Statistics...

. CONTENTS
o Introduction to Statistics
o History of Statistics
o Meanings of Statistics
o Kinds or Branches Statistics
o Definition of Statistics
o Characteristics of Statistics
o Limitations of Statistics
o Functions or Uses of Statistics
o Importance of Statistics in Different Fields
o Some Basic Definitions in Statistics
o Collection of Statistical Data
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.
Meanings of Statistics
The word statistics has three different meanings (sense) which are discussed below:
(1) Plural Sense (2) Singular Sense (3) Plural of the word “Statistic”
(1) Plural Sense:
In plural sense, the word statistics refer to numerical facts and figures collected in a systematic
manner with a definite purpose in any field of study. In this sense, statistics are also aggregates of facts
which are expressed in numerical form. For example, Statistics on industrial production, statistics or
population growth of a country in different years etc.
2) Singular Sense:
In singular sense, it refers to the science comprising methods which are used in
collection, analysis, interpretation and presentation of numerical data. These methods are used to
draw conclusion about the population parameter
For Example: If we want to have a study about the distribution of weights of students in a
certain college. First of all, we will collect the information on the weights which may be
obtained from the records of the college or we may collect from the students directly. The large

number of weight figures will confuse the mind. In this situation we may arrange the weights in
groups such as: “50 Kg to 60 Kg” “60 Kg to 70 Kg” and so on and find the number of students
fall in each group. This step is called a presentation of data. We may still go further and
compute the averages and some other measures which may give us complete description of the
original data.
3) Plural of Word “Statistic”:
The word statistics is used as the plural of the word “Statistic” which refers to a
numerical quantity like mean, median, variance etc…, calculated from sample value
For Example: If we select 15 student from a class of 80 students, measure their heights and find
the average height. This average would be a statistic
Kinds or Branches Statistics
Statistics may be divided into two main branches:
(1) Descriptive Statistics (2) Inferential Statistics
(1) 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.
(2) 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.
Definition of Statistics
.
 Branch of mathematics concerned with collection, classification, analysis, and interpretation
of numerical facts, for drawing inferences on the basis of their quantifiable likelihood
(probability). Statistics can interpret aggregates of data too large to be intelligible by ordinary
observation because such data (unlike individual quantities) tend to behave in regular,
predictable manner. It is subdivided into descriptive statistics and inferential statistics.

 Accordng t o A.L. Bowley defined statistics as
“statistics is the science of counting”
 A.L. Bowley has also defined as
"science of averages”
 Prof: Boddington has defined statistics as
“science of estimate and probabilities”
Characteristics of Statistics
Some of its important characteristics are given below:
• Statistics are aggregates of facts.
• Statistics are numerically expressed.
• Statistics are affected to a marked extent by multiplicity of causes.
• Statistics are enumerated or estimated according to a reasonable standard of accuracy.
• Statistics are collected for a predetermine purpose.
• Statistics are collected in a systemic manner.
• Statistics must be comparable to each other.
Limitations 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
Functions or 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
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.
Some Basic Definitions in
Statistics
Constant:
A quantity which can be assuming only one value is called a constant. It is usually
denoted by the first letters of alphabets .
For Example: Value of and value of
Variable:
A quantity which can vary from one individual or object to and other is called a variable.

It is usually denoted by the last letters of alphabets .
For Example: Heights and Weights of students, Income, Temperature, No. of Children in a
family etc…
Continuous Variable:
A variable which can assume each and every value within a given range is called a
continuous variable. It can occur in decimals.
For Example: Heights and Weights of students, Speed of a bus, the age of a Shopkeeper, the
life time of a T.V etc…
Continuous Data:
Data which can be described by a continuous variable is called continuous data.
For Example: Weights of 50 students in a class.
Discrete Variable:
A variable which can assume only some specific values within a given range is called
discrete variable. It cannot occur in decimals. It can occur in whole numbers.
For Example: Number of students in a class, number of flowers on the tree, number of houses
in a street, number of chairs in a room etc…
Discrete Data:
Data which can be described by a discrete variable is called discrete data.
For Example: Number of students in a college.
Quantitative Variable:
A characteristic which varies only in magnitude from on individual to another is called
quantitative variable. It can be measurable.
For Example: Wages, Prices, Heights, Weights etc…
Qualitative Variable:
A characteristic which varies only in quality from one individual to another is called
qualitative variable. It cannot be measured.
For Example: Beauty, Marital Status, Rich, Poor, Smell etc
Collection of Statistical Data
Statistical Data:
A sequence of observation, made on a set of objects included in the sample drawn from
population is known as statistical data.

