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Introduction to Statistics

Population and Sample

Presentation of Data

Measures of Central Tendency

Measures of Dispersion

Moments

Skewness and Kurtosis

Introduction to Statistics

Statistics refers to the numerical facts and figures collected for special purposes. In fact, statistics is not about the number, it is mainly concerned with data and analysis. In a singular sense, it is Science of Statistics while in plural it depicts data analysis. It mainly deals with the collection, presentation, analysis and interpretation of quantitative data, helping in decision making.
Origin and Development of Statistics
Origin of statistics is estimated to be around 1749 although. It is believed that the word Statistics was originated from one of these words 'Status' of Latin, 'Statistik' of German, 'Statistique' of French and 'Statista' of Italian. Each of these words means 'Political State'. Statistics was then regarded as the science of statecraft or the science of kings and was confined to needs of state administration.
But the scope of Statistics expanded with the passage of time. Back in the sixteenth century, J. Kepler used statistics in his study of movements of heavenly bodies. In the seventeenth century, John Graunt was the first man to study Statistics of birth and death and is called the father of 'Vital Statistics'. J. Bernoulli & Laplace laid the foundation of discovery and development of a modern theory of Statistics in the seventeenth and eighteenth century. Other contributions namely principle of least squares by Gauss, normal probability curve by De-Moivre and the principle of 'constancy of great numbers' by A.J. Outlet. Also, great statisticians like Francis Galton, Karl Pearson, R.A. Fisher & many others made substantial contributions to the development of the statistical method.
Statistics today plays a vital role in nearly all fields of human activities and proven itself an important tool in every major field of studies like Industry, Planning, Medicine, Economics, Science, Commerce etc.
Definition of Statistics
Statistics has been defined and analyzed by many great statisticians but here we will study and analyze few important definitions.
Statistics as Numerical Facts (Plural Sense)
According to Webster," The classified facts representing the condition of the people in state or especially those facts which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement."
Achenewall defined Statistics as " A collection of noteworthy facts concerning state, both historical and descriptive."
Both these definitions are narrow and confine area of Statistics to the affairs of the state. The most comprehensive definition of Statistics as numerical data is given by Horace Secrist as
" Statistics may be defined as the aggregate of facts affected to a marked extent by a multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other."
Statistics as a Science (Singular Sense)
In words of Boddington,"Statistics is the science of estimates and probabilities."
Modern statisticians have defined Statistics in a much broader sense. Among them, definition by Croxton and Cowden says," Statistics is the collection, presentation, analysis and interpretation of numerical data."
But Ya-Lun-Chou defines Statistics as " Statistics is a method of decision-making in the face of uncertainty on the basis of numerical data and calculated risks."
Uses and Functions of Statistics
Statistics have drastically evolved to make a clear impression on various disciplines of studies. Here we will know surfacely, how and where statistics makes an impression on these fields:
  • Demography is the statistical study of population and its change over time and space.
  • Chemometrics is the study relating to measurements of a chemical system via mathematical or statistical methods.
  • Astrostatistics is the discipline that involves statistical analysis in understanding of astronomical data.
  • Actuarial Science refers to the analysis of risk in insurance and finance using statistical analysis.
  • Biostatistics is a branch of biology that studies biological phenomena and observations by means of statistical analysis.
  • Econometrics is a branch of Economics involving a statistical method in the study of economic theories and relationships.
  • Environmental Statistics is a discipline involving statistics to study weather, climate, air and water quality.
  • Psychometric is discipline related to the educational and psychological measurement of knowledge, abilities, attitudes and personality traits.
  • Quality Control is discipline involved in manufacturing and production.

These are also many fields and disciplines that widely uses the statistical method and its calculation.
Limitations of Statistics
Though having numerous applications, functions, and uses but it is not without limitations. Some of them are:

  1. It does not study individuals. Statistics deals with aggregate. Individual and isolated facts and figures are outside the scope of Statistics.
  2. Statistical laws are mainly concerned on the average. As a science, Statistics is not exact as so many other sciences like Physics, Chemistry, Astronomy etc.
  3. It does not study qualitative phenomena. One of the main characteristics of Statistics is that it is a numerical statement of facts.
  4. Statistics is liable to be misused. it can often easily be misused. An unscrupulous person may misuse Statistics to manipulate the truth to his own liking.
  5. It is one of the methods used for the study of a problem. According to Croxton and Cowden," It must not be assumed that the statistical method is the only method to use in research, neither should this method be considered the best attack for every problem."

 


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