The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be
The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be
$4x$
$\frac{1}{4}x$
$2x$
$\frac{1}{2}x$
The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be
Random error in $100$ observations $=x$
Random error in $400$ obsrvation $= ?$
If observation is increased by '$n$' times then random error decreases by $\frac{1}{ n }$ times therefore random error $=\frac{x}{4}$
Hence, the answer is $\frac{x}{4}$.
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