1. Qualitative Aspect Ignored:
The statistical methods don’t study the nature of phenomenon which cannot be expressed in quantitative terms.
Such phenomena cannot be a part of the study of statistics. These include health, riches, intelligence etc. It needs conversion of qualitative data into quantitative data.
So experiments are being undertaken to measure the reactions of a man through data. Now a days statistics is used in all the aspects of the life as well as universal activities.
2. It does not deal with individual items:
It is clear from the definition given by Prof. Horace Sacrist, “By statistics we mean aggregates of facts…. and placed in relation to each other”, that statistics deals with only aggregates of facts or items and it does not recognize any individual item. Thus, individual terms as death of 6 persons in a accident, 85% results of a class of a school in a particular year, will not amount to statistics as they are not placed in a group of similar items. It does not deal with the individual items, however, important they may be.
3. It does not depict entire story of phenomenon:
When even phenomena happen, that is due to many causes, but all these causes can not be expressed in terms of data. So we cannot reach at the correct conclusions. Development of a group depends upon many social factors like, parents’ economic condition, education, culture, region, administration by government etc. But all these factors cannot be placed in data. So we analyse only that data we find quantitatively and not qualitatively. So results or conclusion are not 100% correct because many aspects are ignored.
4. It is liable to be miscued:
As W.I. King points out, “One of the short-comings of statistics is that do not bear on their face the label of their quality.” So we can say that we can check the data and procedures of its approaching to conclusions. But these data may have been collected by inexperienced persons or they may have been dishonest or biased. As it is a delicate science and can be easily misused by an unscrupulous person. So data must be used with a caution. Otherwise results may prove to be disastrous.
5. Laws are not exact:
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.
6. Results are true only on average:
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
7. To Many methods to study problems:
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.
“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
8. Statistical results are not always beyond doubt:
“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.