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# Calculating the uncertainty for average voltage

6 replies to this topic

### #1 slimers7 Posted Apr 06, 2012 - 02:48

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I writing up the lab report for my IA and have encountered some confusion over the uncertainty business. Any help would be greatly appreciated.

I am using the mean voltage on this graph for my data. Since it is an average, and there is a maximum and minimum. How do I calculate this mean's uncertainty? Also, how many significant figures should I use?

### #2 M J Posted Apr 06, 2012 - 05:46

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It would help to provide some context on what the lab is about...

### #3 HiggsHunter Posted Apr 06, 2012 - 11:59

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I writing up the lab report for my IA and have encountered some confusion over the uncertainty business. Any help would be greatly appreciated.

I am using the mean voltage on this graph for my data. Since it is an average, and there is a maximum and minimum. How do I calculate this mean's uncertainty? Also, how many significant figures should I use?

Are the fluctuations in your graph due to variations in the voltage being measured, or are they due to random errors in the measurement of a constant voltage?

### #4 slimers7 Posted Apr 06, 2012 - 14:50

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I am assuming they are due to variations.There is a little less than a .00976 difference between the max and min. For the lab, I measured the voltage across a specific wire in a circuit while increasing the wire's temperature.

### #5 HiggsHunter Posted Apr 06, 2012 - 17:02

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I presume that the temperature of the wire was not being changed during the 9 seconds of the measurement, so the voltage fluctuations are due to noise, and the three levels in the graph are due to your measuring instrument having a resolution of 5mV.
So the uncertainty in the mean voltage is +-2.5mV due to this quantization, plus +-9.8mV (+-3 sd) for the mean calculated over 92 samples, plus the uncertainty in the calibration of the instrument (which you may be able to find from its specifications if you don't have a voltage standard with which to check it)
To make an accurate measurement of a voltage of the order of 37mV it would be better to use an instrument with much better resolution than 5mV, and to filter the noise or take many more samples. A typical inexpensive DVM has a resolution of 100uV.

### #6 slimers7 Posted Apr 06, 2012 - 17:23

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Thank you so much! So I must add the 2.5 to the 9.2 to the devices uncertainty? Also, how many sig figs should I round to?

### #7 HiggsHunter Posted Apr 06, 2012 - 17:38

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I would suggest modifying the experiment or using a more appropriate instrument in order to reduce the uncertainty in the voltage measurement. Without knowing all the details of the experiment, it's difficult to make a concrete suggestion!