When picking the right estimator in statistics, it’s really important to understand two big ideas: bias and variance.

Bias is about the difference between what we expect from an estimator and the real value we're trying to find.

An estimator is called unbiased if what we expect matches the true value.

For example, if we want to find out the average height of all students in a school, we might take a group of students and find their average height. If this average equals the actual average height of all students in the school, then it’s unbiased.

Now, let’s talk about variance.

Variance is a way to measure how much the estimator can change when we use different samples.

If we have high variance, it means the results can look really different from one sample to another.

So, if we keep taking different groups of students to find their average height, a high variance means those averages could be very different each time.

When we choose an estimator, we have to think about both bias and variance.

This balance is called the bias-variance trade-off.

Ideally, we want an estimator that does not have any bias and has low variance.

But in real life, we might need to find an estimator that balances both bias and variance well, so we get reliable estimates to help us make decisions.