Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 , respectively, find the correct standard deviation.

∴ New mean, ∣x¯=100×40+3+27−30−70100=4000−70100=3930100                             =39.3∵ Σx2=Nσ2+x¯2∴ =100(100+1600)=170000 New,  Σx2=170000−(30)2−(70)2+(3)2+(27)2=170000−900−4900+9+729=164938∴ New,  SD= New Σx2N−( New x¯)2=164938100−(39.3)2=1649.38−1544.49=104.89=10.24