Nonetheless, optimism remains more than one standard deviation above its historic average of 39%-a sign that it remains at high levels.

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For example, two of eight American League clubs in 1927 posted winning percentages below .400, leading to a league-wide standard deviation of .123 percentage points above and below the average .500 record.

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If you rank the countries of the world in terms of the academic performance of their schoolchildren, the U.S. is just below average, half a standard deviation below a clump of relatively high-performing countries like Canada and Belgium.

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