1. Tardigrade
  2. Question
  3. Physics
  4. 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 Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

NTA AbhyasNTA Abhyas 2022

Solution:

Random error is inversely proportional to the number of observations
$\therefore $ $Error \propto \frac{1}{o b s e r v a t i o n}$
$\frac{E_{1}}{E_{2}}=\frac{O_{2}}{O_{1}}$
$E_{2}=\frac{x}{\frac{400}{100}}$
$E_{2}=\frac{x}{4}$