Probability and Statistics > Basic Statistics > What is a Parameter in Statistics?

This article is about **population parameters.** For the parameters you would use to define a probability distribution, see: What is parametrization?

## What is a Parameter in Statistics?

In math, a parameter is something in an equation that is passed on in an equation. It means something different in statistics. It’s a value that tells you something about a **population** and is the opposite from a statistic, which tells you something about a *small part *of the population.

A parameter **never changes**, because everyone (or everything) was surveyed to find the parameter. For example, you might be interested in the average age of everyone in your class. Maybe you asked everyone and found the average age was 25. That’s a parameter, because you asked everyone in the class. Now let’s say you wanted to know the average age of everyone in your grade or year. If you use that information from your class to take a guess at the average age, then that information becomes a statistic. That’s because you can’t be sure your guess is correct (although it will probably be close!).

Statistics vary. You *know* the average age of your classmates is 25. You might guess that the average age of everyone in your year is 24, 25, or 26. You might guess the average age for other colleges in your area is the same. And you might even guess that’s the average age for college students in the U.S.. These may not be bad guesses, but they are statistics because you didn’t ask everyone.

### Origin of the word **Parameter**

This word is found in 1914 in E. Czuber, Wahrscheinlichkeitsrechnung, Vol. I and in in 1922 in Ronald A. Fisher’s, “On the Mathematical Foundations of Theoretical Statistics.” Fisher was an English statistician, biologist and geneticist.

### What is a Parameter in Statistics: Notation

Parameters are usually Greek letters (e.g. σ) or capital letters (e.g. P). Statistics are usually Roman letters (e.g. s). In most cases, if you see a lowercase letter (e.g. p), it’s a statistic. This table shows the different symbols. Some might look the same but look closely for small and capital letters.

Measurement | Statistic (Roman or lowercase) | Parameter (Greek or uppercase) |

Population Proportion | p | P |

Data Elements | x | X |

Population Mean | x̄ | μ |

Standard deviation | s | σ |

Variance | s^{2} |
σ^{2} |

Number of elements | n | N |

Correlation Coefficient | r | ρ |

**Tip:** In statistics, the word parameter rarely pops up. That’s because ALL we deal with is statistics! You might see something like “population mean.” That makes it more obvious it’s about the whole parameter. When you see just “mean,” that’s usually a statistic.

### What is a Parameter in Statistics: Accuracy.

Accuracy describes how close your statistic is to a particular population parameter. For example, you might be studying weights of pregnant women. If the sample median of your population is 150 pounds and your sample statistic is 149 pounds, then you can make a statement about the accuracy of your sample.

Statistics in general aren’t as accurate as we’d like, although they are the best tool we have right now for making predictions about populations. According to The Economist, scientific papers aren’t very reliable. John Loannisis, a Greek epidemiologist, thinks that as many as *50 percent of scientific papers turn out to be wrong.*

Factors that contribute to false results include sample sizes that are too small, poorly designed studied and researcher bias caused by financial interests or personal agendas.

## Q. In a census, how do the statistics that get computed compare to the population’s corresponding parameters?

Before you start, you may want to read this article: How to tell the difference between a statistic and a parameter.

What this question is really asking is, *how accurate is the census?*. The answer is (surprisingly) that the census is very accurate, give or take a tiny percentage. That tiny percentage is more likely to be minorities, people of lower income and people who live in rural areas.

At the time of writing, the most recent census was the 2010 census. Historically, the census is getting more accurate:

The 2010 census stated that the total population of the U.S. was 308,745,538 in 2010, a 9.7 percent increase from the 2000 census count. It over-counted the total U.S. population by 0.01 percent. That’s only 36,000 people — not bad when you consider the population of the U.S. is over 300 million. Compare that to an over-count of 0.49 percent in 2000 (about one million people) and an under-count of 1.61 percent in 1990.

Some key facts:

- Renters were under-counted.
- Homeowners were over-counted.
- 2.1 percent of black Americans were missed. According to the Denver Post, this was a huge improvement over the 1940 figures, when it was estimated the black under-count was 8.4 percent.
- 1.5 percent of Hispanics were missed.
- Non-Hispanic whites were over-counted.

### Why are these groups not counted as accurately?

**Accessibility: **People in rural areas can be hard or impossible to reach by mail. Some locations use “general delivery” addresses rather than fixed addresses.

**Language barrier and education: **People who are learning the English language may have difficulty understanding the census form. People with lower education and literacy may also not understand the importance of responding to the census.

**Suspicion of the Government: **Some people may think that the census will be used against them. Some people don’t want to be in a government database. For example: illegal immigrants, people with warrants out on them, people owing debts or child support.

**What is a Parameter in Statistics: Related article:**

How to tell the difference between a statistic and a parameter.

## References

Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.

Kotz, S.; et al., eds. (2006), “Parameter”, Encyclopedia of Statistical Sciences, Wiley.

Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics, Cambridge University Press.