(1) Ungrouped Data:
Data which have been arranged in a systematic order are called raw data or ungrouped
data.
(2) Grouped Data:
Data presented in the form of frequency distribution is called grouped data.
Collection of Data:
The first step in any enquiry (investigation) is collection of data. The data may be
collected for the whole population or for a sample only. It is mostly collected on sample basis.
Collection of data is very difficult job. The enumerator or investigator is the well trained person
who collects the statistical data. The respondents (information) are the persons whom the
information is collected.
Types of Data:
There are two types (sources) for the collection of data.
(1) Primary Data (2) Secondary Data
1) Primary Data:
The primary data are the first hand information collected, compiled and published by
organization for some purpose. They are most original data in character and have not undergone
any sort of statistical treatment.
Example: Population census reports are primary data because these are collected, complied and
published by the population census organization.
(2) Secondary Data:
The secondary data are the second hand information which are already collected by
some one (organization) for some purpose and are available for the present study. The secondary
data are not pure in character and have undergone some treatment at least once.
Example: Economics survey of England is secondary data because these are collected by more
than one organization like Bureau of statistics, Board of Revenue, the Banks etc…
Methods of Collecting Primary Data:
Primary data are collected by the following methods:
• Personal Investigation: The researcher conducts the survey him/herself and collects
data from it. The data collected in this way is usually accurate and reliable. This method
of collecting data is only applicable in case of small research projects.

• Through Investigation: Trained investigators are employed to collect the data. These
investigators contact the individuals and fill in questionnaire after asking the required
information. Most of the organizing implied this method.
• Collection through Questionnaire: The researchers get the data from local
representation or agents that are based upon their own experience. This method is quick
but gives only rough estimate.
• Through Telephone: The researchers get information through telephone this method is
quick and give accurate information.
Methods of Collecting Secondary
Data:
The secondary data are collected by the following sources:
• Official: e.g. The publications of the Statistical Division, Ministry of Finance, the
Federal Bureaus of Statistics, Ministries of Food, Agriculture, Industry, Labor etc…
• Semi-Official: e.g. State Bank, Railway Board, Central Cotton Committee, Boards of
Economic Enquiry etc…
• Publication of Trade Associations, Chambers of Commerce etc…
• Technical and Trade Journals and Newspapers.
• Research Organizations such as Universities and other institutions
Difference between Primary and
Secondary
Data
The difference between primary and secondary data is only a change of hand. The
primary data are the first hand data information which is directly collected form one source.
They are most original data in character and have not undergone any sort of statistical treatment
while the secondary data are obtained from some other sources or agencies. They are not pure in
character and have undergone some treatment at least once.
For Example: Suppose we interested to find the average age of MS students. We collect the
age’s data by two methods; either by directly collecting from each student himself personally or
getting their ages from the university record. The data collected by the direct personal
investigation is called primary data and the data obtained from the university record is called
secondary data

Editing of Data:
After collecting the data either from primary or secondary source, the next step is its
editing. Editing means the examination of collected data to discover any error and mistake
before presenting it. It has to be decided before hand what degree of accuracy is wanted and
what extent of errors can be tolerated in the inquiry. The editing of secondary data is simpler
than that of primary data.
References:
1. Thompson, B. (2006). Foundations of behavioral statistics. New York, NY: Guilford Press
2. Dodge, Y. (2006) the Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
3.^ "Statistic". Merriam-Webster Online Dictionary. http://www.merriam-
webster.com/dictionary/statistic.
4.^ a b
Dodge, Y. (2006) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-
920613-9

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