Difference Between Statistic and Parameter

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.

Content: Statistic Vs Parameter

1. Comparison Chart
2. Definition
3. Key Differences
4. Illustration
5. Conclusion

Comparison Chart

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

Definition of Statistic

A statistic is defined as a numerical value, which is obtained from a sample of data. It is a descriptive statistical measure and function of sample observation. A sample is described as a fraction of the population, which represents the entire population in all its characteristics. The common use of statistic is to estimate a particular population parameter.

From the given population, it is possible to draw multiple samples, and the result (statistic) obtained from different samples will vary, which depends on the samples.

Definition of Parameter

A fixed characteristic of population based on all the elements of the population is termed as the parameter. Here population refers to an aggregate of all units under consideration, which share common characteristics. It is a numerical value that remains unchanged, as every member of the population is surveyed to know the parameter. It indicates true value, which is obtained after the census is conducted.

Illustration

1. A researcher wants to know the average weight of females aged 22 years or older in India. The researcher obtains the average weight of 54 kg, from a random sample of 40 females.
   Solution: In the given situation, the statistics are the average weight of 54 kg, calculated from a simple random sample of 40 females, in India while the parameter is the mean weight of all females aged 22 years or older.
2. A researcher wants to estimate the average amount of water consumed by male teenagers in a day. From a simple random sample of 55 male teens the researcher obtains an average of 1.5 litres of water.
   Solution: In this question, the parameter is the average amount of water consumed by all male teenagers, in a day whereas the statistic is the average 1.5 litres of water consumed in a day by male teens, obtained from a simple random sample of 55 male teens.

Conclusion

To sum up the discussion, it is important to note that when the result obtained from the population, the numerical value is known as the parameter. While, if the result is obtained from the sample, the numerical value is called statistic.