How to calculate percentage uncertainties? Urgent Watch

bobbricks
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I have a physics practical assessment coming up in a few days and one of the criteria is to calculate uncertainties.. How do I calculate this? e.g. would it be the uncertainty/precision of instrument divided by the average x100 or would you need to calculate the percentage uncertainty errors for the different times and then add them up?

I found this somewhere online:
Absolute uncertainty= +-range of values/2
Percentage uncertainty= +-absolute uncertainty/average value x100

Are these formulae correct?

This is for the Unit 3 practical assessment for Edexcel.
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JizzaStanger
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They are correct. For example, say you had these four measurements:

20.5, 20.7, 20.2, 20.6

You calculate the mean: mean = (20.5+20.7+20.2+20.6)/4 = 20.5.

Then you take half the range of the results to be your absolute uncertainty: (20.7-20.2)/2 = 0.25 (you normally only quote this to 1 s.f.)

Therefore your answer will be: 20.5 +/- 0.3 units.

When quoting your answer the number of significant figures you quote your answer to is very important.
The uncertainty is always given to 1 s.f. In this case that happens to be to 1 d.p., so you quote your answer to 1 d.p.

To calculate percentage uncertainty it's : ((absolute uncertainty)/(mean)) * 100.
Note that when calculating anything, never round until the very end. So to calculate the percentage uncertainty you should use 0.25 rather than the rounded 0.3.

(0.25/20.5)*100 = 1.22% (rounded to 3 s.f.)
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bobbricks
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(Original post by JizzaStanger)
They are correct. For example, say you had these four measurements:

20.5, 20.7, 20.2, 20.6

You calculate the mean: mean = (20.5+20.7+20.2+20.6)/4 = 20.5.

Then you take half the range of the results to be your absolute uncertainty: (20.7-20.2)/2 = 0.25 (you normally only quote this to 1 s.f.)

Therefore your answer will be: 20.5 +/- 0.3 units.

When quoting your answer the number of significant figures you quote your answer to is very important.
The uncertainty is always given to 1 s.f. In this case that happens to be to 1 d.p., so you quote your answer to 1 d.p.

To calculate percentage uncertainty it's : ((absolute uncertainty)/(mean)) * 100.
Note that when calculating anything, never round until the very end. So to calculate the percentage uncertainty you should use 0.25 rather than the rounded 0.3.

(0.25/20.5)*100 = 1.22% (rounded to 3 s.f.)
Hmm..If that's the case, then does that mean the absolute uncertainty stated on the instrument- e.g. it's +-0.01mm for a micrometre- is irrelevant when calculating the uncertainties?
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team-punishment
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Here are some formulas;

Uncertainty = precision of instrument / value. That is if you have not taken any repeat readings.
Uncertainty = precision of instrument / mean. This is if you have taken repeat readings.
% uncertainty = precision of instrument / mean x100.

Uncertainty = range of readings /2. That is when they want to know the uncertainty in a certain reading, e.g 'Use your readings to find the uncertainty in the largest angle'. The 's' there is a giveaway.
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bobbricks
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(Original post by team-punishment)
Here are some formulas;

Uncertainty = precision of instrument / value. That is if you have not taken any repeat readings.
Uncertainty = precision of instrument / mean. This is if you have taken repeat readings.
% uncertainty = precision of instrument / mean x100.

Uncertainty = range of readings /2. That is when they want to know the uncertainty in a certain reading, e.g 'Use your readings to find the uncertainty in the largest angle'. The 's' there is a giveaway.
Do you know which formula I should be using for the practical assessment (Edexcel Unit 3) or does it not matter? I'll be taking repeat readings for times
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JizzaStanger
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(Original post by bobbricks)
Hmm..If that's the case, then does that mean the absolute uncertainty stated on the instrument- e.g. it's +-0.01mm for a micrometre- is irrelevant when calculating the uncertainties?

Correct. The only time the uncertainty is the precision of the instrument is when the range of the results is 0, since it is impossible to have an uncertainty of 0.

So to clarify, for absolute uncertainty:
precision of instrument for readings with no repeats.
precision of instrument for multiple readings that are all the same.
half the range for multiple readings, provided the range is more than 0.

Then for percentage uncertainty, divide the absolute uncertainty by the mean and multiply by 100.

