INTRODUCTION TO
STATISTICS
DR. Manish Agarwal

What is Statistics?
Statistics is the science of conducting studies to collect, organize,
summarize, analyze, and draw conclusions from data.

What is Data?
Definition: Facts or figures, which are numerical or otherwise,
collected with a definite purpose are called data.
Everyday we come across a lot of information in the form of facts,
numerical figures, tables, graphs, etc.
These are provided by newspapers, televisions, magazines and other
means of communication.
These may relate to cricket batting or bowling averages, profits of a
company, temperatures of cities, expenditures in various sectors of a five
year plan, polling results, and so on.
These facts or figures, which are numerical or otherwise, collected with a
definite purpose are called data.

Characteristics of statistics
1. Statistics are the aggregates of facts: It means a single figure is not statistics.
For example, national income of a country for a single year is not statistics but
the same for two or more years is statistics.
2. Statistics are affected by a number of factors: For example, sale of a product
depends on a number of factors such as its price, quality, competition, the
income of the consumers, and so on.
3. Statistics must be reasonably accurate: Wrong figures, if analyzed, will lead
to erroneous conclusions. Hence, it is necessary that conclusions must be based
on accurate figures.
4. Statistics must be collected in a systematic manner: If data are collected in a
haphazard manner, they will not be reliable and will lead to misleading
conclusions.
5. Collected in a systematic manner for a pre-determined purpose
6. Lastly, Statistics should be placed in relation to each other: If one collects
data unrelated to each other, then such data will be confusing and will not lead
to any logical conclusions. Data should be comparable over time and over
space.

• Condensation: Explain huge mass of data with few observations.
• Comparison: Helps in comparing two set of data for better decision
making
• Forecasting: With the help of past data we can predict the future
outcomes e.g. regression and time series analysis.
• Estimation: We can estimate about population characteristics with the
help of sample study.
• Hypothesis Testing: A statistical hypothesis is some statement about
the probability distribution, characterizing a population on the basis of
the information available from the sample observations. In the
formulation and testing of hypothesis, statistical methods are
extremely useful. Whether crop yield has increased because of the use
of new fertilizer or whether the new medicine is effective in
eliminating a particular disease are some examples of statements of
hypothesis and these are tested by proper statistical tools.
Functions of Statistics:

Scope of Statistics
• Statistics and Industry: Statistics is widely used in many industries. In
industries, control charts are widely used to maintain a certain quality level.
In production engineering, to find whether the product is conforming to
specifications or not, statistical tools, namely inspection plans, control
charts, etc., are of extreme importance.
• Statistics and Commerce: Statistics are lifeblood of successful commerce.
Any businessman cannot afford to either by under stocking or having
overstock of his goods. In the beginning he estimates the demand for his
goods and then takes steps to adjust with his output or purchases. Thus
statistics is indispensable in business and commerce.
• Statistics and Economics: statistical tools are immensely useful in solving
many economic problems such as wages, prices, production, distribution of
income and wealth and so on. Statistical tools like Index numbers, time
series Analysis, Estimation theory, Testing Statistical Hypothesis are
extensively used in economics.

Scope of Statistics cont…
• Statistics and Education: Statistics is widely used in education. Research
has become a common feature in all branches of activities. Statistics is
necessary for the formulation of policies to start new course,
consideration of facilities available for new courses etc. There are many
people engaged in research work to test the past knowledge and evolve
new knowledge. These are possible only through statistics.
• Statistics and Planning: The government are seeking the help of
planning for efficient working, for the formulation of policy decisions
and execution of the same. In order to achieve its goals, the statistical
data relating to production, consumption, demand, supply, prices,
investments, income expenditure etc and various advanced statistical
techniques for processing, analyzing and interpreting such complex data
are of importance.
• Statistics and Medicine: In Medical sciences, statistical tools are widely
used. In order to test the efficiency of a new drug or medicine, t - test is
used. More and more applications of statistics are at present used in
clinical investigation.

LIMITATIONS OF STATISITICS
• Statistics is not suitable to the study of qualitative phenomenon: Since
statistics is basically a science and deals with a set of numerical data, it is
applicable to the study of only these subjects of enquiry, which can be
expressed in terms of quantitative measurements. As a matter of
fact, qualitative phenomenon like honesty, poverty, beauty, intelligence etc,
cannot be expressed numerically and any statistical analysis cannot be
directly applied on these qualitative phenomenon's. Nevertheless, statistical
techniques may be applied indirectly by first reducing the
qualitative expressions to accurate quantitative terms. For example,
the intelligence of a group of students can be studied on the basis of their
marks in a particular examination.
• Statistics does not study individuals: Statistics does not give any specific
importance to the individual items, in fact it deals with an aggregate of
objects. Individual items, when they are taken individually do not constitute
any statistical data and do not serve any purpose for any statistical enquiry.

LIMITATIONS OF STATISITICS cont..
• Statistical laws are not exact: It is well known that mathematical and
physical sciences are exact. But statistical laws are not exact and statistical
laws are only approximations. Statistical conclusions are not universally
true. They are true only on an average.
• Statistics table may be misused: Statistics must be used only by experts;
otherwise, statistical methods are the most dangerous tools on the hands of
the inexpert. The use of statistical tools by the inexperienced and un traced
persons might lead to wrong conclusions. Statistics can be easily misused
by quoting wrong figures of data.
• Statistics is only, one of the methods of studying a problem: Statistical
method do not provide complete solution of the problems because problems
are to be studied taking the background of the countries culture, philosophy
or religion into consideration. Thus the statistical study should be
supplemented by other evidences.

Primary Data Vs Secondary Data
Primary Data
Primary data is the data that is collected for the first time
through personal experiences or evidence, particularly for
research.
It is also described as raw data or first-hand information.
The mode of assembling the information is costly.
The data is mostly collected through observations, physical
testing, mailed questionnaires, surveys, personal interviews,
telephonic interviews, case studies, and focus groups, etc.

Primary Data Vs Secondary Data
Secondary Data
Secondary data is a second-hand data that is already collected and
recorded by some researchers for their purpose, and not for the
current research problem.
It is accessible in the form of data collected from different sources
such as government publications, censuses, internal records of the
organisation, books, journal articles, websites and reports, etc.
This method of gathering data is affordable, readily available, and
saves cost and time.
However, the one disadvantage is that the information assembled is
for some other purpose and may not meet the present research
purpose or may not be accurate.

Discrete Vs continuous data
• Discrete data (countable) is information that can only take certain
values. These values don’t have to be whole numbers but they are
fixed values – such as shoe size, number of teeth, number of kids, etc.
• Discrete data includes discrete variables that are finite, numeric,
countable, and non-negative integers (5, 10, 15, and so on).
• Continuous data (measurable) is data that can take any value. Height,
weight, temperature and length are all examples of continuous data.
• Continuous data changes over time and can have different values at
different time intervals like weight of a person.

Types of statistics
• Descriptive statistics – Methods of organizing, summarizing, and
presenting data in an informative way
• Inferential statistics – The methods used to determine something
about a population on the basis of a sample
• Population –The entire set of individuals or objects of interest or the
measurements obtained from all individuals or objects of interest
• Sample – A portion, or part, of the population of interest