Asymmetric uncertainty intervals in astrophysical data

[ElectroFractal]

Homework Statement

I have come across astrophysical data where the data have asymmetrical uncertainty intervals like this for example: 4.467[SUP]+0.064[/SUP][SUB]-0.096[/SUB]. I cannot realize how to calculate an average of this quantity, and a percent uncertainty.

Relevant Equations

I calculated the upper and lower value: 4.467+0.064=4.531 and 4.467-0.096=4.371, and found the average which is 4.451, and it's different from the value 4.467.

My initial guess was to calculate the upper and lower value, and then average those two values, but I don't know whether this is correct to make the uncertainty interval symmetric.

After I calculated the average value, I subtracted it form the upper and lower value, and obtained the symmetric interval: 4.451+-0.08. Thus, the percent uncertainty is:
0.08/4.451 = 1.79%

My question is if this way of thinking is a correct one, and if there are other techniques to obtain my goal?

 

[BvU]

is a correct one

Obviously: No. Otherwise the authors would have published their result in that manner.

What is the motivation behind your 'goal' ?

 

[ElectroFractal]

My motivation is to find an average value of the observed quantity, and calculate a percent uncertainty. I am doing an ML project related to astronomical observations, and I am trying to do feature engineering to obtain better results from the model.

 

[Vanadium 50]

My motivation is to find an average value of the observed quantity, and calculate a percent uncertainty.

But the authors clearly did not think this was the correct way to express the uncertainty, otherwise they would have done it the other way.

 

[ElectroFractal]

So, is there a way to calculate what I want, or I should forget about this, and try to do something different?

 

[Vanadium 50]

You want the error to be symmetric. The authors didn't think it was. You need to decide how to handle this disagreement.

 

[phyzguy]

As @Vanadium 50 said, you need to think about what you are trying to do. What do you mean by the "average"? An average usually refers to reducing a list of values to a single number by adding up the values and dividing by the number of values. But here you have just a single value, so using the term average doesn't really make sense. Do you mean the most likely value? The authors have given you that. It is the 4.467 value.