You are sitting in class and the teacher mentions a parameter in statistics. You nod, but deep down, you are confused. Is that the same thing as a statistic? Is it a variable? Do not worry, because this is one of the most common mix-ups for beginners.
In this guide, we will clear up the confusion once and for all. We will explain what a parameter actually is, how it differs from a sample statistic, and give you a simple memory trick so you never forget the difference on an exam.
The Simple Definition
To understand a parameter, you first need to understand a population. In data language, a population is the entire group you are interested in. It could be every single person in the United States, every student in your school, or every pizza ordered in New York City last night.
A parameter is a number that describes that entire population. It is a fixed, true value. For example, if you measure the height of every single student in your high school and calculate the average, that average is a parameter. It is not a guess. It is a fact about the whole group.
Parameter Vs Statistic
This is the most important part of the article. You need to know the difference between these two terms to pass your class. A parameter describes a population. A statistic describes a sample.
There is an easy way to remember this called the P-P and S-S trick. Parameter goes with Population. Statistic goes with Sample.
If you survey ten people to guess what the whole town thinks, that number is a statistic. If you interview the entire town, that number is a parameter.
Why Parameters Are Rare
You might wonder why we do not just use parameters all the time. The answer is practical. It is usually impossible or too expensive to measure an entire population. Imagine trying to weigh every single fish in the Atlantic Ocean. You simply cannot do it.
The parameter exists, but we will never know it exactly. That is why we use statistics. We take a sample, calculate the statistic, and use it to estimate the unknown parameter.
Symbols To Watch Out For
In your textbook, you can tell if a number is a parameter just by looking at the symbol. Parameters usually use Greek letters. For example, Mu represents the population mean, and Sigma represents the population standard deviation.
Statistics usually use English letters. For example, x-bar represents the sample mean, and s represents the sample standard deviation. If you see a Greek letter in a formula, you know you are dealing with the whole population, not just a sample.
Key Takeaway
A parameter is a fixed number that describes an entire population. Just remember the rule: Parameter is for Population. Since it is hard to measure everyone, we usually use sample statistics to guess the parameter.
Frequently Asked Questions
Can a parameter change? Usually, we treat it as a fixed value at a specific point in time. However, populations change over time, so the parameter can change too. The average height of humans today is different from the parameter five hundred years ago.
Is a census a parameter? A census is an attempt to collect data from the entire population. If the census is 100 percent successful, the result is a parameter.
Why do we use Greek letters? Mathematicians use Greek letters to show that the value is the absolute truth of the population, distinguishing it from the estimated values derived from samples.
Ready to describe your data? Check out our guide on What Is Descriptive Statistics to see how we summarize these numbers.