History of Statistics
The Word statistics have been derived from Latin word “Status” or the
Italian word “Statista”, meaning of these words is “Political State” or a
Government. Shakespeare used a word Statist is his drama Hamlet (1602).
In the past, the statistics was used by rulers. The application of statistics
was very limited but rulers and kings needed information about lands,
agriculture, commerce, population of their states to assess their military
potential, their wealth, taxation and other aspects of government.
Gottfried Achenwall used the word statistik at a German University in 1749
which means that political science of different countries. In 1771 W. Hooper
(Englishman) used the word statistics in his translation of Elements of
Universal Erudition written by Baron B.F Bieford, in his book statistics has
been defined as the science that teaches us what is the political
arrangement of all the modern states of the known world. There is a big gap
between the old statistics and the modern statistics, but old statistics also
used as a part of the present statistics.
During the 18th century the English writer have used the word statistics in
their works, so statistics has developed gradually during last few centuries.
A lot of work has been done in the end of the nineteenth century.
At the beginning of the 20th century, William S Gosset was developed the
methods for decision making based on small set of data. During the 20th
century several statistician are active in developing new methods, theories
and application of statistics. Now these days the availability of electronics
computers is certainly a major factor in the modern development of
statistics.
Definition of Statistics
Statistics like many other sciences is a developing discipline. It is not
nothing static. It has gradually developed during last few centuries. In
different times, it has been defined in different manners. Some definitions of
the past look very strange today but those definitions had their place in their
own time. Defining a subject has always been difficult task. A good definition
of today may be discarded in future. It is difficult to define statistics. Some
of the definitions are reproduced here:
The kings and rulers in the ancient times were interested in their manpower.
They conducted census of population to get information about their
population. They used information to calculate their strength and ability for
wars. In those days statistics was defined as
“the science of kings, political and science of statecraft”
A.L. Bowley defined statistics as
“statistics is the science of counting”
This definition places the entries stress on counting only. A common man
also thinks as if statistics is nothing but counting. This used to be the
situation but very long time ago. Statistics today is not mere counting of
people, counting of animals, counting of trees and counting of fighting force.
It has now grown to a rich methods of data analysis and interpretation.
A.L. Bowley has also defined as
“science of averages”
This definition is very simple but it covers only some area of statistics.
Average is very simple important in statistics. Experts are interested in
average deaths rates, average birth rates, average increase in population,
and average increase in per capita income, average increase in standard of
living and cost of living, average development rate, average inflation rate,
average production of rice per acre, average literacy rate and many other
averages of different fields of practical life. But statistics is not limited to
average only. There are many other statistical tools like measure of
variation, measure of correlation, measures of independence etc… Thus this
definition is weak and incomplete and has been buried in the past.
Prof: Boddington has defined statistics as
“science of estimate and probabilities”
This definition covers a major part of statistics. It is close to the modern
statistics. But it is not complete because it stress only on probability. There
are some areas of statistics in which probability is not used.
A definition due to W.I. King is “the science of statistics is the method of
judging collection, natural or social phenomena from the results obtained
from the analysis or enumeration or collection of estimates”. This definition
is close to the modern statistics. But it does not cover the entire scope of
modern statistics. Secrist has given a detailed definition of statistics in plural
sense. His definition is given on the previous. He has not given any
importance to statistics in singular sense. Statistics both in the singular and
the plural sense has been combined in the following definition which is
accepted as the modern definition of statistics.
Classification of Statistics
Statistics may be divided into two main branches:
(1) Descriptive Statistics
(2) Inferential Statistics
Descriptive Statistics:
In descriptive statistics, it deals with collection of data, its presentation in
various forms, such as tables, graphs and diagrams and findings averages
and other measures which would describe the data.
For Example: Industrial statistics, population statistics, trade statistics etc…
Such as businessman make to use descriptive statistics in presenting their
annual reports, final accounts, bank statements.
Inferential Statistics:
In inferential statistics, it deals with techniques used for analysis of data,
making the estimates and drawing conclusions from limited information
taken on sample basis and testing the reliability of the estimates.
For Example: Suppose we want to have an idea about the percentage of
illiterates in our country. We take a sample from the population and find the
proportion of illiterates in the sample. This sample proportion with the help
of probability enables us to make some inferences about the population
proportion. This study belongs to inferential statistics.
Importance of Statistics in Different Fields
Statistics plays a vital role in every fields of human activity. Statistics has
important role in determining the existing position of per capita income,
unemployment, population growth rate, housing, schooling medical facilities
etc…in a country. Now statistics holds a central position in almost every field
like Industry, Commerce, Trade, Physics, Chemistry, Economics,
Mathematics, Biology, Botany, Psychology, Astronomy etc…, so application
of statistics is very wide. Now we discuss some important fields in which
statistics is commonly applied.
(1) Business:
Statistics play an important role in business. A successful businessman must
be very quick and accurate in decision making. He knows that what his
customers wants, he should therefore, know what to produce and sell and in
what quantities. Statistics helps businessman to plan production according to
the taste of the costumers, the quality of the products can also be checked
more efficiently by using statistical methods. So all the activities of the
businessman based on statistical information. He can make correct decision
about the location of business, marketing of the products, financial resources
etc…
(2) In Economics:
Statistics play an important role in economics. Economics largely depends
upon statistics. National income accounts are multipurpose indicators for the
economists and administrators. Statistical methods are used for preparation
of these accounts. In economics research statistical methods are used for
collecting and analysis the data and testing hypothesis. The relationship
between supply and demands is studies by statistical methods, the imports
and exports, the inflation rate, the per capita income are the problems which
require good knowledge of statistics.
