What is the Difference Between Parameter and Statistic?

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Difference Between Parameter and Statistic

The difference between parameters and statistics is what they represent and how certain their values are. It is also fundamental to understanding data analysis. A parameter is a characteristic or measure that describes a population. It is typically denoted by Greek letters such as μ (mu) for population mean or σ (sigma) for population standard deviation. Parameters are fixed values that represent the true characteristics of the entire population. 

On the other hand, statistics is a characteristic or measure that describes a sample drawn from a population. It is calculated from the data collected from the sample and is used to estimate the corresponding parameter of the pollution. Common statistics include sample mean (x), sample standard deviation (s), and sample proportion (p).

Keep reading this blog to get more clarity on the difference between Parameter and Statistics.

What is a Parameter?

A parameter is a numerical value that summarizes a characteristic of a population. It’s a fixed value, usually unknown, that describes the entire population being studied. It is denoted by such as μ (mu) for population mean, σ (sigma) for population standard deviation, and p for population proportion. Although parameters are the best way to describe the features of a population as a whole, they often need to be estimated from sample data using statistics because measuring the whole population is either impractical or impossible.

Here are some key points to remember about parameters.

  • Fixed value: Ideally, a parameter has a specific, unchanging value. It represents some truth about the entire population.
  • Difficult to obtain: In reality, getting data from everyone in a population can be impractical or even impossible. For instance, we can’t measure the height of every single person on Earth.
  • Denoted by: Parameters are commonly denoted by Greek letters like μ (mu) for average, σ (sigma) for standard deviation, or p (pi) for proportion.

What is Statistics?

In a comparison of parameters, statistics are the figures we get from looking at a sample, which is a smaller part of the population. Because we can only receive so much data, they are kind of like expert guesses about the bigger picture of the population. The field of statistics is the study of gathering, organizing, analyzing, interpreting, and showing numerical data. It includes ways to summarize and describe data, as well as ways to use sample data to draw conclusions and make predictions about whole populations.

Here’s a breakdown of the main points about statistical analysis.

  • Sample-based: Statistics are calculated from a sample, a subset of the entire population. This sample is like a smaller group of people we can actually measure from the giant pool mentioned earlier.
  • Estimates: Since they are based on a limited amount of data, statistics are estimates of the true population parameter.
  • Variability: Depending on the specific sample chosen, the statistics can vary. 
  • Denoted by: Statistics are represented by lowercase Latin letters, like x̄ (x-bar) for the sample mean, s for sample standard deviation, and p̂ (p-hat) for a sample proportion.

Also Read: Difference Between GHz and MHz

What is the Difference Between Parameter and Statistic?

Here is the table summarizing the main differences between Parameters and Statistics.

Particular ParameterStatistics
DefinitionA numerical characteristic that describes an entire population.
A numerical measure calculated from a sample drawn from the population.
NatureFixed and constantVariable and can change from sample to sample
ValueUnknown (as it pertains to the
entire population)
Known (as it is derived from the sample data)
RepresentationRepresents the entire population
Represents a sample of the population
UsageUsed in theoretical concepts and hypothesis formulation
Used in practical data analysis and research
AccuracyMore accurate as it represents the entire population
It may vary in accuracy as it depends on the sample size and selection
CalculationIt cannot be calculated exactly in most real-world scenarios
Can be calculated using sample data
PurposeTo describe the characteristics of the population
To estimate the population parameters based on sample data
ExampleThe actual average height of all adults in a countryThe average height calculated from a sample group of adults in a country

Difference Between Parameter and Statistic Formulas

Here are some common parameter and statistic formulas, categorized by.

Central Tendency

Population Mean (μ): μ = Σ(X_i) / N
Sample Mean (x̄): x̄ = Σ(x_i) / n

Spread (Variability)

Population Standard Deviation (σ): σ = sqrt(Σ(X_i – μ)² / N)
Sample Standard Deviation (s): s = sqrt(Σ(x_i – x̄)² / (n-1))

Proportion

Population Proportion (p): p = (# of successes in population) / N
Sample Proportion (p̂): p̂ = (# of successes in sample) / n

Where:

  • Σ (sigma) = It represents the summation of all elements (i) in the data set.
  • X_i = It represents the individual value in the population.
  • x_i = It represents the individual value in the sample.
  • N = It represents the total population size.
  • n = It represents the sample size.

Important: The divisor in the population standard deviation formula (N) is different from the sample standard deviation (n-1) due to a technical correction for estimating population characteristics from a sample.

Application of Difference Between Parameter and Statistic in Real Life

In many real-life situations, parameters, and statistics are the most important parts of data analysis. Here are some real-life examples:

Public Health

  • Parameter: The true infection rate of a disease in a population.
  • Statistic: The infection rate estimated from a sample of people tested.
  • Application: Public health officials can’t test everyone, so they use a statistic (infection rate in a sample) to estimate the parameter (infection rate in the entire population) and guide public health measures.

Market Research

  • Parameter: Average income of all customers in a specific region.
  • Statistic: Average income of a group of customers surveyed in that region.
  • Application: Companies can’t survey every customer, so they use a statistic (average income in a sample) to estimate the parameter (average income of the whole customer base) to develop targeted marketing campaigns.

Sports Analytics

  • Parameter: A basketball player’s true shooting percentage throughout the season.
  • Statistic: The shooting percentage calculated from the player’s shots taken in a particular game.
  • Application: Coaches can’t analyze every shot a player takes over a long season. They use statistics (shooting percentage in a game) to estimate the parameter (shooting percentage for the season) and make informed decisions about player strategy.

FAQ’s

What is an example of a statistic in real life?

Advertisements that say “4 out of 5 dentists recommend this toothpaste” are using numbers to try to get you to buy their product. One study or poll that the marketers did found that 80% of doctors suggest toothpaste.

Is a percentage a parameter or statistic?

A figure is any number that tells you about the group as a whole, like an average or a percentage.

What is an example of a parameter and a statistic in real life?

For example, let’s say you want to know the average income of magazine readers. This is an example of a population statistic.

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