... x2.Wehaveprovedthatx1= 1and 0≤ x2< 1implythatx =(1,t, ,t) =te +(1−t)v1for some t ∈ [0,1). Let x2= 1.INEQUALITIES INVOLVING THE MEAN AND THE STANDARD DEVIATION OF NONNEGATIVE REAL NUMBERSOSCAR ... Accepted 21 Septe mber 2006Let m(y)=nj=1yj/n and s(y) =m(y2) −m2(y) be the mean and the standard deviation of the components of the vector y= (y1, y2, , yn−1, yn), where ... (1.1)be the mean and the standard deviation of the components of x= (x1,x2, , xn−1,xn),where xq= (xq1,xq2, , xqn−1,xqn) for a positive integer q. The following theorem...