Question

the average of 11 number is 10.9 . if the average of first sic nimber is 10.5 and that of the last six numbers is 11.4 then the middle number is.

Answer 1

Given that average of 11 numbers is 10.9

⇒ Sum of the 11 numbers = 10.9 x 11 = 119.9

Given that average of the first 6 numbers is 10.5

⇒ Sum of the 6 numbers = 10.5 x 6 = 63

Given that average of the last 6 numbers is 11.4

⇒ Sum of the 6 numbers i= 11.4 x 6 = 68.4

Sum of the 12 numbers (including the middle number counted twice):

63 + 68.4 = 131.4

Middle number = 131.4 - 119.9 = 11.5

Answer: The middle number is 11.5

Answer 2

Middle numbers = (10.5 x 6 + 11.4 x 6) - 10.9 x 11 = 131.4 - 119.9 = 11.5