Is there a difference between parameter vs statistics?

Parameters and statistics are related terms useful in determining a sample size. They both have important roles in quantitative research as they enable researchers to clearly understand how a given data behaves in different circumstances.

A parameter is a variable kept constant during an experiment or calculation. It’s the number describing an entire population.

Statistics is a systematic collection of data on measurements or observations, often related to demographic information such as population counts, incomes, population counts at different ages and so on.

Parameters and statistics are essential to quantitative research. In general, parameter focuses on every individual in a population, while statistics consider the data obtained from a sample.

## What Is a Parameter?

A simple definition of the term “parameter” refers to a variable kept constant during an experiment or calculation. A parameter is the unchanged numerical value.

A parameter generally indicates the accurate value of the population after the census is conducted. The population describe the aggregate of the entire units under consideration.

Researchers involved in studying the population of people may also consider and include groups of other factors such as regions, cases, species, procedures, organizations, and objects.

To get accurate data, researchers will often conduct their studies to help them determine parameters that may show important results and information about the population being studied.

By conducting their studies, researchers are able to understand and observe the population. This also helps everyone in the field to understand how they can resolve certain problems within the population.

They will also be able to prevent various issues that may arise in the future.

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### Parameter vs Statistics: Most Common Type of Parameters

The common types of parameters include the mean, the median, and the mode.

**Mean:**Also known as the average, the mean is mostly used out of the three measures of central tendency. Researchers rely on the parameters to define the data distribution of ratios as well as intervals.**Median**: The median is generally used to compute variables- those measured on an interval, ordinal, or ratio scale. A simple method to calculate this is by sorting the data from the lowest to the highest and selecting the number (s) in the centre.- The median is the middle number if there are several odd data points. But when the numbers are even, the median is simply calculated by adding the two intermediate values, and then to get the mean, the values are divided by two.
**Mode**: This is the most frequently occurring number in any data distribution- the mode shows which number or value is the most numerous in the data distribution.

## What Is Statistics?

Statistics are the numerical values obtained from a sample of data. A statistic is the descriptive statistical measure, function of sample observation generally used by researchers to overcome challenges and avoid future occurrences.

Statistics and parameters are related terms because they both describe a specific group. While statistics describe a sample obtained from a large group, a parameter describes the entire group.

A sample is just a fraction of the population that only represents a small number within the population.

Statistics is commonly used to estimate a specific population parameter.

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## Parameter vs Statistics: Key Differences between Parameter and Statistics

Parameter and statistics are related terms but the difference between them is that the former is a fixed measure to describe the entire population, while the latter is a characteristic of a sample of the population.

In general, a parameter is an unknown numerical value and statistics is a known number and a variable that depends on the portion of the entire population.

Mathematically, sample statistics and population parameters both that different statistical notations.

Here are the different statistical notations and what they represent;

- Population proportion is represented by P
- Mean is represented by µ (Greek letter mu)
- Variance is represented by σ2
- Population size is represented by N
- Standard deviation is represented by σ (Greek letter sigma)
- The standard error of the mean is represented by σx̄
- The coefficient of variation is represented by σ/µ
- Standard variant (z) is represented by X-µ)/σ
- The standard error of proportion is represented by σp

### In sample statistics;

- x̄ (x-bar) represents the mean
- p̂ (p-hat) represents sample proportion
- s represents the standard deviation
- s2 represents variance
- n represents the sample size
- sx̄ represents the standard error of the mean
- sp represents the standard error of the proportion
- s/(x̄) represents coefficient of variation
- (x-x̄)/s represents standard variate (z)

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## Parameter vs Statistics: How to Identify Parameter and Statistics

How would you identify if a summary value in a report that you just read is a parameter or a statistic?

Well, you will always work with statistics as it has proven to solve specific studies.

If you are taking a statistic test on populations, you need to find a parameter value and you must also be able to measure the entire population.

For instance, a researcher may describe the population of a specific neighbourhood or sports team. It’s possible to survey the entire population of the sports team and the neighbourhood.

The simple way to do this is to determine whether the summary value applies to the entire population or only the sample of the population. Next, you need to read the narrative to help you make the determination.

## Parameter vs Statistics: Comparison Chart

Parameter | Statistics | |

Meaning | A parameter generally indicates the accurate value of the population after the census is conducted. | A statistic is the descriptive statistical measure, function of sample observation generally used by researchers to overcome challenges and avoid future occurrences. |

Numerical value | Fixed and unknown | Variable and known |

Statistical notation | μ = Population Mean P = Population Proportion σ = Population Standard Deviation N = Size of Population ρ = Correlation coefficient X = Data Elements | x̄ = Sample Mean n = Size of sample r = Correlation coefficient x = Data Elements p̂ = Sample Proportion s = Sample Standard Deviation |

## Parameter vs Statistics: Frequently Asked Questions

Below are frequently asked questions about the difference between a parameter vs statistics.

### What is the difference between parameter vs statistics?

Parameter and statistics are related terms but the difference between them is that the former is a fixed measure to describe the entire population, while the latter is a characteristic of a sample of the population.

Also Read: **Odds vs Probability: Difference and Comparison**

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

To identify if a number is a parameter or a statistic, here are a few questions to ask yourself.

Does the given number define the entire population where everyone can be reached to collect data? Can it be possible to collect data for this number from everyone within the population?

If the answer to these questions above is yes, then the number is likely to be a parameter.

### Why are samples used in research?

The main reason samples are mainly used is to make inferences about populations. They are easier to collect data from as they are convenient, cost-effective, and practical.

### When are populations used in research?

Populations are mainly used when a research question needs to obtain data from each member of the entire population.

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## References

- Indeed.com: Parameter vs. Statistic: Definitions, Examples and Uses

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