Average of odd consecutive integers will be equal to middle number (median).
For example, the average of 11 numbers is 6th number, the average of 9 numbers is 5th number in the sequence.
So, both conditions along give us 5th or 7th number in the sequence of 11 consecutive numbers and we can find average=6th number = 5th number + 1 = 7th number - 1.
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