(3) In Mathematics:
Statistical plays a central role in almost all natural and social sciences. The
methods of natural sciences are most reliable but conclusions draw from
them are only probable, because they are based on incomplete evidence.
Statistical helps in describing these measurements more precisely. Statistics
is branch of applied mathematics. The large number of statistical methods
like probability averages, dispersions, estimation etc… is used in
mathematics and different techniques of pure mathematics like integration,
differentiation and algebra are used in statistics.
(4) In Banking:
Statistics play an important role in banking. The banks make use of statistics
for a number of purposes. The banks work on the principle that all the
people who deposit their money with the banks do not withdraw it at the
same time. The bank earns profits out of these deposits by lending to others
on interest. The bankers use statistical approaches based on probability to
estimate the numbers of depositors and their claims for a certain day.
(5) In State Management (Administration):
Statistics is essential for a country. Different policies of the government are
based on statistics. Statistical data are now widely used in taking all
administrative decisions. Suppose if the government wants to revise the pay
scales of employees in view of an increase in the living cost, statistical
methods will be used to determine the rise in the cost of living. Preparation
of federal and provincial government budgets mainly depends upon statistics
because it helps in estimating the expected expenditures and revenue from
different sources. So statistics are the eyes of administration of the state.
(6) In Accounting and Auditing:
Accounting is impossible without exactness. But for decision making
purpose, so much precision is not essential the decision may be taken on the
basis of approximation, know as statistics. The correction of the values of
current asserts is made on the basis of the purchasing power of money or
the current value of it.
In auditing sampling techniques are commonly used. An auditor determines
the sample size of the book to be audited on the basis of error.
(7) In Natural and Social Sciences:
Statistics plays a vital role in almost all the natural and social sciences.
Statistical methods are commonly used for analyzing the experiments
results, testing their significance in Biology, Physics, Chemistry,
Mathematics, Meteorology, Research chambers of commerce, Sociology,
Business, Public Administration, Communication and Information Technology
etc…
(8) In Astronomy:
Astronomy is one of the oldest branches of statistical study; it deals with the
measurement of distance, sizes, masses and densities of heavenly bodies by
means of observations. During these measurements errors are unavoidable
so most probable measurements are founded by using statistical methods.
Example: This distance of moon from the earth is measured. Since old days
the astronomers have been statistical methods like method of least squares
for finding the movements of stars.
Uses of Statistics
(1) Statistics helps in providing a better understanding and exact
description of a phenomenon of nature.
(2) Statistical helps in proper and efficient planning of a statistical inquiry in
any field of study.
(3) Statistical helps in collecting an appropriate quantitative data.
(4) Statistics helps in presenting complex data in a suitable tabular,
diagrammatic and graphic form for an easy and clear comprehension of the
data.
(5) Statistics helps in understanding the nature and pattern of variability of
a phenomenon through quantitative obersevations.
(6) Statistics helps in drawing valid inference, along with a measure of their
reliability about the population parameters from the sample data.
Misuses and Abuses of Statistics
The important limitations of statistics are:
(1) Statistics laws are true on average. Statistics are aggregates of facts. So
single observation is not a statistics, it deals with groups and aggregates
only.
(2) Statistical methods are best applicable on quantitative data.
(3) Statistical cannot be applied to heterogeneous data.
(4) It sufficient care is not exercised in collecting, analyzing and
interpretation the data, statistical results might be misleading.
(5) Only a person who has an expert knowledge of statistics can handle
statistical data efficiently.
(6) Some errors are possible in statistical decisions. Particularly the
inferential statistics involves certain errors. We do not know whether an
error has been committed or not.
Measurement scales of statistics
Normally, when one hears the term measurement, they may think in terms
of measuring the length of something (e.g., the length of a piece of wood) or
measuring a quantity of something (ie. a cup of flour).This represents a
limited use of the term measurement. In statistics, the term measurement is
used more broadly and is more appropriately termed scales of
measurement. Scales of measurement refer to ways in which
variables/numbers are defined and categorized. Each scale of measurement
has certain properties which in turn determines the appropriateness for use
of certain statistical analyses. The four scales of measurement are nominal,
ordinal, interval, and ratio.
Nominal: Categorical data and numbers that are simply used as identifiers
or names represent a nominal scale of measurement. Numbers on the back
of a baseball jersey and your social security number are examples of
nominal data. If I conduct a study and I’m including gender as a variable, I
may code Female as 1 and Male as 2 or visa versa when I enter my data into
the computer. Thus, I am using the numbers 1 and 2 to represent categories
of data.
Ordinal: An ordinal scale of measurement represents an ordered series of
relationships or rank order. Individuals competing in a contest may be
fortunate to achieve first, second, or third place. first, second, and third
place represent ordinal data. If Roscoe takes first and Wilbur takes second,
we do not know if the competition was close; we only know that Roscoe
outperformed Wilbur. Likert-type scales (such as “On a scale of 1 to 10, with
one being no pain and ten being high pain, how much pain are you in
today?”) also represent ordinal data. Fundamentally, these scales do not
represent a measurable quantity. An individual may respond 8 to this
question and be in less pain than someone else who responded 5. A person
