Let the mean of 6 observations 1 , 2 , 4 , 5 , x and y be 5 and their variance be 10 . Then their mean deviation about the mean is equal to

Step-by-step solution

Consider the data 1 , 2 , 4 , 5 , x , y . So, Mean = 1 + 2 + 4 + 5 + x + y 6 ⇒ 5 = x + y + 12 6 ⇒ x + y = 18 And, Variance = ∑ x i 2 n - ∑ x i n 2 ⇒ 10 = 1 2 + 2 2 + 4 2 + 5 2 + x 2 + y 2 6 - 5 2 ⇒ x 2 + y 2 = 164 We have x + y = 18 and x 2 + y 2 = 164 . Now solving above equations we get, x = 10 ,   y = 8 , Now mean deviation about mean will be = ∑ i = 1 6 x i - x 6 = 1 - 5 + 2 - 5 + 4 - 5 + 5 - 5 + 10 - 5 + 8 - 5 6 = 16 6 = 8 3 Therefore, the required answer is 8 3