Introduction to Statistics
Lecture 01
Introduction
The word “statistics”, derived from the Latin word "status",
means information useful to the state. In the early era, statistics were limited to information about armed forces, cattle, fertile fields, etc. Later on, with
the development of society, the parameters of the statistics expand. Now
statistics work as a separate discipline and play a vital role in the development of the natural and social sciences.
Definition of Statistics
A discipline that is concerned with the collection,
analysis, and interpretation of numerical data to make inferences and reach
a decision in the face of uncertainty, as well as the effective communication
and presentation of results relying on data.
Branches of statistics
Statistics as a subject may be divided into two main
branches:
1. Descriptive Statistics
2. Inferential Statistics
Descriptive Statistics
Descriptive statistics is deals with the concepts and methods concerned with the summarization and important characteristics of numerical data and their visual displays. It also includes a few numerical quantities that provide information about the center of the data and their spread.
e.g. measure of central tendency and measure of
dispersion, etc.
Inferential Statistics
Inferential statistics deals with the procedures for
making inferences about population on the basis of information contained in a
sample, selected from the population concerned. This branch of statistics includes
the estimation of parameters and testing statistical hypotheses.
Characteristics of Statistics
The general features of statistics are given below:
i. Statistical laws are valid on average
ii. Statistics deals with aggregates of observations of the
same kind rather than isolated figures.
iii. Statistics deals with the numerical characteristics of
things.
iii. Statistics deals data for a predetermined purpose
Limitations of Statistics
i. Statistics need sufficient care in application.
ii. Statistics only study quantitative data.
iii. Statistics deals with aggregates and therefore throws light on aggregate.
Population
The aggregate of all individuals or objects having some
characteristics of interest and from which individuals or objects are selected
for study. The units of a population are represented by X1, X2,... XN. These units are called
sampling units.
Sample
A small representative part is selected from the population for analysis. The units or members of a population are represented by X1, X2,..., Xn.
Statistic
A numerical function computed from sample data, such as mean and standard deviation. The value of the statistic is varying from sample to sample, and the value of the parameter is fixed.
Let X1, X2,..., Xn are the values of a sample selected from a population. Then
Variable
A variable is anything that can take on differing or
varying values. The values can differ at various times for the same object or
person, or at the same time for different objects or persons.
Examples of variables:
i. Number of children in a family.
ii. Number of shops in a market
iii. Ages of person
iv. Temperature at a place
v. Intelligence
level of a person
Types of Variables
There are two types of variables
Quantitative and Qualitative variables
Quantitative
variable
The characteristics that can be expressed numerically
is called quantitative variables.
Examples:
Age of students
Income of a worker,
Number of children in a family, etc.
A quantitative variable may be classified as discrete or
continuous.
Discrete Variable
A discrete variable is one that can take only whole
numbers or a discrete set of integers. For example, number of children in a
family, number of shops in a market.
Continuous Variable
A variable is said to be a continuous variable if it
can take on any fractional or integral with in a given interval such as age of
person, temperature at a place.
Qualitative variable
The variable that is used to represent the presence or
absence of a quality and is described by verbal grouping.
Examples:
Intelligence
Poverty
Satisfaction etc.
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