# Biased & Unbiased Estimators: Definition & Differences

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• 0:02 What Is Bias?
• 0:55 Difference Between…
• 1:48 Conceptual Example
• 2:47 Mathematical Example
• 3:49 Lesson Summary

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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

When dealing with statistics, you've probably heard about why it is wise to avoid biased estimators. However, as this lesson proves, sometimes a biased estimator can be pretty useful—if you know how to use it.

## What Is Bias?

While we would prefer that numbers don't lie, the truth is that statistics can often be quite misleading. For that reason, it's very important to look at the bias of a statistic. Bias is the distance that a statistic describing a given sample has from reality of the population the sample was drawn from. Now that may sound like a pretty technical definition, so let me put it into plain English for you. If you were going to check the average heights of a high school by looking at a sample of 15 students, you wouldn't just call for members of the basketball team. That sample would not be reflective of the heights of everyone in the school because basketball players tend to be tall. In this lesson, we're going to look at the difference between biased and unbiased when trying to make estimations based off of statistics, as well as to look at two different examples of bias.

## Difference Between Biased and Unbiased

As you might have imagined, statisticians like to avoid bias when they can. In fact, they would often rather work with unbiased data, which is to say a sample that eventually corresponds to the true nature of the population size. In plain English, if the real average height for a high school is 5'5'', then a statistician wants a sample that will give her a sample average height of around 5'5''. However, that doesn't mean that unbiased is always better than biased. In fact, when we can't find a perfectly accurate and random unbiased sample, a biased sample can still prove to be pretty useful. However, there is a catch. For us to get any real use out of a biased sample, we had best know how it is biased and just how much of a bias there is. To see how this looks, let's take a look at a couple of examples.

## Conceptual Example

The first example I want to give you is completely conceptual, meaning that we won't be using numbers to prove it. Let's assume that you are up to bat during a baseball game. You're right-handed, but you've got a problem. You've hit three foul balls in a row! However, the performance of those foul balls can be called biased - each lands just foul of left field. You know that if you can straighten out your swing that you'll be able to hit a home run, but how can you use the information you've got to do so? If you understand baseball and the idea of a biased performance, it's simple.

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