 Now we want to look at the uncertainty of the average value of all that data combined. Now as we said before, if you take lots of readings you are going to know that average value better and better the more readings you take and so the calculation for the the uncertainty of the average value is going to reflect that the more readings you take the better you know that value or the smaller the uncertainty will be. So the uncertainty of the average value starts off again with the half range because obviously it depends on how scattered that data is but we're going to divide it by the square root of the number of measurements that we took or the number of readings we took. So in our example here we would have one half of the range which is 0.06 divided by the square root of five readings that we took and that gives us if I've done my calculations right 0.0134 volts. Now remember this is an uncertainty and we really can't specify our uncertainties to better than one significant figure as we've talked about before. What we'd need to do is round to this one significant figure there but we also always need to round up so we don't underestimate our uncertainty. So what that gives us in the end is the uncertainty on the average value of the voltage 0.02 and you'll notice here that the uncertainty on our average value and we looked at five readings was 0.02 whereas on an individual reading or individual measurement it would be 0.03 so the fact that we took more measurements has given us more certainty on what that average value is and I'm just going to over here give our final answer. So our voltage is the average value that we got plus or minus the uncertainty 0.02 and that would be our final answer and the only other thing I wanted to point out here was that this range that we've got here 1.56 plus or minus 0.02 suggests that the true or that average value lies between 1.54 and 1.58. Now we do have individual readings which are outside of that range but that's just because of random errors and by taking lots of data we can pinpoint that average value with a bit more certainty.