Difference Between Parameter and Statistics

“Parameters” and “statistics” – ever mixed them up? You’re not alone. Why do these terms matter in the data world, and how do they differ?
In this article, we will cover all about parameters and statistics in detail.

Parameters and Statistics are closely related and interlinked, often complementary in data analysis and research. But both these terms are different from each other.

Parameters describe the characteristics of a population, while statistics describe the characteristics of samples. Statistics can be used to estimate parameters, but remember that statistics are only estimates.

This article will discuss the difference between parameters and statistics and their characteristics.

So, let’s get started.

Table of Content

• Difference Between Parameter and Statistics: Parameter vs. Statistics
• What is a Parameter?
  • Characteristics of Parameter
• What is Statistics?
  • Characteristics of Statistics

What is the Difference Between Parameters and Statistics?

	Parameter	Statistics
Definition	A numerical characteristic that describes an entire population.	A numerical measure calculated from a sample drawn from the population.
Nature	Fixed and constant	Variable and can change from sample to sample
Value	Unknown (as it pertains to the entire population)	Known (as it is derived from the sample data)
Representation	Represents the entire population	Represents a sample of the population
Usage	Used in theoretical concepts and hypothesis formulation	Used in practical data analysis and research
Accuracy	More accurate as it represents the entire population	It may vary in accuracy as it depends on the sample size and selection
Calculation	It cannot be calculated exactly in most real-world scenarios	Can be calculated using sample data
Purpose	To describe the characteristics of the population	To estimate the population parameters based on sample data
Example	The actual average height of all adults in a country	The average height calculated from a sample group of adults in a country

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What is a Parameter?

A parameter is a numerical characteristic that represents the properties of an entire population. It is a fixed and unknown value that remains constant, irrespective of the number of studies conducted on the population.

Parameters are intrinsic properties of the population, which means they are inherent and do not change based on the sample selected.

They play a significant role in statistical studies as they:

• Formulate Null and Alternative Hypothesis in Hypothesis testing, serving as a benchmark against which sample statistics are compared.
• Guide researchers in designing their studies, helping them to select appropriate sampling methods and analysis techniques.
• It helps in policy formulation by providing insights into the characteristics of larger groups, such as a country’s population or a specific demographic area.

Characteristics of a Parameter

• Fixed Value: A parameter has a fixed value, which does not change with different samples. It is a constant that represents a particular characteristic of the entire population.
• Population Representation: Parameters are representative of the entire population. They provide insights into the characteristics of the population as a whole.
• Unknown: In most real-world scenarios, the exact value of a parameter is unknown because it is practically impossible to study an entire population. Therefore, parameters are often estimated using statistics derived from sample data.
• Theoretical Concept: Parameters are often theoretical concepts to formulate statistical models and hypotheses. They serve as the basis for various statistical methods and analyses.
• Examples: Some common examples of parameters include the population mean (μ), population variance (σ²), and population proportion (P). These parameters provide insights into the population’s central tendency, dispersion, and distribution of characteristics.

Related Read – Difference between Null Hypothesis and Alternative Hypothesis

What is Statistics?

Statistics is a field of study and numerical measure derived from sample data. It is a practical tool that facilitates
the study of larger populations by analyzing smaller samples.
In simple terms, statistics is a variable or known number which can be changed from sample to sample and gives an idea about the characteristics of the larger population.

• It is used to make informed estimates about population parameters, facilitating the study of larger groups through sample data analysis.
• Statistics derived from sample data are used to test hypotheses about population parameters that help validate or reject the theoretical concept.
• It helps to analyze the data effectively and draw reliable conclusions.

Characteristic of Statistics

Characteristics of Statistics:

• Variable Value: Unlike parameters, statistics are variable. Their values can change with different samples, offering a glimpse into the potential characteristics of the larger population.
• Sample Representation: Statistics represent a sample, which is a subset of the population. They provide insights based on the data collected from a smaller group within the population.
• Known Value: The value of a statistic is known as it is calculated from the sample data. It serves as an estimate of the population parameter, helping researchers make informed decisions.
• Practical Application: Statistics are used in practical data analysis and research. They serve as tools to analyze sample data and derive insights into the population characteristics.
• Examples: Common examples of statistics include sample mean (x̄), sample variance (s²), and sample proportion (p̂). These statistics are calculated from sample data and used to estimate the corresponding population parameters.