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This isn't a homework problem. I'm just having ALOT of trouble understanding how to do error propogation.

[EDIT] These are actually lab results. But its not a "homework" question. Its how to do uncertainty. Just trying to be clear.

Consider we take different measurements of an objects acceleration with uncertainties:

-0.2590 ± 0.0065 m/s^2

-0.2760 ± 0.0019 m/s^2

-0.2800 ± 0.0057 m/s^2

-0.2510 ± 0.0230 m/s^2

-0.2640 ± 0.0073 m/s^2

I want to take the average acceleration with the uncertainty of the average.

So the average is fine and easy however;

There are two ways to take the uncertainty:

1. Standard deviation of the acceleration divided by the square root of the number of accelerations.

2. Since to get the mean accelerate we summed accelerations, we use standard error propogation rules for addition and sum the square of the uncertainties and take their square root.

Notice in both of the above, we ignore the other method. In the first, we ignore the fact that each value has its own uncertainty and just look at the standard deviation.

In the second, we ignore the distribution of our data and only look at their individual uncertainties.

So what do I do...? :(.

[EDIT] These are actually lab results. But its not a "homework" question. Its how to do uncertainty. Just trying to be clear.

Consider we take different measurements of an objects acceleration with uncertainties:

-0.2590 ± 0.0065 m/s^2

-0.2760 ± 0.0019 m/s^2

-0.2800 ± 0.0057 m/s^2

-0.2510 ± 0.0230 m/s^2

-0.2640 ± 0.0073 m/s^2

I want to take the average acceleration with the uncertainty of the average.

So the average is fine and easy however;

There are two ways to take the uncertainty:

1. Standard deviation of the acceleration divided by the square root of the number of accelerations.

2. Since to get the mean accelerate we summed accelerations, we use standard error propogation rules for addition and sum the square of the uncertainties and take their square root.

Notice in both of the above, we ignore the other method. In the first, we ignore the fact that each value has its own uncertainty and just look at the standard deviation.

In the second, we ignore the distribution of our data and only look at their individual uncertainties.

So what do I do...? :(.

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