 is someone came up with an equation that represents a smooth curve that often represents things that happen in nature. And that allows us then to, if we see something that can be represented by the smooth curve to not have to do that, you don't have to go through the math so much because we can do it within Excel. But all we have to do is recognize it and then we can basically use the formula to make predictions about something. So this represents the number of successes in a fixed number of trials. So we'll take a look at examples like sales made in a fixed number of sales calls. So usually the characteristics of this kind of distribution will be that there's gotta be something that has like a yes or no outcome to it. So if you're saying that you're making a number of sales calls, then you're either gonna have a success or non-success. That's why it's gonna be binomial. We can basically say, well, if I get a sale during that call, success, not sale is a not success. If you're thinking about a coin flip situation, then you can do a similar type of test which we'll look at some examples on where you would label the heads or the tails, but let's say the heads as a success and the tails as a non-success. And then we would need to know the percentages of each of those activities in terms of the likelihood of it being a success or not. A coin flip basically being 50-50, a sales call usually being a lot lower for the success, 10% success or something like that. So we'll get more into the specifics again of when something in actual practice will typically follow a binomial distribution. And if it does, then we can use this concept to make predictions about the future. And importance of mathematical models so allows for quantitative analysis. So obviously, if we can get a mathematical model, remember, when we're taking a dataset, the dataset could be any jagged line, just like we said when we looked out the window, it might not have any curve that can easily represent the data. If that's the case, then the data's not useless. We might be able to use calculus or use some complex methodology to take that data and extrapolate it into the future and possibly get some predictive power from it. But if there is a mathematical model that it can be represented by, which is some form of line or a curve, then we have a really nice, powerful tool in order to plug numbers into that equation to give us more insight about what's actually happening. Helps making predictions, assists in understanding underlying phenomenon. So if we know the characteristics of what goes into a particular curve normally, and we see that some data is following that curve, then that might give us some better understanding about actually what is happening within the world. So conclusion, understanding the shape of data is fundamental in statistics. So clearly we need to know what the shape of the data is, which we can use in non-mathematical terms, meaning we can plot the data and use terms such as, it's skewed to the left, it's skewed to the right, it's centered, it's got two peaks and whatnot. And we can then use mathematical models to provide a framework to describe, analyze, and predict. And then we can get into more technical, actual mathematical models, not always something we can do for every data set. We can't do it for every data set. We can do it for those data sets that we see a pattern where the curve is approximating, something that we know to be represented by a line or curve, which happens a lot because nature seems to follow patterns. So if we can recognize those, then we can use these. So combining shape, center, and spread provides a holistic view of the data. So that's the theme of the course here. We cannot represent data with just one number typically because really to represent what is going on, we need to know more and you can summarize that in terms of the shape, the center, and the spread of the data, which we can see pictorially with a histogram and possibly be able to use more mathematical calculations to represent those numbers as well so we can get more specific on the mathematical side. And if we can do that, that would be great.