Join Eddie Davila for an in-depth discussion in this video Bell-shaped curve, part of Statistics Foundations: Probability.
- Three teachers, each has a class of 20 students, each gives an exam. How did these three classes do on an exam? In class number one, quite a few students scored 90 or above and not too many scored below 80. The histogram is skewed to the right, or negatively skewed. Class number two skews to the left, or positively. Most of the exam scores are below 80%. And when we look at class number three, the distribution is all over the place, some high scores, some low scores, some in between. It's hard to find a pattern in class number three. Interestingly, many things do follow a pattern. In the case of heights of people, or national standardized test scores, even health data, often we find that data follows a pattern. Data will take on this bell shape for its probability distribution. When we see a bell-shaped curve, what exactly are we looking at? First, the mean of the data is centered at the highest point of the curve. Second, we'll notice that the data is symmetrical on each side of the mean. In other words, 50% of the data is above the mean, 50% is below the mean. Third, the farther we get from the mean, the lower the probability of those outcomes. The curve gets closer and closer to the X-axis. Also notice the curve never touches the axis. It just keeps going on and on to infinity in either direction. One other thing to remember. The area under the curve is equal to one, which means that the area under the curve accounts for 100% of the possible outcomes. This is what we call the classic normal curve. It is vital to understanding probabilities, especially when you're told that the data is normally distributed. In statistics, when you're told that the data are normally distributed, it's telling you that the data are taking on the shape of a normal curve. Not all normal curves are created equal, though. These are both normal curves, but one of them is taller and more narrow. This indicates many, if not most data points are very close to the mean. Thus, a taller, more narrow curve has a smaller standard deviation. On the other hand, the flatter curve has data points that are more distributed. A majority are close to the mean, but others are more distant from the mean, thus this curve has a larger standard deviation. Still, you might be asking why is this so important? How many data sets are bell-shaped? Well, believe it or not, in nature, the normal distribution is very common and it seems to show up nearly everywhere. So as you hone your statistical skills, make sure to become familiar with the normally distributed bell curve.
Eddie explains that probability is used to make decisions about future outcomes and to understand past outcomes. He covers permutations, combinations, and percentiles, and goes into how to describe and calculate them. Eddie introduces multiple event probabilities and discusses when to add and subtract probabilities. He describes probability trees, Bayes’ Theorem, binomials, and so much more. You can learn to understand your data, prove theories, and save valuable resources—all by understanding the numbers.