
close all
clear all
    disp('Mean and Standard Deviation After Variable Change')
    lw = 3; 
  set(0, 'DefaultAxesFontSize', 16);
 fs = 15;
 msize = 10;



% It is known that $\bar y =  11.6 , $  $s_y= 4.4045 $, and $n=15.$
% The bservation $y_{12} = 7 $ is removed and observation $y_{13}$ was misrecorded,
% it was not 10 but 20.
% Find $ \bar y_{new}$ and $s_{y (new)}$ after the changes.

%sumy -> sum(y_i):old
%sumynew -> sum(y_i): new
%sumy2 -> sum(y_i^2): old
%sumy2new -> sum(y_i^2): new
%NEED:  ybarnew and synew

sumy = 15 * 11.6;
sumynew = sumy - 7 + 10;
ybarnew = sumynew/14;

%recall sy = sqrt(1/14 (sumy2  - 15*11.6^2) )
sumy2 = 14*(4.4045)^2 + 15 * 11.6^2;
% now n=15 drops to n=14...
sumynew2 = sumy2 - 49 + 300; %300=20^2 - 10^2
synew = sqrt( 1/13 * (sumynew2 - 14 * ybarnew^2 ) );
disp(' New ybar   New sy ')
disp( [ybarnew synew] )
% New ybar   New sy 
%   12.6429    4.8295
