Question

A scientist performs an experiment and takes 100 readings. He repeats the same experiment and now takes 400 readings. By doing so :

• A. the probable error remains the same
• B. the probable error is halved
• C. the probable error is doubled
• D. the probable error reduces by a factor of $1/4$

Answer 1

The correct option is D the probable error reduces by a factor of $1/4$

Here, the scientist initially takes 100 readings and tries to reduce the probable error by repeating the procedure for 400 readings.
i.e., Probable error $\propto$ 1 / No. of readings
So, the probable error will now get reduced by a factor of $\frac{1}{4}$.