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Unit 1: Statistics

example, the population of a country can be divided into three categories on the basis of Notes
complexion of the people such as white, whitish or black.
2. Statistics are aggregate of facts: A single numerical figure cannot be regarded as statistics.
Similarly, a set of unconnected numerical figures cannot be termed as statistics. Statistics
means an aggregate or a set of numerical figures which are related to one another. The
number of cars sold in a particular year cannot be regarded as statistics. On the other hand,
the figures of the number of cars sold in various years of the last decade is statistics
because it is an aggregate of related figures. These figures can be compared and we can
know whether the sale of cars has increased, decreased or remained constant during the
last decade.
It should also be noted here that different figures are comparable only if they are expressed
in same units and represent the same characteristics under different situations. In the
above example, if we have the number of Ambassador cars sold in 1981 and the number of
Fiat cars sold in 1982, etc., then it cannot be regarded as statistics. Similarly, the figures of,
say, measurement of weight of students should be expressed in the same units in order
that these figures are comparable with one another.
3. Statistics are affected to a marked extent by a multiplicity of factors: Statistical data refer
to measurement of facts in a complex situation, e.g., business or economic phenomena are
very complex in the sense that there are a large number of factors operating simultaneously
at a given point of time. Most of these factors are even difficult to identify. We know that
quantity demanded of a commodity, in a given period, depends upon its price, income of
the consumer, prices of other commodities, taste and habits of the consumer. It may be
mentioned here that these factors are only the main factors but not the only factors affecting
the demand of a commodity. Similarly, the sale of a firm in a given period is affected by
a large number of factors. Data collected under such conditions are called statistics or
statistical data.

4. Statistics are either enumerated or estimated with reasonable standard of accuracy: This
characteristic is related to the collection of data. Data are collected either by counting or by
measurement of units or individuals. For example, the number of smokers in a village are
counted while height of soldiers is measured. We may note here that if the area of
investigation is large or the cost of measurement is high, the statistics may also be collected
by examining only a fraction of the total area of investigation.
When statistics are being obtained by measurement of units, it is necessary to maintain a
reasonable degree or standard of accuracy in measurements. The degree of accuracy needed
in an investigation depends upon its nature and objectivity on the one hand and upon time
and resources on the other. For example, in weighing of gold, even milligrams may be
significant where as, for weighing wheat, a few grams may not make much difference.
Sometimes, a higher degree of accuracy is needed in order that the problem, to be
investigated, gets highlighted by the data. Suppose the diameter of bolts produced by a
machine are measured as 1.546 cms, 1.549 cms, 1.548 cms, etc. If, instead, we obtain
measurements only up to two places after decimal, all the measurements would be equal
and as such nothing could be inferred about the working of the machine. In addition to
this, the degree of accuracy also depends upon the availability of time and resources. For
any investigation, a greater degree of accuracy can be achieved by devoting more time or
resources or both. As will be discussed later, in statistics, generalisations about a large
group (known as population) are often made on the basis of small group (known as
sample). It is possible to achieve this by maintaining a reasonable degree of accuracy of
measurements. Therefore, it is not necessary to always have a high degree of accuracy but
whatever degree of accuracy is once decided must be uniformly maintained throughout
the investigation.

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