Enumerate some important development of statistical theory; also explain merits and limitations of statistics.

Statistical data analysis is generally considered one of the major scientific achievements of the twentieth century. In hard sciences such as seismology or meteorology, a theory based on physical law is not considered successful unless it predicts better than purely statistical arguments. In other disciplines such as econometrics, statistical finance,  genomics, statistical analysis is essential to identifying phenomena. It is perhaps much less recognized that the constitution in the 20^th century of Statistics as an independent scientific discipline is one of the reasons for this intellectual success as well as a consequence.

Probably the best demonstrations of the vitality of statistical ideas are continuing attempts at their appropriation. For example, a recent Nobel Prize in economics essentially recognized research in statistical time series analysis that had application to econometrics. The past century saw the emergence of what are called the mathematical sciences. These include theoretical physics, quantum chemistry, mathematical statistics, and more.
We are now witnessing the emergence of the statistical sciences: disciplines that rely on statistical theory to express their specific ideas. Examples of statistical sciences include biostatistics, econometrics, statistical finance, genomics, signal processing, machine learning, and more. Supporting the growth of the statistical sciences has been the technological revolution in computing.

Until the late 1950's, writers on competing statistical theories thought in terms of virtual data governed by probability models involving relatively few parameters. That same decade found logical paradoxes in the statistical theory of the time which obliged more careful rethinking. By 1970, sophisticated rigorous development of statistical theory had resolved these paradoxes. From the 1960's onward, computing technology and refined concepts of algorithm provided a new environment in which to extend and reconsider statistical ideas developed with probability technology. Case studies and experiments with artificial data increasingly offered non-probabilistic ways of understanding the performance of statistical procedures.

The fundamental distinctions among data, probability model, pseudo-random numbers, and algorithm returned to prominence. It became clear once again that data is often not certifiably random. The bonds that had for many decades linked statistical theory closely to probability models began to loosen in favour of broader views. Use of heuristic data-analytic algorithms not supported by theoretical analysis grew rapidly. Our phrase “the new statistics” refers to the present, much enlarged, concept of statistical methodology.

The “core of statistics” is the subset of statistical activity that is focused inward, on the subject itself, rather than outward, towards the needs of statistics in particular scientific domains. Of necessity, statistical research that seeks to serve the statistical sciences draws on core knowledge for tools as well as for an understanding of the limitations of the tools. Work in the statistical sciences can be collaboration between a statistician and a scientist in the substantive field. However, with the explosion of data needing attention, such collaborations alone cannot possibly fill the need. The rapidly growing needs of the statistical sciences provide raw material for future core research in statistics and motivates the development of trustworthy, user-friendly statistical methodology. Indeed, statistics fluctuates between import and export mode: importing raw data-analytic ideas inspired by the technology and problems of the moment and exporting refined data-analytic procedures, whose characteristics are understood theoretically and experimentally, to the community of quantitative scientists. The phrase "core of statistics" refers precisely to the intellectual basis for the export mode.

The authors of the 2002/2004 Report on the Future of Statistics mentioned in the Overview, the current lag in developing core statistical theory to meet the data-analytic needs of the statistical sciences. The previous paragraph draws on ideas in this report. A few examples where statistical theory needs major development include:

• Accepted standards for experimental exploration of new statistical methods
• Methods for data-mining;
• Automatic methods for discovering new patterns in extremely large data-sets;
• Automatic methods for classifying and recognizing patterns;
• Methods for verifying data integrity;
• Regularization methods for difficult ill-posed problems such as mass tomography based on noisy data.

Merits of Statistics:

• Presenting facts in a definite form
• Simplifying mass of figure- condensation into few significant figures
• Facilitating comparison
• Helping in formulating and testing of hypothesis and developing new theories.
• Helping in predictions.
• Helping in formulation of suitable policies.

Limitations of statistics:

Statistics with all its wide application in every sphere of human activity has its own limitations.  Some of them are given below.

1. Statistics is not suitable to the study of qualitative phenomenon: Since statistics is basically a science and deals with a set of numerical data, it is applicable to the study of only these subjects of enquiry, which can be expressed in terms of quantitative measurements. As a matter of fact, qualitative phenomenon like honesty, poverty, beauty, intelligence etc, cannot be expressed numerically and any statistical analysis cannot be directly applied on these qualitative phenomenons. Nevertheless, statistical techniques may be applied indirectly by first reducing the qualitative expressions to accurate quantitative terms. For example, the intelligence of a group of students can be studied on the basis of their marks in a particular examination.

2.  Statistics does not study individuals: Statistics does not give any specific importance to the individual items; in fact it deals with an aggregate of objects. Individual items, when they are taken individually do not constitute any statistical data and do not serve any purpose for any statistical enquiry.

3.  Statistical laws are not exact: It is well known that mathematical and physical sciences are exact. But statistical laws are not exact and statistical laws are only approximations. Statistical conclusions are not universally true. They are true only on an average.

4.  Statistics table may be misused: Statistics must be used only by experts; otherwise, statistical methods are the most dangerous tools on the hands of the inexpert. The use of statistical tools by the inexperienced and untraced persons might lead to wrong conclusions. Statistics can be easily misused by quoting wrong figures of data.  As King says aptly ‘statistics are like clay of which one can make a God or Devil as one pleases’.

5.  Statistics is only, one of the methods of studying a problem: Statistical methods do not provide complete solution of the problems because problems are to be studied taking the background of the countries culture, philosophy or religion into consideration. Thus the statistical study should be supplemented by other evidences.