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## Main Question or Discussion Point

My question is simple, and I'm only asking it because most places talk about more advanced problems than this one:

I've measured the radius of a sphere (a very regular one) with a micrometer of 0.01 mm resolution.

I took 3 measures (rotating it between each measure), and all of them were perfectly the same value: 19.23 mm . It was not only the same value, but the lines coincided perfectly on the three.

Each measure is noted as 19.230 mm +- 0.005 mm, however, when averaging the three values (what gives the same value as result), what should be the error of the average?

If I sum up the three measures (propagating the error in the sum) and then divide the result by 3, I get an error of +- 0.002886751 mm (+- 0.003 mm rounding it to a single significant figure).

Is this correct?

Thanks!

I've measured the radius of a sphere (a very regular one) with a micrometer of 0.01 mm resolution.

I took 3 measures (rotating it between each measure), and all of them were perfectly the same value: 19.23 mm . It was not only the same value, but the lines coincided perfectly on the three.

Each measure is noted as 19.230 mm +- 0.005 mm, however, when averaging the three values (what gives the same value as result), what should be the error of the average?

If I sum up the three measures (propagating the error in the sum) and then divide the result by 3, I get an error of +- 0.002886751 mm (+- 0.003 mm rounding it to a single significant figure).

Is this correct?

Thanks!