The mean and variance of 20 observations are initially calculated as 15 and 9 respectively. Upon rechecking, it is found that one observation was incorrectly recorded. When it is replaced by its correct value, the new mean and variance become 16 and 20 respectively. The value of the correct observation is

Step-by-step solution

Let the incorrect observation be x and the correct observation be y . Given n = 20 . Initial mean x ₁ = 15 Incorrect sum of observations = 20 15 = 300 . Corrected mean x ₂ = 16 Correct sum of observations = 20 16 = 320 . Thus, y - x = 320 - 300 = 20 . Initial variance ₁^2 = 9 Incorrect sum of squares = 20 (9 + 15^2) = 20 234 = 4680 . Corrected variance ₂^2 = 20 Correct sum of squares = 20 (20 + 16^2) = 20 276 = 5520 . Thus, y^2 - x^2 = 5520 - 4680 = 840 . Dividing the two differences: y^2 - x^2 y - x = 840 20 y + x