ELI5: Explain Like I'm 5

Empirical distribution function

Oh hello there! Do you like ice cream? Imagine you went to an ice cream store and you were given samples to taste. Each sample had a different flavor and you rated them from 1 to 10, with 10 being the best one. Now, let's imagine that you tried 10 different samples and you rated them accordingly.

The list of those ratings is like a recipe card for us to make a chart. We want to make a chart to show how often each rating occurred. But we want to do it in a way that is easy to understand, so we're going to draw a graph.

This graph is called an empirical distribution function, which is just a fancy way of saying we're graphing the number of times each rating occurred. We're making a little mountain out of Lego blocks to show how we rated each sample.

We're going to start with the lowest rating and work our way up to the highest rating. For each rating, we're going to count how many times we gave that rating. We'll put that number of blocks on the graph at the corresponding rating.

For example, if we gave a rating of 2 to one sample, we'll put one block at the rating of 2. If we gave a rating of 5 to three samples, then we'll put three blocks at the rating of 5. We keep doing this for all the ratings until we reach the highest rating we gave.

Once we're done, we'll have a nice mountain graph that shows how often we rated each sample. This is called an empirical distribution function. It tells us the frequency of each rating we gave, and we can use this information to see which flavor of ice cream we liked the best.

Hope you had fun making this mountain graph with me!