Lecture - Ch 2 Triola

 

Sample standard deviation

Definition vs Computing formula:  Prove that they are the same

   We need to show

            Note  means  so =1 + 1 +...+1 (n terms) = n

           

   Proof:                    Expand binomial square

                                    =        Linearity: 

                                    =       Factor out constants: 2 and x-bar

                                    =    Def. of  is ; 

                                    =   Simplify algebraically