# Parameter vs. Statistic – What Is The Difference?

12.02.23 Time to read: 5min
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In the sphere of statistics, understanding the distinction between a parameter vs. statistic is an imperative factor. A parameter is a numerical value that depicts a particular group of a whole population. In contrast, a statistic is drawn from a sample derived from that entire population. Inferences about a whole population are often made based on samples, which is why it is important to be able to distinguish parameters from statistics in order to ensure accurate representations and results.

## Parameter vs. Statistic – In a Nutshell

• Parameter vs. statistic values depend on the size of the sample used in research.
• A statistic is a variable and known number present in a small section of the population
• A parameter is a fixed and unknown numerical value representing the entire population
• You can use statistical notations to differentiate parameters vs. statistic.

## Definition: Parameter vs. Statistic

When differentiating a parameter vs. statistic, use the size of the groups. If you randomly survey a group of people that use a specific brand, the value you get is a statistic, since you only asked a small percentage of the entire population. In research, the terms parameter and samples are used to denote the extent of the research. In quantitative research, the researcher wants to understand the characteristics of a population by determining the parameters. Since it is unfeasible to collect data from an entire population, data is gathered from samples. In inferential statistics, the conclusions from sample statistics are used to infer and hypothesize about the population parameters.

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## Parameter vs. Statistic: Population vs. Sample

Estimating parameter vs. statistic relies on the population and samples collected for the research. A population represents the entire group you are surveying. You can research a group of people, organisms, countries, organizations, and objects based on your research. A sample is a small group that represents a percentage of a larger population. You will collect data from the samples to make educated guesses about the entire population.

Example

If you want to determine the level of support for abortion rights among US citizens, you are interested in data from the entire population. Since collecting data or surveying the entire population isn’t feasible, you use a random sample to make inferences. For instance, you can sample 4,000 participants for your research.

## Parameter vs. Statistic: Number types

When defining parameter vs. statistic, you summarize any measurable features of the population or sample.

Example

The average height of adult women in the UK is a parameter with an unknown value. In other words, the population parameters for this will be based on the standard deviation and mean of the population.

In research, you get sample statistics when you use the sample collected to calculate the mean and standard deviation. The most common types of numbers in parameter vs. statistic include:

• Categorical variables: The parameter or statistic used is a proportion.

Example

Population parameters: A proportion of all US citizens support abortion rights.

Sample statistic: A proportion of 3,000 US citizens support abortion rights.

• Numerical variables: The parameter vs. statistic numerical variables are reported using mean, median and standard deviation.

Example

Mean population parameters: Mean income of all adult men in the US.

Mean sample statistic: Mean income of 2,000 adult men in the US.

Standard deviation population parameters: Standard deviation of all men’s weight in the US.

Standard deviation sample statistic: Standard deviation of all men’s weight from one town.

### Statistical notation

Diverse symbols are used for parameter vs. statistic to indicate whether you are referring to a population or a sample. Latin and lowercase letters denote samples in most cases, while Greek and capital letters show populations. Some of the statistical notations of parameter vs. statistic include:

 Sample Statistic Population Parameter Mean Standard Deviation Proportion Size

## Distinguish a parameter from a statistic

In research reports and news, it can be challenging to determine whether a number is a parameter or a statistic. When differentiating parameter vs. statistic, use the following questions as a guide:

• Does the value represent the entire population, where every member participated in data collection?
• Can you collect data on a particular characteristic from every member in a reasonable time frame?

When you are distinguishing parameter vs. statistic, the size of the population or sample makes a difference. If the answer to the questions above is yes, the number is a parameter. If the answer is no, then the value represents a statistic.

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## Parameter vs. Statistic: How to estimate

In parameter vs statistic estimations, researchers use a sample to collect data from a large population and generalize the statistic to a broader population. Inferential statistics allow you to estimate population parameters from sample statistics. The two types of estimates about a population include:

• Point estimate: It provides a single numerical value of the population parameter based on the sample statistic. For example, a sample mean can be a point estimate of the population mean.
• Interval estimate: It provides a range of values where the parameter lies. A common interval estimate is the confidence interval.

Example

In your research on the support for abortion rights among US citizens, you could find that 56% of the sample supports abortion rights. You can estimate the parameter using point and interval estimates.

• The point estimate will be that 56% of US citizens support abortion rights.
• The interval estimate is the range of 95% confidence interval.
• The support for abortion rights could range from 52% to 60%.

## FAQs

#### What is the difference between a parameter vs statistic?

A parameter represents an entire population, while a statistic represents a sample. When differentiating parameter vs. statistics, the size of the population used in research matters.

#### How do you know when a number is a parameter or statistic?

If the number describes an entire population and you can collect data from every member, the value represents the parameter. When you are only sampling a section of the entire population, it is a statistic.

#### When is a sample used in research?

If you are studying a large population, you can study random samples and make inferences about the population. The population or sample used for data collection differentiates parameter vs. statistics.

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### Dzastina Ayenew

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Dzastina Ayenew started her studies in Romance languages after her professional training as a foreign language correspondent at Munich’s municipal foreign languages Institute. She is passionate about languages and helping students worldwide with their thesis and dissertations.