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Statistical laws are not exact as in the case of natural sciences. These laws are true only on average. They hold good under certain conditions. They cannot be universally applied.
So statistics have less practical utility. These above are the Scope and Limitations of Statistics which is very important and we also learned about the importance of statistics above.
As discussed above, here the results are interpolated for which time series or regression or probability can be used. These are not absolutely true.
If the average of two sections of students in statistics is the same, it does not mean that all the 50 students are section A has got the same marks as in B. There may be many variations between the two. So we get average results.
The greatest limitation of statistical science is that it can be misused. The only one who has expert knowledge of statistical methods can scientifically handle statistical data.
Statistical methods, if misused by incompetent, unskilled and inexperienced persons, it may lead to false conclusions.
The best solution under all conditions of the given problem is not p by the statistical methods.
Statistics cannot be of much help in studying the provided problem, like a country’s culture, religion, and philosophy unless they are supplemented by other evidence.
There are only a few results that are accurately correct in statistics and almost all are only approximately correct.
In other words, a hundred percent accuracy is impossible in statistical work because statistical laws are based on average.
Statistics always study a group of values instead of single observation studies the mass of phenomena and the conclusion on certain characteristics obtained.
For example, the study of income of one worker of a company is statistics, but the study of incomes of 50 workers of that company form statistics. In other words, the monthly income of Rs. 1,000 workers do not constitute statistics but the average income of Rs. 1000 of a group of workers of that company forms statistics.
“Statistics deals only with measurable aspects of things and therefore, can seldom give the complete solution to problem. They provide a basis for judgement but not the whole judgment.” —Prof. L.R. Connor
Although we use many laws and formulae in statistics but still the results achieved are not final and conclusive. As they are unable to give complete solution to a problem, the result must be taken and used with much wisdom.
In this subject we use so many methods to find a single result. Variation can be found by quartile deviation, mean deviation or standard deviations and results vary in each case.
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“It must not be assumed that the statistics is the only method to use in research, neither should this method of considered the best attack for the problem.” —Croxten and Cowden
As discussed above, here the results are interpolated for which time series or regression or probability can be used. These are not absolutely true. If average of two sections of students in statistics is same, it does not mean that all the 50 students is section A has got same marks as in B. There may be much variation between the two. So we get average results.
“Statistics largely deals with averages and these averages may be made up of individual items radically different from each other.” —W.L King
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As far as two fundamental laws are concerned with statistics:
(i) Law of inertia of large numbers and
(ii) Law of statistical regularity, are not as good as their science laws.
They are based on probability. So these results will not always be as good as of scientific laws. On the basis of probability or interpolation, we can only estimate the production of paddy in 2008 but cannot make a claim that it would be exactly 100 %. Here only approximations are made.