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Easy uncertainty analysis question.

Okay. It's late, I'm tired and I can't find my textbook. Someone help!

I have five calculated values for the speed of sound, each with a different % uncertainty. How do I find the % uncertainty for the mean? Can I just take the mean of the uncertainties, or must I sum the absolute uncertainties?

rep will be awarded :yes:
Reply 1
Avatar for fizzicsfiend
fizzicsfiend
OP
These are my numbers:

342 m/s ± 7.12%
341 m/s ± 7.40%
323 m/s ± 8.24%
345 m/s ± 8.45%
346 m/s ± 9.51%

Mean = 339 (to 3sf) ± ???
I think it's ± 8.14%, by taking the mean of the uncertainties, but I'm not sure :frown:
Reply 2
Avatar for fizzicsfiend
fizzicsfiend
OP
Anyone?
Reply 3
Avatar for james.h
james.h
11
fizzicsfiend
Anyone?

For a sum or difference, uncertainties are combined like this:

For w=x+y,Δw=(Δx)2+(Δy)2[br]where Δw= absolute uncertainty in w.\displaystyle \mathrm{For\ } w=x+y, \Delta w=\sqrt{(\Delta x)^2 + (\Delta y)^2}[br]\newline \mathrm{where\ }\Delta w = \mathrm{\ absolute\ uncertainty\ in\ }w.

For a product or quotient, uncertainties are combined like this:

For w=xyz,Δww=(Δxx)2+(Δyy)2+(Δzz)2[br]where Δww= percentage uncertainty in w.\displaystyle \mathrm{For\ } w=\frac{xy}{z}, \frac{\Delta w}{w}=\sqrt{\left(\frac{\Delta x}{x}\right)^2+\left(\frac{\Delta y}{y}\right)^2+\left(\frac{\Delta z}{z}\right)^2}[br]\newline \mathrm{where\ }\frac{\Delta w}{w}=\mathrm{\ percentage\ uncertainty\ in\ }w.

Since you're calculating an average, I think you'll need both (one after the other). :smile:
Is this what you've done? If not, do you get the same answer?
Reply 4
Avatar for fizzicsfiend
fizzicsfiend
OP
Hey, thanks for replying.
james.h

Is this what you've done? If not, do you get the same answer?


No, not exactly. I know that what you've posted is the correct method (and thanks for typing it all out!) but I'm not expected to know it yet. For IB physics, we are taught that for addition and subtraction you must add the absolute uncertainties, and for products and quotients you add the percentage uncertainties.

So with this in mind I should add the absolute uncertainties together, then divide by the number of values used? My first thought was to average the percentage uncertainties :s-smilie:
Reply 5
Avatar for james.h
james.h
11
fizzicsfiend
So with this in mind I should add the absolute uncertainties together, then divide by the number of values used? My first thought was to average the percentage uncertainties :s-smilie:

I'm not sure, but averaging the % uncertainties seems like a plausible answer. :yep:

I might've made a mistake in calculation, but the method I stated above gives a percentage uncertainty of about 18% in the final answer! :erm:
EDIT: Oops, I might've forgotten to divide by 5. :o: Ah, ~3%, much better. :smile:

Maybe you should wait for someone else to have a look at it. :frown:
If you're adding measurements, you add absolute uncertainties. If you're dividing measurements by a constant, you divide the absolute uncertainties by that constant.

For taking an average, that should be all you need to know.
Reply 7
Avatar for fizzicsfiend
fizzicsfiend
OP
james.h
snip

shamrock92
If you're adding measurements, you add absolute uncertainties. If you're dividing measurements by a constant, you divide the absolute uncertainties by that constant.

For taking an average, that should be all you need to know.


Thanks, both of you. I'm all sorted now :smile:

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