# Calculating uncertainty in data.

## Homework Statement

This is from a laboratory exercise. I was asked to measure the time it took for a pendulum to cover 3 periods. I repeated this 25 times, to get 25 measurements for as many trials. I also calculated the standard deviation from the measured data (calculated for different question).

The question I am stuck on, is however, the one that concerns finding the uncertainty in the overall average of the pendulum data. Any help is appreciated.

## Homework Equations

I am given this equation for finding the average uncertainty.

$$\sigma$$average = $$\sigma$$ individual/ square root of n
n being number of trials.

## The Attempt at a Solution

So, the equations asks for the uncertainties of individual measurements. Can I somehow calculate the individual uncertainties from the standard deviation or the average?

Thanks a lot.

What you are looking for seems to be the variance of measurements.
For the std-deviation of the mean value:
$$s_{m}=\frac{s}{\sqrt{n}}=\sqrt{\frac{1}{n(n-1)}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}$$

here then holds for n->infinity

$$s_{m}\rightarrow0\; s\rightarrow\sigma$$

with

$$s^{2}=\frac{1}{n-1}\sum(x_{i}-\bar{x})^{2}$$