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Uncertainty in measurements.
07-20-2019, 03:49 AM
Post: #1
Uncertainty in measurements.
I recently purchased an HP Prime, a very good calculator, I really like it, but after reading its manual, I could not find anywhere that uncertainty could be used in this calculator.

As an engineering student, I would really appreciate that the calculator contains that possibility to work with uncertainty in the measurements.

I would greatly appreciate if someone could answer me if this is so, or that I did not see it in the manual.

Thank you!
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07-22-2019, 01:37 PM
Post: #2
RE: Uncertainty in measurements.
How do you see it working?

No calculator I know of does this.
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07-22-2019, 03:48 PM (This post was last modified: 07-22-2019 04:25 PM by StephenG1CMZ.)
Post: #3
RE: Uncertainty in measurements.
Although the calculator doesn't have explicit support for this AFAIK, many of the numeric functions do support lists.
So instead of calculating, say, LOG(10), one can calculate LOG({9.999,10,10.001}) or LOG(10×{.95,1,1.05}) and this could be used to show the upper and lower limits of a calculation based on an uncertain measurement.
Perhaps that would help?

Stephen Lewkowicz (G1CMZ)
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07-23-2019, 11:55 PM
Post: #4
RE: Uncertainty in measurements.
Uncertainty in measurement calculations may be affected by variables dependency.

Example: a = b = -4 to 6 = 1 ± 5

a - b = ±10 (if variables totally independent of each other)
a - a = 0

a * b = -24 to 36 = 6 ± 30
a * a = 0 to 36 = 18 ± 18
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07-24-2019, 01:30 AM (This post was last modified: 07-24-2019 01:31 AM by SlideRule.)
Post: #5
RE: Uncertainty in measurements.
Measurement Uncertainty
An Approach via the Mathematical Theory of Evidence
Simona Salicone
© 2007 Springer Science+Business Media, LLC

1 Uncertainty in Measurement

1.2 The Theory of Error

…errors are traditionally divided into two general classes: random and systematic.
Random errors occur with different values and signs in each different measurement (of the same quantity, with the same reference conditions). However, if the measurement of the same quantity is repeated a sufficient number of times N, the mean of these errors tends to zero and the mean of the measurement results tends to the true value of the quantity. Random errors presumably arise from unpredictable or stochastic temporal and spatial variations of the influence quantities.
The random error of a measurement result cannot be compensated by applying a correction, but it can be usefully reduced by increasing the number of observations.

systematic errors have the following characteristic: When the measurement of a certain quantity is repeated, following the same measurement process, with the same measurement instruments and the same reference conditions, they always occur with the same value and sign.
From a strict theoretical point of view, systematic errors, differently from random ones, can be fully compensated, and their effect can be eliminated. This result may happen, however, only if the systematic errors are totally recognized.



A modest reference: does this extract encapsulate your concern?

BEST!
SlideRule

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07-24-2019, 04:18 PM (This post was last modified: 07-24-2019 07:38 PM by Albert Chan.)
Post: #6
RE: Uncertainty in measurements.
(07-22-2019 03:48 PM)StephenG1CMZ Wrote:  ... instead of calculating, say, LOG(10), one can calculate LOG({9.999,10,10.001}) or LOG(10×{.95,1,1.05})
and this could be used to show the upper and lower limits of a calculation based on an uncertain measurement.

this work only if the function is monotonic (at least, locally)

Counter-example: f(x) := (1 .- x) .* (1.1 .- x) .* (1.2 .- x)

x := [1.03, 1.18] // x uncertainly range
f(x) → [-0.000357, 0.000288]

But, in this case, f(x) uncertainly should be evaluated where f'(x) = 0

z := solve(diff(f(x))=0, x) // z ≈ [1.04226, 1.15774], both numbers inside x range
f(z) → [-0.000385, 0.000385]
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