Question

What are the fundamental differences in the uncertainty of individual measurements of a pendulum's period vs. uncertainty in the mean of measurements of a pendulum's period?

also, why is it more reliable to measure the period of a pendulum at the lowest position?

Answer 1

It is always best to observe over as many oscillations as possible because it increases the certainity about the result.

Pendulum’s lowest point is well defined and it passes it at maximum speed, so there is less doubt as to when to begin and stop timing. This is quite different when timing from the highest point where the pendulum lingers as it changes direction, making it hard to identify the decisive moment to begin or halt timing.It is always best to measure at a well defind point.