Parameter Vs. Statistic: What’s The Difference?

Science Terms

Statistics and research have their own jargon and technical terms, and they’ve taken on an aspect of mysticism, making people believe they’re hard to understand. Most of the basic concepts, however, like the difference between a parameter and a statistic, aren’t complex once they’ve been explained to you.

Parameter and statistic are both statistical terms used in research to describe different groups. While both are used to describe populations being studied, it’s important to understand the difference between the two, as it has an effect on results.

In short, the parameter is the entire population being studied, while a statistic is a sample of that population used for research purposes. For example, in polling data, researchers want to find out what the entire population of likely voters thinks of the candidates.

It’s not reasonable to poll every registered voter in a state, so they’ll select a sample of 2,000 voters to ask instead and then extrapolate to the rest of the population.

Key Takeaways:

Parameter	Statistic
The parameter is the entire population that is being studied.	A statistic is a sample used as a representation of the entire population being studied.
Variables used for the parameter are typically capital letters or letters from the Greek alphabet.	Variables used for the statistic are usually lowercase Latin letters, several with diacritical marks.
An example of a parameter would be the entire United States population of high school students.	An example of a statistic would be 2,000 high school students from the midwest.
A parameter or population is an entire group of people, objects, countries, animals, plants, organizations, or whatever you happen to be studying.	A statistic is a sample taken from whatever the parameter is. This means it’s a subset of whatever group of people, countries, organizations, animals, objects, or plants you’re studying.

What Is a Parameter?

A parameter is a population that is being studied for a particular research project or poll. A population need not be limited to people, either, as any project that looks into a statistical analysis of a large group of a similar type is a population.

That means that if you’re looking into how much the feral cat population drops in the state when a spay and neuter program is implemented, this means the entire feral cat population of the state is your parameter.

It need not be anything that we would call a “population” in everyday speech, either. If you want to look into if the average weight of granny smith apples in the northwestern region of the United States has changed in the last twenty years, then all the granny smith apples of the northwestern region of the United States are your population.

If it’s possible, a whole population may be sampled, as that would give the most accurate result of the data. However, due to the fact that most populations are too large to reasonably sample, it’s very unusual for that to be the case.

Different variables are used to represent parameters rather than statistics as well. Parameters are typically represented by Greek letters, such as μ (mu) for the mean and σ (sigma) for the standard deviation. Capital letters are also used, such as a capital P representing the proportion.

What Is a Statistic?

A statistic is a sample taken from the population or parameter. The size of the sample taken will vary depending on the size of the population and how accurate of a result the researchers are aiming for.

Many of the samples for polling and surveys are in the 2,000 to 3,000 range, as that has reasonably high reliability and is possible to orchestrate. In general, statisticians like to have as large of a sample as possible, as that translates into less possibility for error.

That would mean that if you were studying how much time American high school students average playing video games per week, then rather than sampling the entire population of high school students, the students of an individual high school may be sampled. The students of that high school would therefore be the statistic.

If the researchers are looking for a more accurate result for the entire population, or wish to compare differences in different parts of the country, then sampling different high schools would be recommended. However, budget, time, and feasibility all play a role in how large the sample ends up being, as well as how varied.

Variables used to represent samples are typically Latin letters, though several of them have additional marks. Such as p̂ (p-hat) to represent proportion x̄, (x-bar) for the mean, and just the lowercase letter s for the standard deviation.

Parameter vs. Statistic FAQ

Is the mean a statistic or a parameter?

The mean of a research population is neither a statistic nor a parameter. Rather, the mean is calculated from the statistic or sample of the population taken and then extrapolated to apply to the parameter.
Why are samples used in research?

Samples are used in research because trying to study an entire population isn’t feasible. If for instance, you are studying the average height of every orange tree in Florida, it’s completely unreasonable to measure every tree in every Flordia orchard, as well as the private orange trees people own.

Therefore you will select a sample number of trees and measure those, then extrapolate that number to the entire population.
How do you know whether a number is a parameter or a statistic?

A number is a parameter if it represents the entire population, and it’s a statistic if it’s a sample taken as a representation of the population. Therefore, in order to determine whether a number is a parameter or a statistic, you have to consider a few things.

One is the size of the number. The entire population is likely to be a very large number, while a statistic will be something far smaller. Second, the context around it. Does it describe an entire population or just a piece of it?

Lastly, the variables used surrounding it. Variables for a parameter are usually capital letters or Greek letters, while for a statistic, they’re lowercase, often with diacritical marks.
What’s the difference between descriptive and inferential statistics?

The difference between descriptive and inferential statistics is that descriptive statistics describe the characteristics of a set of data, while inferential statistics are for the purpose of testing a hypothesis.

This means that inferential statistics are to help you generalize the data you gathered from your sample and see if it’s possible to apply to the entire broader population. Descriptive statistics, on the other hand, are used to assess and categorize the data that you gathered from the sample population.

Science Terms

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Author

Di Doherty

Di has been a writer for more than half her life. Most of her writing so far has been fiction, and she’s gotten short stories published in online magazines Kzine and Silver Blade, as well as a flash fiction piece in the Bookends review. Di graduated from Mary Baldwin College (now University) with a degree in Psychology and Sociology.

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