# Finding the random uncertainty of a set of values

Tags:
1. Mar 29, 2016

### 123leo

• Thread moved from the technical forums, so no Homework Help Template is shown
Ok, for the switch-on voltage of a red LED I have the readings as follows, all in volts: 1.45, 1.46, 1.46, 1.44, 1.45. The mean of these readings, in volts, is 1.45 (I rounded up to 2 decimal places as my scale reading uncertainty was +/-0.01V, and my teacher told me to round them up since to state my scale reading uncertainty for the mean the mean will have to have the same number of decimal places as the scale reading uncertainty). Now, my random uncertainty for these values is +/-0.004V, which is not to 2 decimal places (it's to 1 significant figure). So, I was wondering if I would have to make my random uncertainty have 3 significant figures (+/-0.00400V?) to express the random uncertainty in absolute form (Mean Value+/-Random Uncertainty). And if I did so, would it be, in terms of physics, correct?

Last edited by a moderator: Mar 29, 2016
2. Mar 29, 2016

### drvrm

To get the uncertainty in one measurement, we need to know the uncertainty in the mean, x .
We expect that because the mean takes into account multiple measurements, its uncertainty will be less than that for a single measurement Indeed this is so.
The standard deviation of the mean, or standard error, is defined as: Sigma(x bar) = sigma (x)/ sqrt (N)

where N is the number of measurements of the quantity x.
The standard deviation of the mean is related to the uncertainty in one measurement, but is reduced because multiple measurements have been taken.
It is easy to see that the more trials performed in an experiment, the smaller the uncertainty will be.

Then for a series of measurements of one quantity x with independent and random errors, the best estimate and uncertainty can be expressed as: (value of x) = x(besT) +/- Sigma(xbar)

i think you should visit the following for details
<http://web.mit.edu/fluids-modules/www/exper_techniques/3.Statistical_Anal._of_Unce.pdf>

3. Mar 29, 2016

### mathman

Looking at the figures, .004 has all the significance that is possible for these data.

4. Mar 29, 2016