The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2,3,5,10,11,13,15,21 , then the mean deviation about the median of all the 10 observations is

Step-by-step solution

Given 10 observations with mean = 9 and variance = 34.2. Eight known values: 2, 3, 5, 10, 11, 13, 15, 21. Sum of all 10: x_i = 90 . Sum of 8 known: 80. So the two unknowns sum to 10. From variance: x_i^2 = 10(34.2 + 81) = 1152 . Sum of squares of 8 known: 1094. So unknown squares sum to 58. With x₉ + x₁₀ = 10 and x₉^2 + x₁₀^2 = 58 : we get x₉ x₁₀ = 21 , giving roots t^2 - 10t + 21 = 0 , so the unknowns are 3 and 7. All 10 sorted: 2, 3, 3, 5, 7, 7, 10, 11, 13, 15, 21. Median = 7+10 2 = 8.5 . Mean deviation = 1 10 (6