The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40 . Then the correct variance is

Step-by-step solution

Incorrect mean is ∑ i = 1 10 x i 10 = 20 ⇒ ∑ i = 1 10 x i = 200       . . . . i So, corrected mean is ∑ i = 1 10 x i - 50 + 40 10 = 200 - 10 10 = 19 Incorrect variance is ∑ i = 1 10 x i 2 10 - 400 = 64 ⇒ ∑ i = 1 10 x i 2 = 4640 Now, corrected variance is = ∑ i = 1 9 x i 2 + 40 2 - 50 2 10 - 19 2 = 4640 - 900 10 - 19 2 = 374 - 361 = 13