The mean of five observations x₁, x₂, 3, 4, 8 (where x₁ < x₂ ) is 5 and their mean deviation about the mean is 2.4 . The value of 10 ( Variance of these observations ) is equal to

Step-by-step solution

Given the mean of the observations is 5 : x₁ + x₂ + 3 + 4 + 8 5 = 5 x₁ + x₂ + 15 = 25 x₁ + x₂ = 10 The mean deviation about the mean is 2.4 : |x₁ - 5| + |x₂ - 5| + |3 - 5| + |4 - 5| + |8 - 5| 5 = 2.4 |x₁ - 5| + |x₂ - 5| + 2 + 1 + 3 = 12 |x₁ - 5| + |x₂ - 5| = 6 Substitute x₂ = 10 - x₁ into the equation: |x₁ - 5| + |(10 - x₁) - 5| = 6 |x₁ - 5| + |5 - x₁| = 6 2|x₁ - 5| = 6 |x₁ - 5| = 3 x₁ - 5 = 3 x₁ = 8 or x₁ = 2 Since x₁ The observations are 2, 8, 3, 4, 8 . Now, calculate the variance: Variance = x_i^2 n - ( Mean )^2