The Lowest Score!

In a chess tournament, players get 1 point for a win, 0 points for a loss and \(\frac{1}{2}\) point for a draw. In a tournament where every player plays against every other player exactly once, the top four scores were 5\(\frac{1}{2}\) , 4\(\frac{1}{2}\) , 4 and 2\(\frac{1}{2}\) . What was the lowest score in the tournament?

This question is from NMTC-AMTI 2011.
Image credit: Dutch National Archives
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