Video solution:

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Written solution:

The answer is the same as the average of all $12$ numbers. To understand why this is the case, it is actually generally true that if a whole bunch of numbers is split up into pairs, and each pair is averaged, and then all those pair-averages are averaged, the answer is the average of all the numbers.

To see why this is true, consider a smaller example of $6$ numbers $a,$ $b,$ $c,$ $d,$ $e,$ and $f.$ The average of the pair-averages is: $$\frac{1}{3} \left( \frac{a+b}{2} + \frac{c+d}{2} + \frac{e+f}{2} \right)$$ and that is equal to $$\frac{a+b+c+d+e+f}{6}.$$ The same type of simplification happens with $12$ numbers.

Since the $12$ numbers are equally spaced (in an arithmetic progression), the answer is the same as the average of the first and last number, which is $$\frac{1+12}{2} = \frac{13}{2} = 6.5,$$ or choice B.