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September 26th, 2018, 05:46 PM   #1
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Standard Deviations and Standard Deviations of Reciprocals

If the standard deviation of A, B, and C is greater than the standard deviation of X, Y, and Z, what does that say about the standard deviation of 1/A, 1/B, and 1/C compared to the standard deviation of 1/X, 1/Y, and 1/Z? A, B, C, X, Y, and Z are rational numbers > 1.
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September 27th, 2018, 02:32 PM   #2
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Why are you asking about two sets of three variables? One each is enough for the question.
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September 27th, 2018, 04:39 PM   #3
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I'm comparing the odds for soccer games with three possible outcomes. I attached a file. The odds are 3.20/1 for Team 1 winning, 3.05/1 for a draw, and 2.10/1 for Team 2 winning. I take the reciprocals of odds to get probabilities. 1/3.20 + 1/3.05 + 1/2.10 > 1, so to make probabilities you divide each reciprocal by the sum of the reciprocals.
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September 28th, 2018, 02:18 PM   #4
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The odds are just wrong, unless they are bookie odds, which include bookie profit. To get probabilities you need to add 1 to the numerators before taking reciprocals, but it doesn't add up to 1, therefore leaving a bookie profit.
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