The SD of a variate x is σ. The SD of the variate (ax + b)/c, where a, b, c ate constants, is

Let y=αx+bc, i.e., y=acx+bc i.e, y=acx+bc∴y¯=Ax¯+B∴y−y¯=A(x−x¯)⇒(y−y¯)2=A2(x−x¯)2⇒Σ(y−y¯)2=A2Σ(x−x¯)2⇒n⋅σy2=A2⋅nσx2⇒σy2=A2σx2⇒σy=|A|σx⇒σy=acσx Thus, new SD=acσ