Parameter vs. Statistics

Attribute	Parameter	Statistics
Definition	A numerical characteristic of a population	Numerical values calculated from a sample of a population
Population	Entire group being studied	Subset of the population
Symbol	Usually denoted by Greek letters (e.g., μ for population mean)	Usually denoted by Latin letters (e.g., x̄ for sample mean)
Estimation	Used to estimate population parameters	Used to estimate population statistics
Variability	Parameters are fixed values	Statistics can vary from sample to sample

Definition

Parameters and statistics are two important concepts in the field of statistics. Parameters are numerical characteristics of a population, while statistics are numerical characteristics of a sample. In other words, parameters are fixed values that describe a population, while statistics are estimates of those values based on a sample.

Population vs. Sample

One of the key differences between parameters and statistics is the population they refer to. Parameters are calculated using data from an entire population, while statistics are calculated using data from a sample of the population. For example, if we want to know the average income of all residents in a city, the parameter would be the actual average income of all residents, while the statistic would be the average income of a sample of residents.

Accuracy

Parameters are generally more accurate than statistics because they are calculated using data from the entire population. Since parameters are fixed values, they provide a precise description of the population. On the other hand, statistics are estimates of parameters and may vary depending on the sample chosen. The larger the sample size, the closer the statistic is likely to be to the parameter.

Use in Inference

Parameters and statistics play different roles in statistical inference. Parameters are used to make inferences about a population, while statistics are used to make inferences about the population based on a sample. For example, if we want to estimate the average height of all students in a school, we would use statistics to make an inference about the population parameter.

Estimation

Parameters and statistics are both used for estimation, but in different contexts. Parameters are used to estimate population characteristics, while statistics are used to estimate population characteristics based on a sample. For example, if we want to estimate the proportion of voters who support a particular candidate in a country, we would use statistics to estimate the parameter based on a sample of voters.

Variability

Parameters are fixed values that do not change, while statistics can vary depending on the sample chosen. This variability is known as sampling variability. Since statistics are estimates of parameters, they are subject to sampling variability, which means that different samples from the same population may yield different statistics. Parameters, on the other hand, remain constant regardless of the sample chosen.

Conclusion

In conclusion, parameters and statistics are both important concepts in statistics, but they serve different purposes. Parameters are fixed values that describe a population, while statistics are estimates of those values based on a sample. Parameters are generally more accurate than statistics because they are calculated using data from the entire population. Both parameters and statistics are used for estimation, but parameters are used to estimate population characteristics, while statistics are used to estimate population characteristics based on a sample. Understanding the differences between parameters and statistics is crucial for making accurate and reliable statistical inferences.