In this video, learn how to describe, calculate, and interpret percentiles.
- To get accepted into a prestigious graduate program, you'd likely need to take a standardized exam. GRE, GMAT, LSAT, MCAT, et cetera. If your score is recorded in the 98th percentile, what does that mean? Well, among all the people that took it, your score was in the top 2%. Nice job. Here's another example. If we look at US annual incomes, in 2018, someone that had an annual income of $250,000 was in the 95th percentile, the top 5%, while an annual salary of $63,000 put you in the 50th percentile. In other words, 50% of the adults in the US had higher incomes. Therefore, this is also our median. Percentiles are easy to understand, but how do we calculate percentile rank? Well, there are actually a few acceptable methods but here is one that is fairly easy to use. Let's use these 20 exam scores as our data set. If someone scored an 85%, what would be their percentile rank? Don't get confused, 85% is their score but it isn't necessarily their percentile rank. So let's use a formula. The total number of values is 20, because we have 20 exam scores in our dataset. Next, we count up how many values are below the score of 85%. We have two scores of 85, so we don't count those nor do we count any scores above 85, so there are only six scores below 85 and this is how we set up our formula. According to this, we get an answer of 32.5 and in percentiles we always round down. So a student that scored an 85% on their exam is in the 32nd percentile. How about the one student in the class that got a hundred percent on the exam? We use the same formula. 20 is the total number of values. 19 is the number of values below 100%. Here we get 97.5, so this student is in the 97th percentile. You might be asking why isn't the top student in the hundredth percentile? Well, the hundredth percentile is not possible, since that would be like saying you're in the top 0% of your class. So the top student would likely say they're in the top 1% or in the 99th percentile. But in this situation, the top student is in the 97th percentile. Why didn't we put them in the 99th percentile? Well, according to the formula, the 97th percentile would be the highest value for a dataset of 20 exam scores. More data would lead to more precision, so if we had more exam scores, it is likely that the highest score would be in the 99th percentile. Other techniques for finding percentile may differ as does Excel's method for finding percentile, but don't worry about it. Most calculations will give you fairly similar numbers and often as the size of the data set gets bigger, these differences become negligible. So for those of you that are ultra-competitive, now you'll have the ability to set your goals by using percentiles.
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.