clear
%% 
     X=(2*randn(50,1)+6)           % mean(X)~6  std(X)~2
     Y=(3*randn(50,1)+8)           % mean(Y)~? std(Y)~? (think about range and shift)
 
       % subplot(1,3,1)
         plot(X,Y,'rO','linewidth',2)
         hold on   % the mode of adding new charts is enabled - on
         mx=mean(X), my=mean(Y)
         plot(mx,my, 'rsq','markersize',16,'linewidth',2)
         grid on 
%%    Centering:
             XX=X-mean(X);    
             YY=Y-mean(Y);
              %  subplot(1,3,2)
             plot(XX,YY,'b<','linewidth',2)
             mxx=mean(XX), myy=mean(YY)
               plot(mxx,myy, 'b<','markersize',18,'linewidth',2)
%%           Standardization:
                    XXX=(X-mean(X))/std(X);
                    YYY=(Y-mean(Y))/std(Y);
                    sy=mean(YYY), sx=mean(XXX)
%                        subplot(1,3,3)
                    plot(XXX,YYY,'gsq','linewidth',2)   %'gsq' - means 'green' & 'square'
                    plot(sx,sy,  'g>', 'markersize',16,'linewidth',2)
C={'Initial Data', 'center Point', 'After Centering','center Point','After Standardization','center Point'}
lg=legend(C{:}); lg.FontSize=14; set(gca,'fontsize',12)