Statistics

1. DEFINTIONS
• Statistics has been defined differently by
different statisticians from time to time. The
reasons for a variety of definitions are two.
• In ancient times, statistics was confined only to
the affairs of the state. But in modern times, the
field of utility of statistics has widened
considerably. Hence, a number of old
definitions which were confined to a very
narrow field of enquiry were replaced by new
definitions which are much more
comprehensive and exhaustive.

2. Contd…
• Statistics has been defined in two ways. Some
statisticians have defined it as statistical data
i.e.; numerical statement of facts, while others
define it as statistical methods, i.e.; complete
body of principles and techniques used in
collecting and analyzing such data.

3. Some important definitions.
• Statistics as statistical data:
• Webster defines statistics as “classified facts
representing the conditions of people in a State
– especially those facts which can be stated in
numbers or in any other tabular or classified
arrangements.” This definition confines
statistics only to the data pertaining to a State.
• Bowley defines statistics as “numerical
statements of facts in any department of
enquiry placed in relation to each other.”

4. Contd…
• An exhaustive definition is given by Prof.
Horace Secrist, “By statistics, we mean
aggregate of facts affected to a marked extent
by multiplicity of causes numerically expressed,
enumerated or estimated according to
reasonable standards of accuracy collected in a
systematic manner for a predetermined purpose
and placed in relation to each other.”

5. Contd..
• Statistics as Statistical Method:
Bowley defines statistics in the following three
ways:
• Statistics may be called the science of
counting.
• Statistics may be rightly called the science of
averages.
• Statistics is the science of the measurement of
social organism.

6. Contd…
• But none of Bowley’s definition is adequate.
Firstly, Statistics is not merely confined to the
collection of data as other aspects like
Presentation, analysis and interpretation are also
covered by it.
• Secondly, averages are only a part of statistical
tools used in the analysis of the data. Others
being dispersion, skewness, correlation etc.
• Finally, his definition restricts the application of
statistics to Sociology alone. But in modern days,
statistics is used in almost all the fields.

7. Contd…
• According to Boddington, “Statistics is the
science of estimates and probabilities.” This
definition constitutes only a part of statistical
methods.
• According to King, “Statistics is the method of
judging collective, natural or social phenomenon
from the results obtained from the analysis or
enumeration or collection of estimates.”
• Lovitt defines statistics as the “Science which
deals with the collection, classification and
tabulation of numerical facts as the basis for
explanation, description and comparison of
phenomenon.”

8. Contd….
• The best definition is given by Croxton and
Cowden. According to them, “Statistics is
defined as the science which deals with the
collection, analysis and interpretation of
numerical data.”

9. FUNCTIONS OF STATISTICS
It presents the facts in a definite form:
Statistics presents facts in a precise and definite
from by expressing it in the numerical or
quantitative from. For e.g., the statement ‘the
number of students passed in statistics paper in
NUALS in the year 2021-22 was higher than that in
2020-21 will not give a clear idea of the situation.
However, the statement ‘the number of students
who passed in statistics paper in NUALS in the year
2021-22 was 54 as compared to the year 2020-21
in which the number of students passed was 50
conveys a definite information.

10. Contd…
• It simplifies a mass of figures: Statistics helps in
condensing mass of data into few significant
figures. Hence, the statistical methods present
meaningful overall information of the mass of
data.
• It helps in formulating and testing of
hypothesis: Statistical methods are extremely
helpful in formulating and testing hypothesis to
develop new theories. For e.g., whether students
have benefited from extra coaching can be tested
by appropriate statistical tools.

11. Contd…
• It helps in prediction: Statistical methods
provide helpful means of forecasting future
events. For e.g., a cement manufacturer can
predict how much cement he should produce in
2022 based on the demand for it in the current
year.
• It helps in formulation of suitable policies:
Statistics provide the basic material for framing
suitable policies for the Government and other
agencies. For e.g., the data regarding population
helps in determining the future needs such as
food, clothing etc.

12. Contd…
• It facilitates comparison: Statistical methods
provide comparison for same kind of figures. For
e.g., if we know the average marks of students of
2 batches for a particular subject, we can
compare the average marks and conclude
students of which semester is better in that
subject.
•

13. LIMITATIONS
• Statistics and its techniques are widely used in
every branch of knowledge. W.I. King rightly
said: “Science of statistics is the most useful
servant, but only of great value to those who
understand its proper use. The scope of statistics is
very wide and it has great utility; but these are
restricted by its limitations. Following are the
important limitations of statistics.

14. Contd…
Statistics does not deal with individual items:
statistics deals with groups or aggregates only
and the study of an individual fact lies outside
the scope of statistics. For example the mark
secured by a student in legal history is 40 does
not constitute a statistical statement, where as
the average marks secured by students of 2012
batch in legal history is 55 constitute a statistical
statement.

15. Contd…
Statistics deals with quantitative data: Statistics does
not study the data which cannot be measured in
quantitative terms. For e.g., average height of students
of a class, per capita income etc can be studied by the
statistical methods. But qualitative aspects such as
honesty beauty etc cannot be studied directly.
According to Prof. Horace Secrist,” Some
phenomenon cannot be quantitatively measured;
honesty, resourcefulness, integrity, goodwill, all
important in industry as well as in life, is generally not
susceptible to direct statistical measurement.” If we
convert the qualitative data into quantitative data,
comparison is possible

16. Contd….
Statistical laws are true only on average:
statistical laws are not perfect as the laws of
physics or astronomy. The reason is that “statistical
laws are true only on average”. Statistics deals with
such phenomenon which is affected by multiplicity
of causes and it is not possible to study the effects
of each of these factors separately as is done under
experimental methods. It is due to this limitation in
statistical methods, the conclusions arrived at are
not perfectly accurate and consequently the same
conclusions cannot be arrived at under similar
conditions at all times. Statistics are the means and
not a solution to a problem.

17. Contd..
Statistics does not reveal the entire story: since
most of the problems are affected by such factors
which are incapable of statistical analysis, it is not
possible to examine a problem in all its
manifestations only by a statistical approach.
According the Marshall, “statistics are like straw, of
which, I like every other economist have to make
bricks”.

18. Contd…
Statistics is liable to be misused: the most
important limitation is that it must be used by
experts. According to Bowley, “Statistics only
furnishes a tool though imperfect, which is
dangerous in the hands of those who do not know
its use and deficiencies. W.I King states, “Statistics
are like clay of which you can make a god or devil
as you please”. He remarked “Science of Statistics
is the useful servant, but only of great value to those
who understand its proper use”

19. Contd…
Statistics is a good tool to an expert. The greatest
limitation of statistics is that it deals with figures
which can be easily distorted, manipulated or
moulded by politicians, corrupt, dishonest or
unskilled workers for personal selfish motives.
Statistics neither prove nor disprove anything. It is
only a tool, if rightly used may prove quite useful
but if misused by unskilled and dishonest
statisticians might lead to very fallacious
conclusions.