So in class we are doing an experiment on the period of a pendulum where you measure the period of oscillation with a stopwatch.

Now the way the lab manual shows how to do the error analysis is by computing the mean and getting the standard deviation. I get this much. However, elsewhere I read that the error in measurements are the smallest unit possible on the measurement apparatus, so for example on a metre stick whose smallest unit is 1mm the error/uncertainty on any measurement would be 1mm (or 0.5mm it says elsewhere, I suppose it's the smallest unit you feel confident estimating).

So, if I were to take 10 measurements of a piece of string, each measurement would have an uncertainty of 1mm. Now, when I computed the average of these would the uncertainty be 1mm or would I have to use the formulas for the propogation of errors to compute the uncertainty of the average. Or do we disregard this 1mm and simply compute the mean and standard deviation?

Is it the case that the standard deviation would include all sources of uncertainty, i.e. the 1mm measurement uncertainty as well as others. If so, what is the point of taking notes of the measurement error in the first place when it is included in the statistical analysis?

Can anyone help me? I know I am making some fundamental misconception but I am struggling to suss it out.

• "Now the way the lab manual shows how to do the error analysis is by computing the mean and getting the standard deviation. I get this much. ": This is probably the most basic example of statistical estimation, but don't take it as a universal law: not for every repeated measurement you have to take the mean and not for every repeated measurement the uncertainty can be evaluated by the standard deviation. – Massimo Ortolano Sep 7 '16 at 17:57
• "However, elsewhere I read that the error in measurements are the smallest unit possible on the measurement apparatus": This, instead, is utterly wrong: wherever you read it, forget about it and throw the source in the fireplace. – Massimo Ortolano Sep 7 '16 at 17:58
• www2.fiu.edu/~dbrookes/ExperimentalUncertaintiesCalculus.pdf Section 1.1 explains what I mean in case I didn't explain it clearly – RonGiant Sep 7 '16 at 18:00
• Notice that your linked document, though incorrect in many points, doesn't say what you have reported in the question. – Massimo Ortolano Sep 7 '16 at 18:03
• "Every measuring instrument has an inherent uncertainty that is determined by the precision of the instrument. This value is taken as a half of the smallest increment of the instrument scale. " and mine: "However, elsewhere I read that the error in measurements are the smallest unit possible on the measurement apparatus, so for example on a metre stick whose smallest unit is 1mm the error/uncertainty on any measurement would be 1mm (or 0.5mm it says elsewhere, I suppose it's the smallest unit you feel confident estimating)." – RonGiant Sep 7 '16 at 18:09