The mean and variance of 20 observations are 10 and 5 , respectively. It was later found that one observation was wrongly recorded. When this incorrect observation is replaced by the correct one, the new mean becomes 11 and the new variance becomes 14 . The value of the original incorrectly recorded observation is

Step-by-step solution

Let the incorrect observation be I and the correct observation be C . Given n = 20 , initial mean x = 10 , and initial variance ^2 = 5 . Initial sum of observations, x_i = 20 10 = 200 . Initial sum of squares, x_i^2 = 20 (5 + 10^2) = 20 105 = 2100 . After replacement, the new mean is 11 and the new variance is 14 . New sum of observations, x_ i( new ) = 20 11 = 220 . New sum of squares, x_ i( new ) ^2 = 20 (14 + 11^2) = 20 (14 + 121) = 20 135 = 2700 . From the sums of observations: 220 - 200 = C - I C - I = 20 From