The mean and variance of 7 observations are 11 and 36 respectively. If five of these observations are 2, 5, 14, 17 and 20 , and the remaining two are a and b ( a b ), then the mean deviation about the median of all the 7 observations is

Step-by-step solution

Let the remaining two observations be a and b . Given, Mean = 11 2 + 5 + 14 + 17 + 20 + a + b 7 = 11 58 + a + b = 77 a + b = 19 Given, Variance = 36 2^2 + 5^2 + 14^2 + 17^2 + 20^2 + a^2 + b^2 7 - 11^2 = 36 4 + 25 + 196 + 289 + 400 + a^2 + b^2 7 - 121 = 36 914 + a^2 + b^2 = 7 157 = 1099 a^2 + b^2 = 185 We have (a + b)^2 = a^2 + b^2 + 2ab 361 = 185 + 2ab 2ab = 176 ab = 88 The values of a and b are the roots of t^2 - 19t + 88 = 0 (t - 11)(t - 8) = 0 Since a b , we get a = 11 and b = 8 . The 7 observations in ascending