If the mean and variance of the following data: 6 , 10 , 7 , 13 , a , 12 , b , 12 are 9 and 37 4 respectively, then a - b 2 is equal to:

Step-by-step solution

Mean = 6 + 10 + 7 + 13 + a + 12 + b + 12 8 = 9 ⇒ 60 + a + b = 72 ⇒ a + b = 12         . . . 1 variance = ∑ x i 2 n - ∑ x i n 2 = 37 4 Here, Σ x i 2 = 6 2 + 10 2 + 7 2 + 13 2 + a 2 + b 2 + 12 2 + 12 2 = a 2 + b 2 + 642 So, variance is a 2 + b 2 + 642 8 - 9 2 = 37 4 ⇒ a 2 + b 2 8 + 321 4 - 81 = 37 4 ⇒ a 2 + b 2 8 = 81 + 37 4 - 321 4 ⇒ a 2 + b 2 8 = 81 - 71 ∴   a 2 + b 2 = 80 From 1 a 2 + b 2 + 2 a b = 144 ⇒ 80 + 2 a b = 144  &#16