Estimator facts for kids

An estimator is like a smart rule or a special recipe that helps us guess something we don't know for sure. Imagine you want to know the average height of all students in your school. You can't measure everyone, right? So, you pick a smaller group, like your class, and measure their heights. The rule you use to calculate the average height from your class is the estimator. The average height of your class is the estimate, and the actual average height of everyone in the school (which you don't know) is the estimand.

Think of it this way:

• Estimator: The method or formula you use to make a guess.
• Estimand: The true value you are trying to guess.
• Estimate: The actual guess you get from using the method.

What is an Estimator?

An estimator is a tool used in statistics to make educated guesses about a larger group based on a smaller sample. It's a bit like trying to figure out what's in a big box of candies by only looking at a handful. The handful is your "sample," and the way you guess about the whole box is your "estimator."

Why Do We Use Estimators?

We use estimators because it's often impossible or too expensive to measure everything. For example, if scientists want to know the average temperature of the ocean, they can't measure every single drop of water. Instead, they take many measurements at different places and depths. The method they use to combine these measurements and guess the overall average is an estimator.

How Do Estimators Work?

Estimators use information from a small part of a group to make a good guess about the whole group. For instance, if you want to know the average age of people who live in your town, you might ask 100 people their age. The estimator would be the rule you use to calculate the average age from those 100 people.

Different Kinds of Estimators

There are many different types of estimators, each designed for specific situations. Some common ones include:

• Mean: This is the average, like when you add up all the numbers and divide by how many there are. It's often used to estimate the average of a larger group.
• Median: This is the middle number when all numbers are listed in order. It's useful if there are some very high or very low numbers that might skew the average.
• Mode: This is the number that appears most often. It's good for estimating the most common value.

Unbiased and Biased Estimators

When we use an estimator, we want it to be as accurate as possible. Statisticians have special words to describe how good an estimator is: unbiased and biased.

What is an Unbiased Estimator?

An estimator is called unbiased if, on average, it hits the target exactly. Imagine you're playing darts, and the bullseye is the true value you're trying to guess. If your darts (your estimates) sometimes land a little high and sometimes a little low, but on average they land right on the bullseye, then your throwing method (your estimator) is unbiased. It doesn't consistently guess too high or too low.

Example of an Unbiased Estimator

Let's say you want to know the average height of all 8th graders in your country. If you randomly pick many different groups of 8th graders and calculate their average height, an unbiased estimator would mean that the average of all those sample averages would be very close to the true average height of all 8th graders in the country.

What is a Biased Estimator?

An estimator is called biased if it consistently misses the target in one direction. Using the dart analogy, if your darts always land a little to the left of the bullseye, then your throwing method is biased. It's systematically guessing too low or too high.

Example of a Biased Estimator

Imagine you're trying to estimate the average number of hours students spend on homework each week. If you only ask students who are known to be very studious, your estimate might be too high. The method of only asking studious students would be a biased estimator because it consistently overestimates the true average.