The mean and variance of 8 observations are 6 and 10 respectively. If two observations are removed, the mean and variance of the remaining 6 observations become 5 and 8 respectively. The absolute difference between the two removed observations is

Step-by-step solution

Let the 8 observations be x₁, x₂, , x₈ . Given mean x = x_i 8 = 6 _ i=1 ⁸ x_i = 48 Variance ^2 = x_i^2 8 - ( x )^2 = 10 x_i^2 8 - 36 = 10 _ i=1 ⁸ x_i^2 = 8 46 = 368 Let the two removed observations be a and b . The remaining 6 observations have a mean of 5 and variance of 8 . Sum of remaining 6 observations = 6 5 = 30 Sum of squares of remaining 6 observations = 6 (8 + 5^2) = 6 33 = 198 Now, we can find the sum and sum of squares of the removed observations: a + b = 48 - 30 = 18 a^2 + b^2 = 368 - 198 = 170 We need