The mean of the numbers a , b , 8 , 5 , 10 is 6 and their variance is 6 . 8 . If M is the mean deviation of the numbers about the mean, then 25 M is equal to

Step-by-step solution

Mean x ¯ = a + 6 + 8 + 5 + 10 5 = 6 (given) ⇒ a + b = 7           . . . i Variance = ∑ x i 2 n - x ¯ 2 = a 2 + b 2 + 8 2 + 5 2 + 10 2 5 - 6 2 = 6 . 8 (given) ⇒ a 2 + b 2 = 25           . . . ii on solving equations i & ii , we get a = 3 ,   b = 4 Now, Mean deviation about Mean M = ∑ x i - x ¯ n ⇒ 3 - 6 + 4 - 6 + 8 - 6 + 5 - 6 + 10 - 6 5 ⇒   3 + 2 + 2 + 1 + 4 5 = 12 5 ∴     M = 12 5 ⇒