Getting an average figure with ±

[Monocerotis]

Homework Statement

Quick question, working on a lab

Just wondering how I could go about getting an average value for a series of figures with +- values.

For instance
1) 1.5 ± 0.02
2) 1.7 ± 0.84
3) 1.7 ± 0.08

The Attempt at a Solution

I tried enclosing the figures within parenthesis and then trying to find an average with wolfram alpha but no success.

I was just reading something on the net

would it be x "avg" ± Δx "avg

1.5 + 1.7 + 1.7 /3 = 1.63
(sqrt) 0.02^2 + 0.84 + 0.08 = 0.844

so we arrive at 1.63 ± 0.844

correct ?

 

[D H]

would it be x "avg" ± Δx "avg

1.5 + 1.7 + 1.7 /3 = 1.63
(sqrt) 0.02^2 + 0.84 + 0.08 = 0.844

so we arrive at 1.63 ± 0.844

correct ?

Incorrect, and very much so. Assuming the measurements are statistically independent (are they? There's no telling from the original post) then

1. That 1.5 measurement is considerably more precise than either of the other two measurements. You should get something closer the 1.5 than 1.7 for your final estimate.

2. You combined error is larger than the largest error. It should be smaller than any of individual errors.Google "weighted mean".

 

[Monocerotis]

k I've been reading and it seems as though what I'm dealing with is a common mean rather than a weighted mean

I'm dealing with slope figures of a v(t) graph and trying to find g avg +- delta g avg as to compare it with my theoretical results

the values I gave above were ambigous but the figures I'm actually dealing with from my perspective appear to have equal weight so

still confused as to what to do however because even the common mean will only give me a single value

 

[D H]

What exactly are you measuring here? Without details it is a bit hard to help you.

 

[rwisz]

Yes, your approach is correct. To find the average value when dealing with uncertainties, you should use the weighted average method. This takes into account the individual uncertainties of each measurement. In your example, the weighted average would be 1.63 ± 0.844, as you calculated. Just make sure to include the units of the uncertainties in your final result.