Question

A physicist performs an experiment and takes $200$ readings. He repeats the same experiment and now takes $800$ readings. By doing so :

• A. the probable error remains same.
• B. the probable error is four times.
• C. the probable error is halved.
• D. the probable error is reduced by a factor $\frac{1}{4}$.

Answer 1

The correct option is D the probable error is reduced by a factor $\frac{1}{4}$.

More the number of experiments we do, improvement in our output will be achieved. And on an average our expected value of output will become more accurate. Therefore, probable error which is determined on average basis will get reduced by $\frac{1}{4}$ in this case.