Introduction
Md. Shafique Nawaz Talukder
Associate Professor, Statistics
M.C.College, Sylhet.
Definition of Statistics :
Statistics has been defined differently by different author from time to time. The reasons for a
variety of definitions are primarily two. First, 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. Secondly statistics has been defined in two ways. Some writers defined it as, “statistical
data” ice, numerical statement of facts, while others defined it as, “statistical methods” i,e,
complete body of the principles and techniques used in collecting and analyzing such data.
Some important definitions are given below:
Webster defines statistics as, “classical facts representing the conditions of the people in a state –
specially those facts which can be stated in numbers or in any other tabular classified
arrangement.”
Bowley defined statistics as, “numerical statement of facts in any department of enquiry placed in
relation to each other.”
Prof. Herace Secrist defined statistics as, “by statistics we mean aggregates of facts affected to a
marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according
to reasonable standard of accuracy, collected in a systematic manner for a pre-determined purpose
and placed in relation to each other.”
According to R.A.Fisher “ The science of statistics is essentially a branch of applied mathematics
and may be regarded as mathematics applied to observational data.”
Characteristics of Statistics:
i) Statistics must be expressed in numerical form. Any other form of facts is not statistics.
ii) Statistics deals with populations or aggregates of individuals rather than individuals.
iii) Statistics should be affected by a large number of random causes.
iv) The logic used in statistical inference is inductive.
v) Statistical inference are uncertain.
vi) Statistical results might lead to fallacious conclusions if they are quoted shorn of their context
or manipulated.
Dispersion
A measure of central tendency tells us something about the general level of magnitude of the
distribution but it fails to give its complete description. It does not tell how the items scatter around
the measure of central tendency. Dispersion means scatter ness of the values of a series from their
central value. That is the extent of values from the mean point is termed as dispersion or variation.
Measures of Dispersion :
The statistical tools by which dispersion is measured are called measures of dispersion. A measure
of dispersion describes the degree of scatter shown by the observations and is usually measured as
an average deviation about some central value or by an order statistic.
Types of measure of dispersion :
There are mainly two types of measure of dispersion :-
1. Absolute measure of dispersion 2. Relative measure of dispersion
Absolute measure of dispersion:
The measure of dispersion which defined from the main definition of dispersion and expressed in
the units by which raw data are collected is called the absolute measure of dispersion. Absolute
measure of dispersion consists of four measures, these are-
(i) Range
(ii) Quartile Deviation
(iii) Mean Deviation
(iv) Standard Deviation
Relative measure of dispersion:
The ratio of an absolute measure of dispersion and an average is called the relative measure of
dispersion. This is an absolute number, it has been used for comparing two or more distributions
given in a different units. Relative measure of dispersion consists of four measures, these are-
(i) Coefficient of range
(ii) Coefficient of quartile Deviation
(iii) Coefficient of mean Deviation
(iv) Coefficient of variation
Difference between absolute and relative measure of dispersion: :
Absolute measure of dispersion Relative measure of dispersion
The measure of dispersion which defined from
the main definition of dispersion and expressed
in the units by which raw data are collected is
called the absolute measure of dispersion.
The ratio of an absolute measure of
dispersion and an average is called the
relative measure of dispersion.
Absolute measure of dispersion has some unit. It is a pure number
It has not been used for comparing two or more
distributions given in a different units.
It has been used for comparing two or more
distributions given in a different units.
It has not been expressed in percentage. For convenience sometimes It has been
expressed in percentage.
Central Tendency
Central Tendency :
In a series of statistical data it can be observed that the values have a tendency to cluster around a
certain point, usually at the center of the series. This tendency of the values to cluster around a
certain value is called central tendency.
Measures of Central Tendency:
In a series of statistical data it can be observed that the values have a tendency to cluster around a
certain point, usually at the center of the series. That central point or single value to which the
values of the series tend to cluster is known as average or measure of central tendency. An average
of a set of values is typical or representative value of the whole set.
Advantages of arithmetic mean
Arithmetic mean is rigidly defined.
It is based on all the observations.
It is amenable to further mathematical treatment.
Disadvantages of arithmetic mean
Arithmetic mean is affected by extreme values.
If any value of the data set is unknown then arithmetic mean can be founded.
For the open end class interval frequency distribution arithmetic mean can be calculated.
Central Tendency
Advantages of geometric mean
Geometric mean is rigidly defined.
It is based on all the observations.
It is not affected much by sampling fluctuations.
Disadvantages of geometric mean
Geometric mean is not easy to understand and to calculate.
If any one of the observations is zero then geometric mean can not be calculated.
If any one of the observations is negative then geometric mean gives imaginary value.
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