If each observation of a raw data whose variance is σ2  is multiplied by h, then the variance of the new set is

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