The mean and variance of 8 observations are 10 and 13 . 5 , respectively. If 6 of these observations are 5 , 7 , 10 , 12 , 14 , 15 , then the absolute difference of the remaining two observations is :

Step-by-step solution

Let remaining two observations are a and b Σ x i n = 5 + 7 + 12 + 10 + 15 + 14 + a + b 8 = 10 ⇒ 63 + a + b = 80 ⇒ a + b = 17 σ 2 = Σ x i 2 n − Σ x i n 2 ⇒ 13 .5 = 25 + 49 + 144 + 100 + 225 + 196 + a 2 + b 2 8 − 100 ⇒ 908 = a 2 + b 2 + 739 ⇒ a 2 + b 2 = 169 ⇒ a + b 2 − 2 a b = 169 ⇒ 289 − 169 = 2 a b ⇒ a b = 60 ∴ a − b 2 = a + b 2 − 4 a b = 289 − 240 = 49 ∴ a − b = 7 .