**What is a parameter in statistics?**

In statistics, a parameter is a numerical value that describes a specific characteristic of the entire population, such as the average age of the students in a class or the standard deviation of the age of the students. Parameters are a very important part of inferential statistics. It helps us to draw conclusions about a large population based on a small sample of data. McCluskey & Lalkhen state that:

“Parameters in statistics are measurable characteristics of populations or models, distinct from variables, which are attributes of samples (McCluskey & Lalkhen, 2007).”

## Types of** parameter in Statistics**

Common statistical parameters include measures of central tendency such as mean, median, and mode, along with measures of variability like variance and standard deviation (Adams, 1955). In order to save cost and time, generalising findings from a sample of the entire population to understand the true values of a population parameter is essential. When choosing parameters for data analysis, consider factors such as their informativeness, robustness, and prediction (Godambe & Thompson, 1984). It’s important to note that the concept of a parameter in statistics differs from its mathematical definition and requires specific formulation within a statistical framework.(Cortínez Pontoni et al., 2020).

While parameters have fixed but usually unknown values in populations, they are estimated using sample statistics (McCluskey & Lalkhen, 2007). The concept of parameter in statistics differs from its mathematical counterpart and requires specific formulation within the statistical context (Cortínez Pontoni et al., 2020). It is essential to understand the population parameters to interpret and analyze the numerical data in different domains of research study. Statistical techniques like confidence intervals and hypothesis testing are used in the estimation and interpretation of population parameters in order to make inferences about the population. The accuracy of these inferences heavily depends on the validity of the assumptions made about the population parameters and the sampling methods used to obtain the sample data.

**The parameters can be understood by the following examples:**

**Example 1: Football – Probability of Scoring in a Specific Match**

**Statistical Parameter:** Probability of Scoring in a Match

**Example Player:** Cristiano Ronaldo

**Historical Performance:** In the UEFA Champions League, Cristiano Ronaldo has scored 125 goals in 131 matches.

**Calculation of Probability of Scoring:** To estimate the probability of Ronaldo scoring in his next match, we can use his historical goals per match:

*Goals Per Match (GPM) = Total Goals ScoredTotal Matches Played=125131 0.995*

**Interpretation:**

This suggests that Cristiano Ronaldo has a 95.5% probability of scoring in a UEFA Champions League match based on his past performance. Such a high probability highlights his consistent scoring ability at the highest level of competition.

**Example 2: Cricket – Batting Average**

**Statistical Parameter:** Batting Average

**Example Player:** Sachin Tendulkar

**Total Runs Scored in Tests:**15,921 runs**Total Innings Played in Tests:**329 innings**Times Out in Tests:**96 times

**Calculation of Batting Average:**

Batting Average = Total Runs ScoredTimes Out = 15921296 = 53.79

**Interpretation:**

Sachin Tendulkar’s batting average of approximately **53.79** (using his total runs and innings) means that he scores an average of **53.79 runs** every time played in a Test match. This impressive average underscores his excellence and consistency as one of cricket’s all-time greats.

Statistical methods for parameter estimation offer advantages over deterministic approaches by incorporating error models, allowing for precision analysis and systematic error evaluation (Bos, 1977). Researchers use both descriptive and inferential statistics to analyse sample data and draw conclusions about populations of interest, employing various data types and variables to calculate sample statistics as approximations of population parameters (McCluskey & Lalkhen, 2007).

**Related articles:**

Adams, J. K. (1955). Parameters and statistics.

Aguilar, O., Allmaras, M., Bangerth, W., & Tenorio, L. (2015). Statistics of parameter estimates: a concrete example. *siam REVIEW*, *57*(1), 131-149.

Geisser, S. (1992). Introduction to Fisher (1922) On the mathematical foundations of theoretical statistics. In *Breakthroughs in Statistics: Foundations and Basic Theory* (pp. 1-10). New York, NY: Springer New York.

Student. (1982). PARAMETER. *Pediatrics*, *70*(2), 287-287.

Poor, H. V., & Poor, H. V. (1994). Elements of parameter estimation. *An Introduction to Signal Detection and Estimation*, 141-204.

Rao, C. R. (1992). Information and the accuracy attainable in the estimation of statistical parameters. In *Breakthroughs in Statistics: Foundations and basic theory* (pp. 235-247). New York, NY: Springer New York.