Thursday 24 October 2019

measurements - Propagation of uncertainties


I have five values for the volume of sodium hydroxide needed to neutralise a fixed quantity of hydrochloric acid, each trial with an uncertainty of 0.05 mL. If I take the average of these five values, in what way would the uncertainty propagate? I can think of three of the following ways, but don't understand which would be correct:





  1. Because we can see the calculation of an average as the sum of the values for the five trials (with their uncertainties), and then a division by 5, we sum up the uncertainty to get 0.25 mL and then divide it by 5 to get the uncertainty of the average to be 0.05 mL.




  2. Because we can see the calculation of an average as the sum of the values for the five trials (with their uncertainties), and then a division by 5 (which has no uncertainty), we sum up the uncertainty to get 0.25 mL and then divide it by 5 to get the uncertainty of the average to be 0.25 mL.




  3. Range divided by two is often another way to calculate the uncertainty of an average value, which for my case results in a value different to the above two for the uncertainty of the average.





Which one, and why, would be the correct one to state next to the average value (with a plus-minus sign), as an uncertainty of the average value?




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