The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations Share with your friends Share 3 Mayank Jha answered this Dear student, Let the given observations be x1, x2, x3, ....... , x20 and xM be their mean.Given that n = 20 and the variance is 5 So, 120∑i = 120 (x - xM)² = 5⇒∑i = 120 (x - xM)² = 100 ----(1)If each observation is multiplied by 2, then the new observations are yi = 2xi, i = 1, 2, 3, ..... , 20So, xi = yi2Hence, yM = 120∑i = 120 yi = 120∑i = 120 2xi = 2*120*xMThis gives us, xM = 12yMSunstituting the values of xi and xM in (1). We have, ∑i = 120 (yi2 -12yM)² = 100⇒∑i = 12014(yi - yM)² = 100⇒∑i = 120(yi - yM)² = 400Hence, the variance of the resulting observations is = 120*400 = 20 Regards 1 View Full Answer Sivapriya G Kamat answered this when the observations is multiplied by a no. say x , we multiply the variance by the square of x . so here the new variance = 5 * 4= 20 -2
