Parameter and Statistics

 

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.

Statistics:

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.

Differences between Parameter and Statistics:

STATISTIC	PARAMETER
a. Statistic is a measure which describes a fraction of population.	i.Parameter refers to a measure which describes population.
b.It’s numerical value is Variable and Known.	ii.It’s numerical value is Fixed and Unknown
c.Statistical Notation of Statistics: x̄ = Sample Mean	iii.Statistical Notation of Parameter: 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
d.It shows the characteristics of the sample.	iv.It shows the characteristics of the population.
e.Romans letters are used to denote statistics	v.Greek letters are used to denote parameter.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

For example:

1.      A researcher wants to know the average weight of females aged 22 years or older in Nepal. 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 Nepal 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.

Adopted from: https://keydifferences.com/difference-between-statistic-and-parameter.html