To answer your last question, you should use the appropriate formula out of the ones above. There is no one formula that will work every time.
Chances are that if you're timing things with repeats then you'll probably end up using the 'half the range' one.
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teachercol
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There are different causes of uncertainty.
Use the one that gives you the biggest uncertainty. Its more important than the others.

Usually half the range will be bigger than the precision of the measuring instrument so use that.
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JizzaStanger
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(Original post by teachercol)
There are different causes of uncertainty.
Use the one that gives you the biggest uncertainty. Its more important than the others.

Usually half the range will be bigger than the precision of the measuring instrument so use that.

You are wrong! ALWAYS use half the range, unless all of the readings are the same.
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teachercol
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(Original post by JizzaStanger)
You are wrong! ALWAYS use half the range, unless all of the readings are the same.
Depends which board. I moderate G483 for OCR.
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Stonebridge
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(Original post by teachercol)
Depends which board. I moderate G483 for OCR.
Have you got a link to the ocr site with these guidelines, please?

I'm trying to put together a summary of the guidelines from different boards as this is obviously causing a lot of confusion at the moment.
I have found the AQA guidelines, which clearly give a different interpretation.
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teachercol
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This is the link to the OCR practical handbook

http://www.ocr.org.uk/Images/70735-p...s-handbook.pdf

P46 has the relevant details.
My replies are gleaned from experience, previous mark schemes and talking to the chief examiner for this module.

Of course, its a shame that different exam boards use different 'rules' but its also important for students to realize that there are different rules and its not a matter of 'right' and 'wrong'.

I teach that there are many causes of experimental uncertainty - including limitations of the instrument; inherent variations of what we are measuring; human judgment. We need to consider all of them and use the largest. To me, that the 'correct' method regardless of what chief examiners may say.
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Stonebridge
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(Original post by teachercol)
This is the link to the OCR practical handbook

http://www.ocr.org.uk/Images/70735-p...s-handbook.pdf

P46 has the relevant details.
My replies are gleaned from experience, previous mark schemes and talking to the chief examiner for this module.

Of course, its a shame that different exam boards use different 'rules' but its also important for students to realize that there are different rules and its not a matter of 'right' and 'wrong'.

I teach that there are many causes of experimental uncertainty - including limitations of the instrument; inherent variations of what we are measuring; human judgment. We need to consider all of them and use the largest. To me, that the 'correct' method regardless of what chief examiners may say.
Thanks for this. I agree with you wholeheartedly.
The whole area of experimental uncertainties at A Level causes a lot of confusion.
I guess it's because, to treat them "properly" you need to consider more advanced statistical methods and use standard deviations, variance etc.
A Level is (necessarily) a watered down and simplified version of how it should be done. This is not to detract from what is done at A Level, as this provides an excellent introduction to this topic, but to point out the difficulty of getting a consistent approach.
It takes a lot of experimental experience to obtain a good feel for uncertainties and I think students at this level struggle with it for this reason.
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asadmoosvi
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(Original post by JizzaStanger)
They are correct. For example, say you had these four measurements:

20.5, 20.7, 20.2, 20.6

You calculate the mean: mean = (20.5+20.7+20.2+20.6)/4 = 20.5.

Then you take half the range of the results to be your absolute uncertainty: (20.7-20.2)/2 = 0.25 (you normally only quote this to 1 s.f.)

Therefore your answer will be: 20.5 +/- 0.3 units.

When quoting your answer the number of significant figures you quote your answer to is very important.
The uncertainty is always given to 1 s.f. In this case that happens to be to 1 d.p., so you quote your answer to 1 d.p.

To calculate percentage uncertainty it's : ((absolute uncertainty)/(mean)) * 100.
Note that when calculating anything, never round until the very end. So to calculate the percentage uncertainty you should use 0.25 rather than the rounded 0.3.

(0.25/20.5)*100 = 1.22% (rounded to 3 s.f.)
Why is the final percentage uncertainty rounded to 3 s.f.?
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Stonebridge
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(Original post by asadmoosvi)
Why is the final percentage uncertainty rounded to 3 s.f.?
It shouldn't have been.

Final % uncertainty should be rounded to the nearest whole percent. (1 sig fig)
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