\(P\) is a set of integers. If \(a\) is the average of the odd integers and \(b\) is the average of the even integers in set \(P,\) what is the of \(|a-b|?\)

1. \(P\) consists of consecutive integers starting from \(1\)
2. There are not more than \(50\) integers in the set \(P\)

The OA is E