Mar30 - MEASURE EVERYTHING MULTIPLE TIMES! Average results...

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Unformatted text preview: MEASURE EVERYTHING MULTIPLE TIMES! Average results together to get much better value Random errors will occur in any measurement Average together N observations: X average = (X 1 +X 2 +X 3 ++X N )/N = Sum(X i )/N Scatter of measures shows you the accuracy of each measure For example, if you measure 100, 101, 99, 98, 101, 102, then scatter ~1 For example, if you measure 103, 89, 98, 115, 92, 102, then scatter ~10 Quantify the scatter for any one observation as ! 1 : Also called RMS or Standard deviation ! 1 = Sqrt [ Average{ (X i-X average ) 2 }] = Sqrt[ Average{X i 2 } - (Average{X i }) 2 ] Get estimate of the accuracy of your average value The uncertainty on an average ( ! average ) is much better than the uncertainty of any one observation ( ! 1 ) Average together N observations: ! average = ! 1 / Sqrt[N] Averaging 4 observations improves accuracy by 2X, 25 observations by 5X Express final averaged result as X average...
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Mar30 - MEASURE EVERYTHING MULTIPLE TIMES! Average results...

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