This tutorial introduces normal distributions. Now we don't say the word normal because it's the most common or because it's normal and all the other ones aren't. That's just a name that we use to refer to it.
So another set of names we could use to refer to a normal distribution are bell shaped, bell curve, Gaussian, or Gaussian curve. All of those words mean exactly the same thing. We're all talking about the same shape, any of those words that we use. So I might switch between them, other things you read or are looking at might switch between them, but they're all talking about the same thing.
What is it that they're talking about? They're talking about a single peaked distribution. It's symmetric. And the mean, median, and mode are all the same.
Now with a normal distribution, one reason that they're so useful is if we know what the mean and the standard deviation are, then we can totally characterize the curve. We can draw a picture of it. Here's some examples.
Now, this graph here shows several normal curves. The information they gave us is the mean and the variance. So then I took the variance, I took the square root of that, to give us the standard deviations. Now just as a reminder, normal, again, is not saying that the other kinds of curves are abnormal. It's just that this follows this particular distribution.
So here, we can figure out that the mean is telling us where the peak is occurring. Because look here, for the blue, the red, and the yellow curves, the mean is all at 0. And then if we look here, our axis, the x-axis, is 0. And we hit the maximum for the yellow, the blue, and the red.
Now the mean for the green curve is -2. And then again, if we look on the x-axis to -2, we see the peak for the green curve. So that's what the mean is telling us.
Now the standard deviation is giving us a clue about how spread out the data is. Here, where the standard deviation is 0.45 for the blue, it's the smallest standard deviation of the set. And we can see here that the blue curve has the data that is the closest to the mean. And there's not very much data that is spread out from it that's far away. So the blue has the data that's concentrated the closest to the mean.
On the other hand, the yellow has the highest standard deviation. And we can see here that the yellow is a relatively low and flat curve. It has a lot more data that is spread out from the mean, and that's what the standard deviation is telling us.
So normal curves, as long as you know the mean and the standard deviation, you can get a picture of it. This has been your tutorial on the normal distribution. Normal distributions can be completely characterized by the mean and the standard deviation.