Mean and variance of 20 observations are 10 and 4 respectively. It was found that in place of 11, 9 was taken by mistake. The correct variance, is

Let x1,x2,…,x20 be 20 observations. Then,           uncorrected ∑xi=20×10=200 and 120∑xi2−(10)2=4⇒ uncorrected ∑xi2=2080    Corrected ∑xi=200−9+11=202     Corrected ∑xi2=2080−92+112=2120 ∴ Correct variance =120 Corrected ∑xi− Corrected ∑xi202                                  =212020−202202=106−102.01=3.99