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Unit 1: Definition of Statistics, Importance and Scope of Statistics and Its Limitations

in the past, what psychological and sociological factor need to be developed for economic development Notes
and for the success of a plan.
1.3 Limitations of Statistics

Though statistics is an important instrument of quantitative method and research in social sciences,
physical science and life sciences, it suffers from a number of limitations. The following are the main
limitations of statistics:
(1) Absence of uniformity: In any statistical inquiry the data obtained are heterogeneous in nature.
Statistical methods alone cannot bring in perfect uniformity. Generally results obtained need
not be uniform and hence will serve no purpose.
(2) Statistics does not study individuals: Statistics deals only with aggregate of facts. Hence, single
figures, however important they might be, cannot be taken up within the purview of statistics.
For example, the marks obtained by X student of a class are not the subject-matter of statistics
but the average marks has statistical relevance.
(3) Statistical results speak about only average: Prof. A. L. Bowley has rightly remarked that
Statistics is a science of average. It implies that statistical results are true only on average. For
example, if we say that per capita income in India is Rs. 12,000 per annum, it does not mean that
the per capita income of the members of the Birla’s family and the income of the poor fellows
who sleep in the slum area are equal. Therefore, averages give only contradicting results.
(4) Statistics can be misused: Statistics is misused very often in the sense that a corrupt man can
always prove all that he wants to do by using false statistics. In the words of W. I. King, “One
of the shortcomings of statistics is that they do not, bear on their face the label of their quality.”
(5) Laws are not stable: The statistical laws are obtained on the basis of information available at
one stage need not be true at another stage. The basic data changes and hence the basic laws
governing them also change. Moreover, what is applicable to India need not be true in Japan.
(6) Statistics cannot be applied to qualitative statistics: The Statistic studies cannot be applied to
qualitative attributes like good, bad, beautiful etc. For a whole sum coverage, the statistical
tools must be applicable for quantitative and qualitative data.
Self-Assessment
1. Fill in the blanks:
(i) The word statistics is used in .......... senses namely .......... and .......... .
(ii) The word statistics refers either .......... information or to a method of dealing with ..........
information.
(iii) Any collection of related observations is called as ........
(iv) Applied statistics is divided into two groups, they are ........ and ........
(v) All the rules of procedures and general principles which are applicable to all kinds of groups
of data are studied under ........
1.4 Summary

• In the traditional period the scope of Statistics was very much limited to the collection of facts
and figures pertaining to the age-wise and sets-wise distribution of population, wealth etc. But
now-a-days we can say that Statistics constitutes an integral part of every scientific and economic
inquiry: Social and economic studies without Statistics are useless. Statistics thus play a vital
role and as Tippet has rightly remarked, “It affects everybody and touches life at many points.”
• Now-a-days Statisticians use statistics both in singular and plural sense. In the singular sense the
term Statistics is associated with “A body of methods for making decisions when there is
uncertainty arising from incompleteness or the instability of the information available for making
such decisions.” In its plural sense Statistics refers to numerical Statements of facts such as per
capita income, population etc. Thus, some authorities have defined Statistics as Statical data (Plural
sense) whereas other as Statistical method (Singular sense). According to Oxford Concise

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