/sci/ - Science & Math

[Anonymous No.3970894]

soup /sci/

I'm doing a lab report for a chemistry class, and I need to know how to deal with uncertainties in a particular way. I need to find the mean of the results of three samples, each of which has its own degree of uncertainty. Say that for example I have three samples which returned a result of 100±10, and I need to find the mean of those three samples. Would the mean of that be 100±10, 100±30, something else I can't think of perhaps?

[Anonymous No.3970897]

http://en.wikipedia.org/wiki/Propagation_of_uncertainty

[Anonymous No.3970905]

>>3970897
Mentions nothing about finding averages.

[Anonymous No.3970920]

take the errors and use Protagoras theorem on them, so the error is sqrt(10^2 + 10^2 + 10^2)= 10sqrt(3)

[Anonymous No.3970925]

The most each can be is 110, the least is 90.
The most the mean can be is (110*3)/3 = 110.
The least the mean can be is (90*3)/3 = 90.

So, 100±10.

Follow that logic and you should understand how to handle uncertainties in addition, subtraction, multiplication and division.

[Anonymous No.3970936]

>>3970920
>protagoras

[Anonymous No.3970946]

>>3970925
that's not how uncertainties work.

>>3970920
is correct for this special case.

>>3970894
if you have a more general formula that just summing you take the Taylor expansion of the function of the form

f(A+-a,B+-b,C+-c) = f(A,B,C) + some higher terms

and truncate after the linear term.

[Anonymous No.3970947]

>>3970905
Only because you can't understand it.

[Anonymous No.3970968]

>>3970947
No shit. I wouldn't be asking questions about uncertainties if I understood the concept.

[Anonymous No.3970972]

>>3970968
But the link was provided so that you *could* understand it. Since you are unwilling to do that, what good would any of my posts be? None.

[Anonymous No.3970984]

>>3970972
Believe me, I have read extensively on the propagation of uncertainty. I can't find sufficient information to be able to figure out how to determine an average of uncertainty, so I asked here hoping that someone might be able to explain it to me in a way I can comprehend. Sending a link to an article I have already gone over does not help at all.

[Anonymous No.3970988]

>>3970984
So you don't know calculus, but are trying to deal with propagation of uncertainty?

[Anonymous No.3971002]

>>3970988
Exactly. I'm in the first couple of months of IB in high school, so unfortunately I haven't touched calculus yet. Is calculus basically a prerequisite for solving these kinds of problems?

[Anonymous No.3971022]

...waiting patiently to find out that I've been assigned something that is impossible for me to do...

[Anonymous No.3971029]

>>3970946
>>3970988

ITT: aspies who confuse measurement uncertainty with something else

Measurement uncertainties provide hard upper and lower bounds, not statistical certainty ranges.

[Anonymous No.3971071]

Still waiting for some kind of a tangible response.

[Anonymous No.3971073]

>>3971029
> When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate to the combination of variables in the function.
Fail more.

OP, the formula for sums is on the wikipedia page. You can tell because of the +. Otherwise you probably are expected to use sig figs. Honestly, whatever you're supposed to use must have already been covered in your text.

[Anonymous No.3971095]

>>3971073
This lab was more along the lines of the teacher throwing us some instruments to find the raw data and telling us to figure it out ourselves. I do believe we're supposed to be using sig figs though.

[Anonymous No.3971107]

In the case that I am using sig figs, how would that effect things?

[Anonymous No.3971131]

bumping out of necessity

[Anonymous No.3971175]

Still waiting

[Anonymous No.3971189]

>>3971029
>Measurement uncertainties provide hard upper and lower bounds, not statistical certainty ranges.
thats the most retarded thing ive ever read on sci, and im including the whole e=/= mc2 thing.

[Anonymous No.3971216]

>>3971189
So while you're still around, could you please at least answer this one question:

Do I need calculus to answer this question? Even when dealing with significant figures?

[Anonymous No.3971239]

>>3971216
no, unless you want to derive the formulas yourself.

is this what you want?
http://www.upscale.utoronto.ca/PVB/Harrison/ErrorAnalysis/Propagation.html

[Anonymous No.3971254]

>>3970920
was almost correct, but he forgot to divide by 3 at the end, so you get 100+-10/sqrt(3)

[Anonymous No.3971383]

bump

[Anonymous No.3971452]

average() +- 1.96*stdev()/sqrt(n)

[Anonymous No.3971455]

OP, you've already received several answers. Also, the wikipedia one provided you with everything you needed, but here's another link for you:

http://chemwiki.ucdavis.edu/Analytical_Chemistry/Quantifying_Nature/Propagation_of_Error#Arithmetic_
Error_Propagation

They give some examples. However, you're trying to find an average, right? Oh no! There's no example for that!

Well, what the hell do you think you're doing when you find an average? You're summing the individual values and dividing them by the number of terms.

So, you need to figure out the error propagated from the addition of the values. Then, you can take that, and use the formula provided for finding the error of multiplication or division. Since you're dividing by a number which doesn't have error, though, it might make sense to just consider that the uncertainty of the measurement is unaffected by that action.

Seriously OP, you were given the means to solve this, you just need to think about it. All of the manipulations you're making with these numbers are just the arithmetical operations you've been given error propagation formulas for in series. Don't complain about it not saying anything about your specific operation if it is just a combination of operations it gives formulas for.