Statistic vs parameter: What is the difference?

You might find yourself wondering what the difference is between a statistic and a parameter. The two terms are similar, so it’s easy to see how some might get a little mixed up. Well, we are here to clear up the confusion between statistic vs parameter.

What is a statistic?

A statistic describes a characteristic of just a subset, or sample, of a population. It is not a generalized claim; it applies only to the group of people to which it refers. When talking about statistics and reporting data in a given study, you would refer to the sample mean (x̄), sample standard deviation (s), and sample proportion (p̂).

What is a parameter?

Put simply, a parameter describes a characteristic of an entire population. So, a parameter applies to a larger group rather than just a sample of the larger group, as a statistic does. When reporting parameters in a given study, you would refer to the population mean (μ), population standard deviation (σ), and population proportion (p). Parameters are often used to generate estimates about expected outcomes, and are useful when a population size is so large that it wouldn’t be practical or possible to test every single subject in that population.

Examples

Let’s walk through an example. Imagine there is a study researching men’s wingspans. An example of a statistic in this study would be the average wingspan of the 200 men randomly selected to be a part of the study. An example of a parameter would be the average wingspan of ALL men. This is a parameter because “all men” refers to a large population and not just a select sample, as the statistic does. 

Let’s walk through a few more examples:

Imagine a study conducted to find out how long New York Times op-ed articles are. In this case, a parameter would be: In general, how long are New York Times op-ed articles? A statistic would be: How long are these particular articles that we have chosen to test?

Another example would be a study measuring the length of the tail of eastern grey kangaroos that live in Australia. A statistic would be the proportion of all eastern grey kangaroos that have tails longer than three feet. A statistic would be the proportion of the particular sample of kangaroos studied that have tails longer than three feet.

Statistic vs parameter: A quiz to test your understanding

For each of the following questions, try to figure out which statements (A or B) are parameters and which are statistics. Some of these statements will go hand-in-hand with one being a statistic and one a parameter; others will be standalone statements.

1)

A: 61% of registered voters in Utah support candidate Johnson

B: In a poll of 500, 58% of voters in Utah support candidate Johnson

2)

A: The average chicken at a farm weighs 1.8 pounds

B: Of 100 chickens that were tested, the average weight was 1.6 pounds

3)

A: A teacher surveys all 300 of his students to find out which proportion of them like his unique grading system

4)

A: The mean height of Russian men is 5′ 11″’

5)

An estimated 4% of people experience anxiety disorder

6) 

2 out of every 3 teenagers killed in car accidents were male

Scroll down to the following page when you’re ready with all your answers.

Answers to the test

1. A is a parameter and B is a statistic.
2. A is a parameter and B is a statistic.
3. This one is a little trickier since it specifies that a certain number of people are surveyed, which typically can indicate that it is a statistic. However, the word “all” is used so we know that an entire population is being surveyed, and therefore this is a parameter.
4. This is a parameter since it would be impossible to survey ALL Russian men.
5. This is also a parameter since it is talking about 4% of all people.
6. This is a statistic.

Sometimes it can be a little tricky to tell the difference between statistic vs parameter, hopefully this article has been useful and helped shed some light on the major differences.