# How to calculate the average with uncertainties?

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1. Feb 28, 2017

### Tyler S

1. The problem statement, all variables and given/known data
How to calculate the average given the uncertainties in each measurement 8.70 +/- 0.28, 9.680 +/- 0.046, 9.700 +/- 0.055, 9.720 +/- 0.067?

2. Relevant equations

3. The attempt at a solution
I know I add the values and divide by 4. I also know I add the absolute uncertainties but idk if I divide them by 4. Please help I've gotten 9.45 +/- 0.448 meters

2. Mar 1, 2017

### BvU

Hello Tyler,

In the case off different accuracies, you have to weight the measurements when averaging. The appropriate weight of a measurement is $1\over \sigma^2$.
Here, $\sigma$ is the (estimated) inaccuracy

Last edited: Mar 1, 2017
3. Mar 1, 2017

### haruspex

It's "weight the measurements".
Well, it's not so much the accuracy as the inaccuracy.