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I'm reading a printed document(learning material) which says "Person A made measurements of a quantity, with Gaussian errors". To me this expression seems odd and the meaning is unclear.

Is that a valid expression? If so, would the sentence mean that the measured values follow a Gaussian distribution?

If I measure the length of a pencil, using a ruler that has a precision of 1mm. I would obtain a vector with the measure values and then the systematic errors of the values are all $\pm$1mm. So my errors are all fixed and have nothing to do with the Gaussian distribution. Then in which situation would I have Gaussian distributed errors?

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