The random error in the arithmetic mean of 10 | vedclass

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Question

(D) The random error in the arithmetic mean of $n$ observations is given by $\Delta \bar{a} = \frac{\Delta a}{\sqrt{n}}$,where $\Delta a$ is the error

Vedclass · Accepted Answer

$\frac{1}{2}x$

Vedclass · Answer

(D) The random error in the arithmetic mean of $n$ observations is given by $\Delta \bar{a} = \frac{\Delta a}{\sqrt{n}}$,where $\Delta a$ is the error in a single observation.For $n_1 = 100$ observations,the random error is $x = \frac{\Delta a}{\sqrt{100}} = \frac{\Delta a}{10}$.For $n_2 = 400$ observations,the random error is $x' = \frac{\Delta a}{\sqrt{400}} = \frac{\Delta a}{20}$.Dividing the two expressions: $\frac{x'}{x} = \frac{\Delta a / 20}{\Delta a / 10} = \frac{10}{20} = \frac{1}{2}$.Therefore,$x' = \frac{1}{2}x$.

The random error in the arithmetic mean of $100$ observations is $x$; then the random error in the arithmetic mean of $400$ observations would be

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