 This is a histogram of the number of measurements taken at any given measured value. And this is for data that has a normal distribution. It means that if you take a data point, it might lie at this measured value. You take another data point, it might lie here and one might lie here. But what you would find is if you took repeated readings over and over and over again, that most of them would be clustered in the middle. And you would have fewer as you went further away from the mean value, which for a normal distribution would be right in the center. It's possible that you might have one or two at the very extreme values all the way out there. And for the purposes of our U11 analysis of data, we're going to call this distance here between the most extreme value on each side. That whole distance there is called the range. And we'll often refer to the half range, which is obviously just that length of one of those from the center out to the extreme value. What we're going to talk about in this video are two ways to quantify the uncertainty. One is the uncertainty on a single measurement. And what is the uncertainty for the average value of a whole bunch of repeated readings? Working at the uncertainty for an individual measurement is actually pretty straightforward. We just need to say, given any individual measurement that we take, how far from the average value is it likely to be? So if we took a measurement, we would know that that measurement would be within that half range from the average value. We can only estimate that uncertainty for the individual measurement after we've taken a whole bunch of data to see what that distribution looks like. How certain we are or uncertain we are about the average value depends on how many measurements we've taken. If we've only taken a couple of readings down here and took an average, it might be that our average was a little bit further this way or a little bit further this way. It's actually really hard to tell if you've only got, say, two or three measurements. The more measurements you take, you actually see this pattern starting to build up, which gives us this nice curve here. So the more measurements you take, the more tightly constrained this average value is. And we'll see how we can quantify that, put a number on that. If we take repeated readings, how we can give a number to the uncertainty of that average. Here is an example. I have five trials or repeated readings of measuring the voltage across a power supply. Now you'll learn more about that when we get to the electricity unit, but you probably come across something like it at high school. I am not going to go through the maths because I'm sure you can do it to work out the average value of these five readings. And it's 1.56 volts. Now just keep in mind that this statistical analysis that we're doing here is not particularly sophisticated, but it will do for the level of the stuff that we're looking at in this course.