Average of middle number

Question

I was doing a question on average and the question was that - If the average of 1st 12 number is 10.8, average of 1st 6 number is 10.4 and the last 6 number is 11.5. Find the 6th number. Now according to me i thought the number which is the middle one is counted twice but the actual solution subtracts the sum of last and 1st 6 number sum and subtracts with the sum of 12 numbers. Can anyone help me why is it correct and does it not double counts the middle number twice?

Answer 1

If you have a list of $12$ numbers, the first six numbers are in positions $1-6$ and the last six numbers are in positions $7-12$. As stated, the data you are given is inconsistent with the list being $12$ numbers. If the first six average $10.4$ and the last six average $11.5$, the whole list would have to average $10.95$. Please check the problem and state it clearly.