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

Question

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 (A) 4x (B) (x/4) (C) 2x (D) (x/2)

Tardigrade Admin · Accepted Answer

Random error is inversely proportional to the number of observations ∴ Error propto (1/o b s e r v a t i o n) (E1/E2)=(O2/O1) E2=(x/(400)100) E2=(x/4)

Q. 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

$4 x$

$\frac{x}{4}$

$2 x$

$\frac{x}{2}$

Random error is inversely proportional to the number of observations
$∴$ $E rror \propto \frac{1}{o b ser v a t i o n}$
$\frac{E _{1}}{E _{2}} = \frac{O _{2}}{O _{1}}$
$E_{2} = \frac{x}{\frac{400}{100}}$
$E_{2} = \frac{x}{4}$

Q. 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

4x

4x​

2x

2x​