Question

What is the difference between a statistic and a parameter?

Answer 1

ANSWER:-

In statistics vocabulary, we often deal with the terms parameter and statistic, which play a vital role in the determination of the sample size. Parameter implies a summary description of the characteristics of the target population. On the other extreme, the statistic is a summary value of a small group of population i.e. sample.

The parameter is drawn from the measurements of units in the population. As against this, the statistic is drawn from the measurement of the elements of the sample.

While studying statistics it is important to the concept and difference between parameter and statistic, as these are commonly misconstrued.

BASIS FOR COMPARISON	STATISTIC	PARAMETER
Meaning	Statistic is a measure which describes a fraction of population.	Parameter refers to a measure which describes population.
Numerical value	Variable and Known	Fixed and Unknown
Statistical Notation	x̄ = Sample Mean	μ = Population Mean
	s = Sample Standard Deviation	σ = Population Standard Deviation
	p̂ = Sample Proportion	P = Population Proportion
	x = Data Elements	X = Data Elements
	n = Size of sample	N = Size of Population
	r = Correlation coefficient	ρ = Correlation coefficient

Key Differences Between Statistic and Parameter

The difference between statistic and parameter can be drawn clearly on the following grounds:

1. A statistic is a characteristic of a small part of the population, i.e. sample. The parameter is a fixed measure which describes the target population.
2. The statistic is a variable and known number which depend on the sample of the population while the parameter is a fixed and unknown numerical value.
3. Statistical notations are different for population parameters and sample statistics, which are given as under:
   • In population parameter, µ (Greek letter mu) represents mean, P denotes population proportion, standard deviation is labeled as σ (Greek letter sigma), variance is represented by σ², population size is indicated by N, Standard error of mean is represented by σ_x̄, standard error of proportion is labeled as σ_p, standardized variate (z) is represented by (X-µ)/σ, Coefficient of variation is denoted by σ/µ.
   • In sample statistics, x̄ (x-bar) represents mean, p̂ (p-hat) denotes sample proportion, standard deviation is labeled as s, variance is represented by s², n denotes sample size, Standard error of mean is represented by s_x̄, standard error of proportion is labeled as s_p, standardized variate (z) is represented by (x-x̄)/s, Coefficient of variation is denoted by s/(x̄)