The mean and variance of 20 observations are reported as 30 and 100 respectively. Later, it is found that two observations were wrongly recorded as 10 and 15. After replacing these two incorrect observations with the correct ones, say x and y , the correct mean and correct variance are found to be 31 and 74 respectively. The absolute difference between the two correct observations, |x - y| , is equal to

Step-by-step solution

Let the incorrect sum of the 20 observations be S₁ and the incorrect sum of squares be S₂ . Given incorrect mean = 30 and incorrect variance = 100: S₁ = 20 30 = 600 S₂ 20 - (30)^2 = 100 S₂ 20 = 100 + 900 = 1000 S₂ = 20000 Let the correct sum of the observations be S₁' and the correct sum of squares be S₂' . Given correct mean = 31 and correct variance = 74: S₁' = 20 31 = 620 S₂' 20 - (31)^2 = 74 S₂' 20 = 74 + 961 = 1035 S₂' = 20700 The correct sum is obtained by removing the incorrect observations and adding the co