Which method is more accurate for determining peak time in data analysis?

[marcusesses]

Homework Statement

Say I perform an experiment, and I make a number measurements over a given interval (e.g t=0s to t = 10s, every 1s), and I perform this experiment many times.

Now, let's say I make a plot of data vs. time, and I want to find when the data peaks in time on average.

Which measurement of the peak time would provide more accuracy: if I take the average of the individual data points over the number of runs I did and and then determine the peak time, or if I determine the peak time within a given run and then find the average peak for all the data runs?

Homework Equations

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The Attempt at a Solution

I don't even know where to start...there doesn't seem to be any simple relation between the two...at least, not that I know of...

 

[Delphi51]

Well, I would find the peak in each run first. Not sure just why, but for example you might have two points equally high and notice that the peak must be in between them - likely midway. So you would gain a bit of accuracy that way.

 

[Redbelly98]

Well, I would find the peak in each run first.

I was thinking the same thing. In different runs, the peak heights or widths could be different, and averaging all the data runs before doing the height would effectively weight the various runs differently.

 

[marcusesses]

Thanks for the replies...
Would there be some analytical way to determine which way is more efficient?

I guess I can intuitively see how finding the peak for each run and then taking the average would be a better way, since for each individual data point, there may be random errors, but if you wait until the end of the run, the randomness may "smooth out", and the results will converge to the (presumably) correct value...

But if you have a distinct peak, wouldn't that also be apparent by taking the average of the individual data points?

I understand what you're both saying, but is there a way to determine which method has the greater uncertainty? I can probably just figure it out computationally, but I was hoping there was an analytical method that might make things a bit more...concrete.