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- Homework Statement
- Propagation of uncertainties, standard deviation

- Relevant Equations
- $\frac{\deltaQ(x,y,z,...)}{Q(x,y,z,...)} = \sqrt{(\frac{\partial Q}{\partial x}\delta x)^2+(\frac{\partial Q}{\partial y}\delta y)^2+(\frac{\partial Q}{\partial z}\delta z)^2+...}$

I understand how to compute and propagate errors but have trouble with conceptualizing all things put together.

I have performed an experiment to determine a value for some quantity. This quantity depend on two variables. The first one depend in turn on some other quantities as well but I think I have managed to propagate errors correctly.

For the experiment I have made measurements for some ten or so points. The fractional error for the first variable is constant for all these points. The second variable is magnetic flux density B for which there is a constant error of say 5 mT at each point . As B increases, the fractional error in B then decreases and so the final outcome also has decreasing error as B gets higher. and gets lower and lower for each point. The quantity I want to measure then has errors that ranges from 5.5% to 3.5%. How do I choose an uncertainty from this? I'm thinking 5 % because the value that has this error is closest to the average value, but I don't know. The thing is 5 % is kind of a good outcome because then the true value is just within the error range. But 3.5 % is a little disappointing, so is it cheating if I choose among the highest error?

I narrowed it down to 2 questions:

1. How do I choose and uncertainty here? do I pick one from the higher end, like 5% or should I average the errors? that would make it about 4 %. It feels like I'm nit picking but I'm just thinking conceptually.

2. I calculated the standard deviation as well but that narrowed down the error to about 1 % but I feel that is too low. Do we use standard deviation only when we have values without uncertainties?

Just some pointers would be appreciated.

I have performed an experiment to determine a value for some quantity. This quantity depend on two variables. The first one depend in turn on some other quantities as well but I think I have managed to propagate errors correctly.

For the experiment I have made measurements for some ten or so points. The fractional error for the first variable is constant for all these points. The second variable is magnetic flux density B for which there is a constant error of say 5 mT at each point . As B increases, the fractional error in B then decreases and so the final outcome also has decreasing error as B gets higher. and gets lower and lower for each point. The quantity I want to measure then has errors that ranges from 5.5% to 3.5%. How do I choose an uncertainty from this? I'm thinking 5 % because the value that has this error is closest to the average value, but I don't know. The thing is 5 % is kind of a good outcome because then the true value is just within the error range. But 3.5 % is a little disappointing, so is it cheating if I choose among the highest error?

I narrowed it down to 2 questions:

1. How do I choose and uncertainty here? do I pick one from the higher end, like 5% or should I average the errors? that would make it about 4 %. It feels like I'm nit picking but I'm just thinking conceptually.

2. I calculated the standard deviation as well but that narrowed down the error to about 1 % but I feel that is too low. Do we use standard deviation only when we have values without uncertainties?

Just some pointers would be appreciated.