If each observation of a raw data whose variance is σ is multiplied by h, then the variance of the new set is

Let x1,x2,…,xnbe the raw data. Then, σ2=1n∑i=1n xi−X¯2If each value is multiplied by h, then the values become hx1hx2,…,hxn.Then AM of the values ishx1+hx2+⋯+hxnn=hX¯Therefore, the variance of the new set of values is1n∑i=1n hx1−hX¯2=h21n∑i=1n xi−X¯2=h2σ2