How to calculate the average with uncertainties?

[Tyler S]

Homework Statement

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?

Homework Equations

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

 

[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

 

[haruspex]

have to weigh the measurements

It's "weight the measurements".

Here, σ is the (estimated) accuracy

Well, it's not so much the accuracy as the inaccuracy.