Stats Anjal

Define the Statistics and illustrate the concept.

The subject of Statistics, as it seems, is not a new discipline but it is as old as the human society itself. Statistical methods and principles have found applications in many fields, business, the social sciences, engineering and the natural and physical sciences. In fact, modern age is the age of statistics. H.G. Well’s prediction that, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”, has become valid in the context of today’s competitive business environment where many organizations find themselves data-rich but information-poor. Thus for decision-makers it is important to develop the ability to extract meaningful information from raw data to make better decisions. It is possible only through the careful analysis of data guided by statistical thinking.

Almost every aspect of natural phenomenon and human and other activity is now subjected to measurement and interpretation in terms of statistics. Through application of appropriate statistical methods, current performance may be measured, significant relationships may be studied, past experience may be analysed and probable future trends appraised. To acquire knowledge and to express it precisely statistical methods and statistics, have a vital role to play.

Meaning and Definition of Statistics

The word ‘statistics’ of English Language has either been derived from the Latin word ‘Status’ or Italian word ‘Statistics’ or German word ‘Statistics’. In each case it means, ‘an organized political state.’

Broadly speaking the word statistics means:

  1. Statistics or statistical data;
  2. Statistical methods or science of statistics;
  3. Statistics, plural of the word statistic.

The common man refers the word statistics as numerical data. In Kendall and Buckland Statistical Dictionary the word statistics is explained as:

The three meanings of the word ‘statistics’ are contained in the statement due to Tute. ‘You compute statistics by statistics from statistics’.

Definition of Statistics. Different authors have given different definitions of statistics. Some of the definitions of statistics describing it as quantitatively are:

“Statistics are the classified facts representing the conditions of the people in a state especially those facts which can be stated in number or in a table of numbers or in any tabular or classified arrangement”.

Another definition due to Bowley is:

“Statistics is a numerical statement of facts in any department of enquiry placed in relation to each other “.

These definitions are not clear and exhaustive. But the following definition given by Secrist is modern and convincing.

It is ‘a body of knowledge’; a branch of applied mathematics. It has its own symbols, techniques and theorems.

  1. “By Statistics we mean aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a pre-determined purpose and placed in relation to each other.”
  2. Statistics are an aggregate of facts:

The series of observations of temperature of patients over a period of, say, one week taken at regular intervals will constitute statistics. If you say the temperature is 102° F, at a particular time, this single isolated figure is not statistics. The collection of figures of height, weight, income etc., of a group of persons can be called ‘Statistics’.

  • Statistics are affected to a marked extent by multiplicity of causes:

In fact, only when the problem is complex we turn to statistics. In the above example, the rise and fall in the temperature of a patient are caused by many factors such as his diet, his constitution, the climate, the drugs etc. There are usually many factors which affect the figures of production of sale, price, import, export etc. of any commodity.

  • Statistics are numerically expressed:

The statements made in the numerical form are statistics. “A particular student has an excellent academic record” or Mr. X is an efficient administrator”, neither is a statistical statement. But “the student has scored 60% marks at B.Com., 65% at M.Com.”; or “Mr. X increased the production in his factory by 7% in the last but one year, 10% in the last year.” Both are statistical statements as they are expressed numerically.

  • Statistics are estimated according to reasonable standard of accuracy:

As statistics are numerical expressions, the figures can be obtained either by actual counting and measuring or by estimation. But in either case, complete accuracy is neither possible nor desirable. For example, when heights of students are measured it is sufficient to measure unto centimeters. The meaning of “reasonable standards of accuracy” should be taken in the context of the problem. For example, gold will have to be weighed in grams and even in milligrams.

  • Statistics are collected in systematic manner :

If the figures are collected by an untrained man without any method, the results will not be reliable. In the above example, the temperatures would be noted at regular intervals of, say, four hours, in centigrade by a trained nurse with a particular type of thermometer.

  • Statistics are collected for a pre-determined purpose:

In our daily life also our actions are usually guided by our purpose. For example, the purpose was to study and compare the effects of the drugs ‘A’ and ‘B’ on the patients suffering from fever. Data collected with no purpose often result in waste of money, time and energy.

  • Statistics are placed in relation to each other:

It is only by comparing the results of drugs ‘A’ and ‘B’ a conclusion as to which drug is more effective can be arrived at.

  • Statistics as ‘Statistical Methods’: The best of the definitions which emphasizes this aspect is given by Croxton and Cowdon. It is as follows:

“Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data.” This definition points out the following characteristics of Statistics as a branch of knowledge and its methods.

  1. Collection of data:

Collection of data is the first step of statistical methods. Since the whole base of statistics stands on the foundation of the collected data, maximum care should be taken at this stage. The results obtained can never be better than the data on which they are based.

