Error propagation in an average of two values

[beth92]

I'm writing up an experiment I did for a lab course and I am calculating the error in quantity V. I have two runs and have ended up with a value of V for each one, as well as an error. Ie, I have

V = 0.1145±0.0136 for Run 1
V= 0.1146± 0.0134 for Run 2

I got my errors through some tedious propagation which I won't go into, but what I'm wondering is what's the best way to calculate the error for my final V? (which will be the average V for the two runs) I have looked around and can't seem to find anything which gives a straight answer.

Would it be ridiculous to use the fact that V_average=(V₁+V₂)/2 and then propagate the error in (V₁+V₂) using the addition/subtraction propagation formula, then equate this quantity's fractional error to the fractional error in V_average? This seems a little over complicated.
Normally I would take the error in an average using Standard Deviation but that doesn't seem appropriate for just two values.

 

[BruceW]

Would it be ridiculous to use the fact that V_average=(V₁+V₂)/2 and then propagate the error in (V₁+V₂) using the addition/subtraction propagation formula, then equate this quantity's fractional error to the fractional error in V_average? This seems a little over complicated.

That is how I would do it. It is just one of the simplest examples of propagation of error.

 

[Emilyjoint]

I find these figures fascinating. Is it possible to explain what you measured and what instruments were used.
I would like to know about the tedious propagation you used to arrive at the errors.
The explanation may be there.

 

[CWatters]

Been many years since I did much statistics but I think you normally use a weighted average where the weighting is 1/Δ². That way the result is biased towards the value with the lowest error.

In this case the two values and their error are virtually the same so it won't make much difference.

 

[Nickie]

I would recommend using the standard deviation method to calculate the error in your final V value. While it may seem like overkill for just two values, it is a more accurate and reliable method compared to simply propagating the error in (V1+V2) using the addition/subtraction formula.

By using the standard deviation method, you are taking into account the variability of each individual measurement and how they contribute to the overall error in the average. This method is commonly used in scientific experiments and is a more robust approach to calculating error.

Additionally, if you are concerned about the validity of using standard deviation for just two values, you can also report the range of values for your final V, which would be (V1+V2)/2 ± standard deviation. This way, you are providing both the average value and the range of values that encompass the error.

In summary, while it may seem complicated, using the standard deviation method is the most appropriate and accurate way to calculate the error in your final V value. It takes into account the variability of each individual measurement and provides a more comprehensive understanding of the error.