The SD of a variate x is σ. The SD of the variate (ax + b)/c, where a, b, c are constants, is
acσ
a2c2σ
None of these
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