Question

The random error in arithmetic mean of $100$ observations is x are taken then random error in arithmetic mean of $400$ observations becomes

• A. $\frac{x}{4}$
• B. $x^2$
• C. $10x$
• D. $\sqrt{x}$

Answer 1

Answer: (A)

$\frac{x}{4}$

Random error in $100$ observations $=x$

Random error in $400$ obsrvation $=?$

If observation is increased by ${}^{\prime }{n}^{\prime }$ times then random error decreases by $\frac{1}{n}$ times therefore random error $=\frac{x}{4}.$

Hence, the answer is $\frac{x}{4}.$