# Parameter

In inferential statistics, a parameter refers to a population parameter, which describes some characteristic of the population. The population parameter is related to a statistic in that a statistic is a numerical characteristic of the sample that estimates the corresponding parameter of the population. For example, if you were to poll a specific group of voters to determine how they plan to vote in the upcoming election, the results would be a statistic, since the group of voters does not represent all the potential voters. If every single potential voter were included in the poll (which is highly unlikely), then the result would be a parameter.

## Parameter vs statistic

As mentioned above, a parameter describes a characteristic of a population while a statistic describes a characteristic in a sample of a population. While a parameter never changes since it is a characteristic that is determined by surveying the entire population of interest, a statistic varies. This is because a statistic is based on a smaller portion of the population, so it can never fully represent the population.

Very generally, it is possible to determine whether a statement is a statistic or a parameter based on the likelihood that an entire population could have been measured, or if the exact number of subjects is known.

Examples

The following statements (all of which are fabricated) are parameters.

• 15% of the 56 dog owners in neighborhood A also own a cat.
• 8% of the 152 students in the senior class of high school B have taken a calculus course.
• 100% of all US presidents were older than 41 when they started their presidency.

The following statements (all of which are fabricated) are statistics. It is highly unlikely, or near impossible for the following populations to have been measured.

• 30% of all dog owners own, or have owned, more than 1 dog.
• 80% of all students in the United States have taken an algebra course by the time they graduate high school.
• 34% of all world leaders lived past the age of 85.