Hodges' estimator

Okay kiddo, so let me tell you about Hodges' estimator. Do you remember when we learned about averages? It's when you add up a bunch of numbers and then divide by how many numbers there are to get the "average" of all the numbers. Well, Hodges' estimator is another way of finding the "average".

Let's say you have a bunch of numbers, like 3, 5, 7, 9, and 11. And you're trying to find the average of these numbers. To do that, you add them up and divide by how many numbers there are. So, we add 3 + 5 + 7 + 9 + 11, which equals 35. And since there are 5 numbers, we divide 35 by 5 to get an average of 7.

Now, Hodges' estimator is different because it doesn't just use the average of all the numbers. It actually looks at each individual number and figures out if one of them is really different from the others. That number is called the "outlier".

Let's say that one of our numbers in the list was actually a mistake and shouldn't be there. Like maybe we accidentally put in 31 instead of 11. Well, that's a really big mistake and it would make our average way off. But with Hodges' estimator, it would look at all the numbers and figure out that something was wrong. Then, it would "toss out" the outlier (31 in this case) and use the average of the other numbers (3, 5, 7, and 9) to get a better estimate of what the "real" average is.

So, that's the basic idea of Hodges' estimator. It's a way to find the average of a bunch of numbers, but it's smarter because it can detect mistakes and give us a better estimate of what the average should be.