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The following presentation is adapted from conversational dialogues with Lancelot Link for stochastic measurement errors in the physical sciences.  

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To calculate the error range for uncorrelated and random errors, use Gauss’s equations for normal distribution of errors. Using the Gauss equations, gives a 68% confidence interval the measurement error is within this range.

Here are some basic derivatives from the Gauss equations:

 

\(\small \text{If Q is a combination of sums and/or differences, then the sigma (error) of Q is equal to } \\ \sigma Q = \sqrt{(\sigma a)^2 + (\sigma b)^2 . . . + (\sigma x)^2 . . . } \\ \text{If } Q = b^2 \text{ then } \sigma Q = 2(\sigma (b)) \text{ where } \sigma (b) \text{ is the error of (b)}\\ \text{If } Q = \sqrt{(b)} \text{ then }\sigma Q = \frac{1}{2} (\sigma (b)) \text{ where } \sigma (b) \text{ is the error of (b)}\\ \text{Note how the exponent becomes the multiplier of the error.}\\ \small \text {For this equation, the easiest method is to calculate each error as a }\\ \small \text {decimal and then use the sum of the decimals to calculate the error range. }\\ \text {Uncertainties (In decimal) for a, b, and c. }\\ a_1 = \frac{0.1}{1.3} = 0.0769\\ b_1 = (2)\frac{0.2}{2.8} = 0.1428\\ c_1 = (0.5)\frac{0.1}{0.8} = 0.0625\\ Q= \frac{1.3 \times (2.8)^2}{\sqrt {0.8}} = 11.4 \pm ((0.0769 + 0.1428+ 0.0625) * (11.4))\\ Q= 11.4 \pm 3.2 \\ \small \text { note: pay attention to significant figures when recording the final error range. }\\ \\\)

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Relating to this question and others you’ve posted on here , another important thing you need to do is Stop being a lazy dolt!

I would have answered your chemistry questions, except I was too lazy. I caught this laziness from you—it’s more contagious than dumbness.indecision

 

 

GA

Jan 6, 2018
Jan 5, 2018

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