The random error in the arithmetic mean of 100 observations is x;… - Vidyadip

MCQ

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

A
$4x$
✓
$\frac{1}{4}x$
C
$2x$
D
$\frac{1}{2}x$

✓

Answer

Correct option: B.

$\frac{1}{4}x$

b
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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