What is the experimental uncertainty of an ensemble measurement?

Question

Let's say you measure the time it takes for 10 oscillations of a mass undergoing simple harmonic motion to within ± 0.01s, what is the uncertainty of the period of one oscillation?

Answer 1

Given the slew of comments to your question I'll summarise them in an answer to make it simple to read.

If we assume that you know the oscillations are regular and your time for ten of them is $T \pm \Delta T$, then the time for a single oscillation $\tau$ is:

$$ \tau = \frac{T \pm \Delta T}{10} = \frac{T}{10} \pm \frac{\Delta T}{10} $$

So you divide your error by 10 and the error in the time for a single oscillation is $\pm 0.001$ seconds.

Carl's point arises if you measure a single oscillation ten times in separate measurements. In that case if $T$ is now the sum of all ten times, and $\Delta T$ is the error in any single measurement the time for a single oscillation is:

$$ \tau = \frac{T}{10} \pm \frac{\Delta T}{\sqrt{10}} $$