Anton and Antonia are chess masters. Each one thinks they are the best. They rec

Question

Anton and Antonia are chess masters. Each one thinks they are the best. They recently played in separate tournaments where both of them finished first. To determine who was the better player, they agreed to use the amount of time it took them to win their matches as the marker of who was best (faster/lower time = better player).

They agreed that one tournament might have been more difficult than the other, so they decided to use a measure of how fast each play wasrelative to the field as the indicator of the best player.

Anton won his matches in 25 minutes; the average match time for all competitors in that tournament was M = 30 (s = 5).

Antonia won her matches in 27 minutes; the average match time for all competitors in that tournament was M = 33 (s = 3).

When considering how fast each player was relative to the other competitors in their tournaments, who was the better player?

Explanation / Answer

Anton won his matches in 25 minutes which is within the plus-minus 1 of the standard deviation from the mean. Whereas, Antonia won her matches in 27 minutes is outside from the plus-minus 1 of the standard deviation. Hence, Antonia has significant differences from the remaining of his group players. Hence, Antonia was the better player.

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