Question

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. $4x$
• B. $\frac{x}{4}$
• C. $2x$
• D. $\frac{1}{2^x}$

Answer 1

Answer: (B)

$\frac{x}{4}$

$\begin{array}{c}\text{Error in 100 observations}=x\\ \text{if no. of observation is increased by 4 times , then error in mean will become}\frac{1}{4}\text{times}\\ \therefore \text{error in}400\text{observations}=\frac{x}{4}\end{array}$