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# Difference Between Parameter and Statistic

Parameter vs Statistic

Consider these questions; what is the average income of a person in your country, what is the average height of women in the world, and what is the average weight of the eggs produced by certain breeds of fowl? It is impossible to do a survey that includes all the subjects of interest. In the first case, it is all the people in your country, in the second, all the women in your world, and in the third, all the eggs produced by that breed of fowl. This larger set containing all the elements is known as the population in statistics lingo.

However, by choosing a limited number of elements from the population in such a way that it represents all the others, we can deduce the properties of the population by analyzing the subset. This subset of the population is known as the sample. Measures of descriptive statistics are used to summarize and explain the main attributes of the population.

A descriptive measure (such as mean, mode, or median) of a population is known as a parameter. It numerically expresses the value for an attribute by summarizing the available data. As indicated earlier, it is impossible to consider the values for attribute over the whole population. Therefore, the sample is used to calculate the measures and then infer them into the population.

However, in exceptional cases, such as a complete census and standardized tests, the parameters are calculated from the population.

In classical probability theory, a parameter is a constant, but has “unknown value,” which is determined by the estimates based on samples. In modern Bayesian probability, the parameters are random variables, and their uncertainty is described as a distribution.

The statistic is a descriptive measure of the sample. Unlike the parameter, the sample values are calculated from the random sample obtained from the population. More formally, it is defined as a function of the sample, but independent from the distribution of the sample.

In inference, the statistics act as the estimator for the parameters. Sample mean, sample variance and standard deviation, quantiles such as quartiles and percentiles, and order statistics such as maximum and minimum are all belong to the category of statistics of a sample.

The observability of the statistics is a major factor separating the statistics and the parameter. In a population, the parameter is not directly observable, but in a sample, the statistic is readily observable, most of the time one or two calculations away. Additionally, the statistics have important properties such as completeness, sufficiency, consistency, unbiasedness, robustness, computational convenience, low variance, and the mean square error is a minimum.

What is the difference between Parameter and Statistic?

• Parameter is a descriptive measure of the population, and statistics is a descriptive measure of a sample.

• Parameters are not directly calculable, but statistics are calculable and directly observable.

• Parameters are deduced (inferred) from statistics and statistics acts as the estimator for the population parameter. (Sample mean (x ̅) acts as the estimator for the population mean µ)

• In parameter, values are not necessarily equal to the sample values, but approximate.

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