += pow(weights[i],2.);
  mean += points[i]*weights[i];
 }
 mean /= sumOfWeights; // final results for mean 
 
 // manual calculation of spread (unbiased estimator):
 Double_t spread = 0.;
 for(Int_t i=0;i<4;i++)
 {
  spread += weights[i]*pow(points[i]-mean,2.);
 }
 spread *= (1./sumOfWeights)*(1./(1.-sumOfSquaredWeights/pow(sumOfWeights,2.)));
 spread = pow(spread,0.5); // final result for spread
 
 Double_t error = (pow(sumOfSquaredWeights,0.5)/sumOfWeights)*spread; // final result for statistical error
 
 // print mean and statistical error from manual calculation:
 cout<<endl;
 cout<<"Manual calculation:"<<endl;
 cout<<"mean  = "<<mean<<endl;
 cout<<"error = "<<error<<endl;
}