Hey everyone. So in this series of videos we're going to talk about the Gaussian distribution. First realize that performing an experiment numerous times with no systematic error results in a smooth curve called the Gaussian distribution. Here we have an image of a typical curve. With this curve we have our f(x), which serves as our function. x here represents our population as a whole. With this we have our formula, but what's most important in terms of this formula is what do these variables represent.

If we take a look at this curve in terms of the Gaussian distribution curve, increasing the number of measurements in the experiments changes the mean. Remember mean is just our x with a line on top. It's going to transition to μ, so μ looks like this. This represents the population mean or average. Here is our μ, and one thing about it is that it's always in the exact center of our curve.

Next, we're going to say it changes our standard deviation, which is typically s, to Sigma. So Sigma is this. If we take a look here at our curve, here goes Sigma, and Sigma looks like it is the distance from the exact center of our curve, which is μ, to the edge of one of the other parts of the curve. Here on this side, it also represents Sigma, and this is going to represent our population standard deviation.

Now the shape of the Gaussian distribution curve can occur here if we change our μ, it'll shift the population distribution curve to the left or to the right. Remember we said that μ represents the exact center of our curve, our population mean. So if I made μ here, that would mean that the curve shifts now the exact center more or less is right here. If I made here, then it would be like this. If we change our standard deviation, our population standard deviation, which is Sigma, it's going to increase or decrease the broadness of the distribution curve. So if we had a very high population standard deviation, that means we'd have a very broad curve.

Right? So here's μ, and then here goes our standard deviations on either side. If I had a very small population standard deviation, a very, very low one, that means our curve would be very thin, very narrow. So here's μ again, and since our Sigma is so small, the distance from μ to one side of the curve will be very, very narrow. Okay. So just remember these are the key variables associated with any typical type of Gaussian distribution curve.