Generally, parameter is a quantitative characteristic, which indexes/identifies the respective distribution. In many cases, statistical quantitative characteristics calculated based on all the units in the population are the respective parameters.

**PARAMETER AND STATISTIC**

A **population**, as described in Section 2.4 in XI Standard text book, is a
collection of units/objects/numbers under study, whose elements can be
considered as the values of a random variable, say, *X.* As mentioned in
Section 9.3 in XI Standard text book, there will be a probability distribution
associated with *X*.

**Parameter: **Generally,** ****parameter**** **is a quantitative characteristic, which indexes/identifies** **the respective
distribution. In many cases, statistical quantitative characteristics
calculated based on all the units in the population are the respective
parameters. For example, population mean, population standard deviation,
population proportion are parameters for some distributions.

**Recall: ****The unknown constants
which appear in the**** ***probability density
function or probability*** ***mass function ***of the random variable X, are also called **

The parameters are commonly denoted by Greek letters. In
Statistical Inference, some or all the parameters of a population are assumed
to be unknown.

**Random sample: **Any set of reliazations** ***(X _{1}, X_{2}*

**Statistic: **Any statistical quantity calculated on the basis of the random
sample is called** **a **statistic***.* The sample mean, sample standard deviation, sample proportion *etc*.,
are called **statistics
**(plural form of** ***statistic*)*.*They will be
denoted by Roman letters.

Let (*x _{1}, x_{2}, …, x_{n}*) be an
observed value of (

**Note 1**

A set of n sample observations can be made on X, say, x_{1},
x_{2}, …, x_{n} for making inferences on the unknown
parameters. It is to be noted that these n values may vary from sample to
sample. Thus, these values can be considered as the realizations of the random
variables X_{1}, X_{2}, ..., X_{n} ,which are assumed
to be independent and have the same distribution as that of X. These are also
called independently and identically distributed (iid) random variables.

**Note 2:**

In Statistical Inference, the sample standard deviation is
defined as *S = * where . It may be noted that the divisor is *n*
– 1 instead of *n*

**Note 3:**

The statistic itself is a random variable, until the numerical
values of *X*_{1}, *X*_{2}, ..., *X _{n}*
are observed, and hence it has a probability distribution.

Notations to denote various population parameters and their
corresponding sample statistics are listed in Table 1.1. The notations will be
used in the first four chapters of this book with the same meaning for the sake
of uniformity.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

12th Statistics : Chapter 1 : Tests of Significance - Basic Concepts and Large Sample Tests : Parameter and Statistic |

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