1. DEFINITIONS, SCOPE AND LIMITATIONS

1.  DEFINITIONS, SCOPE AND LIMITATIONS

     Introduction:

In   the   modern   world   of   computers   and   information technology, the importance of statistics is very well recogonised by all the disciplines. Statistics has originated as a science of statehood and   found   applications   slowly   and   steadily   in   Agriculture, Economics, Commerce, Biology, Medicine, Industry, planning, education and so on. As on date there is no other human walk of life, where statistics cannot be applied.

Origin and Growth of Statistics:

The word ‘ Statistics’  and ‘ Statistical’  are all derived from the  Latin  word  Status,  means  a  political  state.  The  theory  of statistics   as   a   distinct   branch   of   scientific   method   is   of comparatively recent growth. Research particularly into the mathematical theory of statistics  is  rapidly proceeding  and  fresh discoveries are being made all over the world.

Meaning of Statistics:

Statistics  is  concerned  with  scientific  methods  for collecting, organising, summarising, presenting and analysing data as  well  as  deriving  valid  conclusions  and  making  reasonable decisions on the basis of this analysis. Statistics is concerned with the systematic collection of numerical data and its interpretation. The word ‘ statistic’ is used to refer to

1.   Numerical facts, such as the number of people living in particular area.

        2.   The study of ways of collecting, analysing and interpreting

the facts.

Definitions:

Statistics is defined differently by different authors over a period of time.    In the olden days statistics was confined to only state affairs but in modern days it embraces almost every sphere of

human activity. Therefore a number of old definitions, which was confined to narrow field of enquiry were replaced by more definitions, which are much more comprehensive and exhaustive. Secondly, statistics has been defined in two different ways – Statistical data and statistical methods. The following are some of the definitions of statistics as numerical data.

1.   Statistics are the classified facts representing the conditions of people in a state. In particular they are the facts, which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement.

2.   Statistics are measurements, enumerations or estimates of

natural  phenomenon  usually  systematically  arranged, analysed and presented as to exhibit important inter- relationships among them.

Definitions by A.L. Bowley:

Statistics are numerical statement of facts in any department of enquiry placed in relation to each other.                - A.L. Bowley

Statistics may be called the science of counting in one of the departments  due  to  Bowley,  obviously  this  is  an  incomplete

definition as it takes into account only the aspect of collection and ignores    other    aspects    such    as    analysis,    presentation and interpretation.Bowley gives another definition for statistics, which states

‘ statistics  may  be  rightly  called  the  scheme  of  averages’ .  This definition is also incomplete, as averages play an important role in understanding and comparing data and statistics provide more measures.

Definition by Croxton and Cowden:

Statistics  may  be  defined  as  the  science  of  collection,

presentation analysis and interpretation of numerical data from the logical  analysis.  It  is  clear  that  the  definition  of  statistics  by Croxton and Cowden is the most scientific and realistic one. According to this definition there are four stages:

1. Collection of  Data: It is the first step and this is the foundation upon which the entire data set. Careful planning is essential before collecting  the  data.  There  are  different  methods of collection of

data such as census, sampling, primary, secondary, etc.,  and the investigator should make use of correct method.

2.  Presentation  of  data:  The  mass  data  collected  should  be presented  in  a  suitable,  concise  form  for  further  analysis.  The

collected  data  may  be  presented  in  the  form  of  tabular  or diagrammatic or graphic form.

3.  Analysis  of  data:  The  data  presented  should  be  carefully analysed  for  making  inference  from  the  presented  data  such  as

measures of central tendencies, dispersion, correlation, regression etc.,

4.  Interpretation  of data:  The final step is drawing conclusion from the data collected. A valid conclusion must be drawn on the

basis of analysis. A high degree of skill and experience is necessary for the interpretation.

Definition by Horace Secrist:

Statistics may be defined as the aggregate of facts affected

to   a   marked   extent   by   multiplicity   of   causes,   numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other.

The above definition seems to be the most comprehensive and exhaustive.

Functions of Statistics:

There are many functions of statistics. Let us consider the

following five important functions.

Condensation:

Generally speaking by the word ‘ to condense’ , we mean to reduce or to lessen. Condensation is mainly applied at embracing the understanding of a huge mass of data by providing only few observations. If in a particular class in Chennai School, only marks in an examination are given, no purpose will be served. Instead if we are given the average mark in that particular examination, definitely it serves the better purpose. Similarly the range of marks is also another measure of the data. Thus, Statistical measures help to   reduce   the   complexity  of   the   data   and   consequently  to understand any huge mass of data.

Comparison:

Classification and tabulation are the two methods that are

used to condense the data. They help us to compare data collected from different sources. Grand totals, measures of central tendency measures of dispersion, graphs and diagrams, coefficient of correlation etc provide ample scope for comparison.

If we have  one group of data, we can compare within itself. If the rice production (in Tonnes) in Tanjore district is known, then we can compare one region with another region within the district. Or  if  the  rice  production  (in  Tonnes)  of  two  different  districts within Tamilnadu is known, then also a comparative study can be made. As statistics is an aggregate of facts and figures, comparison is always possible and in fact comparison helps us to understand the data in a better way.

Forecasting:

By the word forecasting, we mean to predict or to estimate

before  hand.  Given  the  data  of the  last  ten  years  connected  to rainfall of a particular district in Tamilnadu, it is possible to predict or  forecast  the  rainfall  for  the  near  future.  In  business  also forecasting plays a dominant role in connection with production, sales, profits etc. The analysis of time series and regression analysis plays an important role in forecasting.

Estimation:

One of the main objectives of statistics is drawn inference

about a population from the analysis for the sample drawn from that population. The four major branches of statistical inference are

1.   Estimation theory 

2.   Tests of Hypothesis

3.   Non Parametric tests

4.   Sequential analysis

In estimation theory, we estimate the unknown value of the

population parameter based on the sample observations. Suppose we are given a sample of heights of hundred students in a school, based upon the heights of these 100 students, it is possible to estimate the average height of all students in that school.