In experimental physics, it is important to repeat
measurements. Assuming that errors are random,
show that if the error in making a single measurement of a quantity X is ∆, the error obtained after using n measurements is ∆/
√n. (Hint: After n measurements, the procedure would be to
take the n results and average them. So you require the standard deviation of the quantity Y =
(X1+X2+···+Xn)/n where X1, X2 ...Xn can be
assumed to be independent, and each has standard
deviation ∆.)

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