Introduction:
In the modern world
of computers and information technology, the importance of statistics is very
well recognised 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
i) Numerical
facts, such as the number of people living in particular area.
ii) 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.
i) 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.
ii) Statistics
are measurements, enumerations or estimates of natural phenomenon usually
systematically arranged, analysed and presented as to exhibit important
interrelationships 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.
1) 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.
2) 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.
3) 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.
4) 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
i) Estimation
theory
ii) Tests
of Hypothesis
iii) Non
Parametric tests
iv) 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.
5) Tests of Hypothesis: A
statistical hypothesis is some statement about the probability distribution,
characterising 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.
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