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Unit 1: Statistics

comparing national income of various years, one can know whether performance of the Notes
country is improving or not. Further, by comparing national income of different countries,
one can know its relative position vis-a-vis other countries.
3. Statistical results are true only on the average: Statistical results give the behaviour of the
group on the average and these may not hold for an individual of that very group. Thus,
the statement that average wages of workers of a certain factory is 1,500 p.m. does not
necessarily mean that each worker is getting this wage. In fact, some of the workers may
be getting more while others less than or equal to 1,500. Further, when value of a
variable is estimated by using some explanatory variable, the estimated value represents
the value on the average for a particular value of the explanatory variable. In a similar
way, all the laws of statistics are true only on the average.

4. Statistical results are only approximately true: Most of the statistical studies are based on
a sample taken from the population. Under certain circumstances the estimated data are
also used.
Therefore, conclusions about a population based on such information are bound to be true
only approximately. Further, if more observations are collected with a view to improve
the accuracy of the results, these efforts are often offset by the errors of observation. In the
words of Bowley, “When observations are extended, many sources of inaccuracy are
found to be present, and it is very frequently impossible to remove them completely.
Statistical results are, therefore, very general estimates rather than exact statements.”
Thus, whether statistical results are based on sample or census data, are bound to be true
only approximately.

5. Statistical methods constitute only one set of methods to study a problem: A given
problem can often be studied in many ways. Statistical methods are used to simplify the
mass of data and obtain quantitative results by its analysis. However, one should not
depend entirely on statistical results. These results must invariably be supplemented by
the results of alternative methods of analysing the problem. It should be kept in mind that
statistics is only a means and not an end. According to D. Gregory and H. Ward, “Statistics
cannot run a business or a government. Nor can the study of statistics do more than
provide a few suggestions or offer a few pointers as to firm’s or government’s future
behaviour.”
6. Statistics are liable to be misused: Statistical data are likely to be misused to draw any type
of conclusion. If the attitude of the investigator is biased towards a particular aspect of the
problem, he is likely to collect only such data which give more importance to that aspect.
The conclusions drawn on the basis of such information are bound to be misleading.
Suppose, for example, the attitude of the Government is biased and it wants to compute a
price index which should show a smaller rise of prices than the actual one. In such a
situation, the Government might use only those price quotations that are obtained from
markets having lower prices.

7. Statistics must be used only by experts: Statistics, being a technical subject, is very difficult
for a common man to understand. Only the experts of statistics can use it correctly and
derive right conclusions from the analysis. In the words of Yule and Kendall, “Statistical
methods are the most dangerous tools in the hands of inexperts.” Hence, this is the most
important limitation of statistics.

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