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How To Incorporate Sensor Uncertainties With Multiple Measurements? 
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#1
Sep1513, 12:50 PM

P: 47

Lets say a sensor measures within accuracy of +/ 0.05N
And you take multiple measurements and graph it out. (I.e., 5.12N, 5.15N, 5.05N...). What is the uncertainty of the final average? One way I read is: Sx = s/√N where s = std. dev. N = number of data points But this doesn't incorporate the sensor's uncertainty. 


#2
Sep1513, 02:28 PM

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P: 16,981

The standard deviation of the mean (aka the standard error) is equal to ##1/\sqrt{N}## times the standard deviation of the measurement. You can derive this from the equation in the paper I posted to your previous thread.



#3
Sep1513, 02:35 PM

P: 47

That uncertainty comes from variance of the data.
But it does not incorporate the fact that the data points themselves have imprecision. Does it? 


#4
Sep1513, 04:07 PM

P: 1

How To Incorporate Sensor Uncertainties With Multiple Measurements?
RANDOM errors decrease with the square root of the number of measurements. (If the measurements are roughly normally distributed.) SYSTEMATIC errors do not.
In order to see if multiple leasurements help at all, you have to break the stated measurement uncertainty into those two components. Simple instruments only give an overall uncertainty, which makes it almost impossible. Random errors can be estimated by taking the standard deviation (the SAMPLE standard deviation should be used) of a large number of measurements. Systematic errors are much harder to estimate. They impose a lower bound on the quality that can be attained with even an infinite number of remeasurements. If you look at metrology papers, you will see that they generally remeasure until the random error is somewhat lower than the systematic error; additional effort gains too little to bother. 


#5
Sep1513, 04:30 PM

Mentor
P: 16,981

Perhaps you are leaving out some information in the description. 


#6
Sep1513, 04:57 PM

P: 47

Ah, so a systematic error cannot be reduced. I appreciate it a lot.
I left out information of the experiment but it was irrelevant. 


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