The mean diameter of a thin brass rod is measured by vernier callipers. Why is a set of 100 measurem

Question

The mean diameter of a thin brass rod is measured by vernier callipers. Why is a set of 100 measurements expected to yield a more reliable estimate than a set of 5 measurements?

Professor PC Thomas Classes · Answer

Random errors tend to cancel out when averaged. The standard error of the mean is inversely proportional to $\sqrt{N}$. Increasing the number of measurements ($N$) decreases the random error, yielding a more reliable estimate.