I have 3 measurements and was trying to take the average of the measurements and calculate the error of the average:

replicate 1 = 8.9 (+/-) 0.71mg

replicate 2 = 9.3 (+/-) 0.69mg

replicate 3 = 8.8 (+/-) 0.70mg

I get an average of 8.9333 (+/-) e where e=sqrt((rep 1 error)^2 + (rep 2 error)^2 + (rep 3 error)^2) which gives me a value of 1.21. But why is the error value so much higher in the average?

What step am I missing? I don't know the derivation behind the error propagation formula - so I just use it as it is: e=sqrt((e1)^2+(e2)^2+...)