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I am taking the following example:

Lengths of an object are measured as : 5cm , 5.2cm , 5.1cm , 5.5 cm. Calculate the true value and the error .

The answer is True value = 5.2 cm error = 0.15 cm.

I am unable to interpret the answer. I have the following two explanations.

  1. If the length of the object is measured again , it is likely to lie between 5.2 +- 0.15 cm i.e. between 5.05 cm and 5.35 cm.

  2. The "actual length " of the object is somewhere between 5.05 cm and 5.35 cm.

I also cannot understand whether the error of 0.15 is the same as the uncertainty.

I don't know which of the explanations is correct or there is some other correct explanation.

Please provide me the correct explanation.

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There are two kinds of errors, systematic and random. Both deviate your measurements from the "true value", which you can never reach. Systematic errors deviate always the same way the measurement (like parallax for example, you might be measuring always 1mm more) and random errors deviate the measurements from the true value like a gaussian function.

So, to discuss your interpretations. 1) is correct, even though it's convenient to talk on more mathematical terms (statistical certainty and sigmas, look those up). Basically, as you make your confidence interval bigger, the probability of the next measurement falling there increases. 2) is correct only if there are no systematic errors, which might or might not happen, thats something that needs to be studied for each individual experiment.

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