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(C) The relative error or the standard error in a measurement is inversely proportional to the square root of the number of observations,$n$,if the er

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the possible error is halved.

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(C) The relative error or the standard error in a measurement is inversely proportional to the square root of the number of observations,$n$,if the errors are random.However,in the context of the mean absolute error,the error is often expressed as $\Delta x_{m} = \frac{\sum |\Delta x|}{n}$.For a large number of observations,the statistical error (standard deviation of the mean) is given by $\sigma_{m} = \frac{\sigma}{\sqrt{n}}$.When the number of observations $n$ increases from $100$ to $400$,the factor $n$ increases by a factor of $4$.Since the error is inversely proportional to $\sqrt{n}$,the new error becomes $\frac{1}{\sqrt{4}} = \frac{1}{2}$ of the original error.Thus,the possible error is halved.

$A$ scientist performs an experiment in order to measure a certain physical quantity and takes $100$ observations. He repeats the same experiment and takes $400$ observations. By doing so,

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