  1. Presentation of data:

The data collected are in the form of figures spread irregularly or in the form of answers. These figures cannot tell us much unless they are properly arranged. The second stage in the statistical investigation is to classify the data and put them in the form of tables.

  1. Analysis of data:

It is necessary to analyse the data further in order to arrive at some definite results. The characteristic properties of the problem are revealed only when quantities like measures of central tendency, measures of variation, correlation etc; are calculated. These single figures tell us much about the problem.

Interpretation of data:

This is the last stage in the process and therefore, is perhaps the most difficult part, requiring a high degree of skill and experience. The results of the third stage are in the form of numbers and need to be transformed into statements. These interpretations are, to some extent, probable but could never be taken as absolutely certain. The probability of the results depends upon every stage from the beginning to the end.

Development of Statistics and Statistical Thinking

Statistics has different meanings to different people which depend largely on its use. For example,

  • For the census department, statistics consists of information about the birth rate per thousand and the sex ratio in different states
  • For a cricket fan, statistics refers to numerical information or data relating to the runs scored by a cricketer
  • For a share broker, statistics is the information on changes in share prices over a period of time
  • For an environmentalist, statistics refers to information on the quantity of pollution released into the atmosphere by all types of vehicles in different cities; and so on.

Moreover, with the developments in the statistical techniques during the last few decades, today, statistics is viewed not only as a mere device for collecting numerical data but as a means of sound techniques for their inferences from them. Accordingly, it is not merely a by-product of the administrative set up of the state but it embraces all sciences-social, physical and natural, and is finding numerous applications in various diversified fields. It is rather impossible to think of any sphere of human activity where statistics does not creep in. It will not be exaggeration to say that statistics has assumed unprecedented dimensions these days and statistical thinking is becoming more and more indispensable every day for an able citizenship. In fact to a very striking degree, the modern culture has become the statistical culture and the subject of statistics has acquired tremendous progress in the recent past so much so that an elementary knowledge of statistical methods has became a part of the general education in the curricula of many Universities all over the world.

The development of mathematics in relation to the probability theory and the advent of fast-speed computers have substantially changed the field of statistics in the last few decades. The use of computer softwares, such as SAS and SPSS has brought about a technological revolution.

An integral part of the managerial approach focuses on the quality of products manufactured or services provided by an organization. This approach requires the application of certain statistical methods and the statistical thinking. Statistical thinking may be defined as the thought process that focuses on ways to identify, control and reduce variations present in all phenomena. A better understanding of a phenomenon through statistical thinking and use of statistical methods for data analysis enhances opportunities for improvement in the quality of products or services.

The steps of statistical thinking necessary for increased understanding of an improvement in the process are as follows:

  • Specify the aim of the study;
  • Understand how the process works;
  • Assess the current process performance;
  • Identify strategies for improvement;
  • Test the effectiveness of the proposed strategy;
  • If successful, implement the strategy; if not then identify some other strategy.

Characteristics of Statistics

Following are the characteristics of statistics (According to Secrist):

  • Statistics are the aggregate of facts.
  • Statistics are numerically expressed.
  • Statistics should be collected in a statistic manner.
  • Statistics should be collected for a predetermined purpose.
  • Statistics are affected to a marked extent by multiplicity of causes and not by a single cause.
  • Statistics should be placed in relation to each other.
  • The reasonable standard of accuracy should be maintained in statistics.

Importance and Usefulness of Statistics

Statistics help in presenting large quantity of data in a simple and classified form.

  1. It gives the methods of comparison of data and it weighs and judges them in the right perspective.
  2. It simplifies unwieldy and complex data so as to make them understandable.
  3. It enlarges individual experience.
  4. It helps in finding the conditions of relationship between the variables.
  5. It provides guidance in the formation of business policies.
  6. It helps in establishing cause and effect relationships.
  7. It proves useful in a number of fields like Banks, Railways, Army etc., etc.

Is Statistics   Science or Art?

Statistics as a Science

Science is a body of systematized knowledge from which specific propositions are deducted in accordance with a few general principles. Although all sciences differ, the logical scientific methods are common to all the sciences. Using the approach of systematic doubt, scientific method is a process of discovering the truth in a systematized manner by logical considerations. There are in general four stages in a scientific inquiry: (i) Observation, (ii) hypothesis, (iii) prediction and (iv) verification. Since statistical methods are based on the some fundamental ideas and processes as other sciences, so statistics is said to be a science. But statistics is different from physics, chemistry etc.

Statistics as an Art

An art is an applied knowledge and creation of beauty of leading to perfection. If science is knowledge then art is action. Since the successful application of statistical methods depends to a considerable degree on the skill and special experience of the statistician and his knowledge of the field of application, statistics may be called an art of applying scientific methods similar to an artist who possesses and can apply the requisite skill, experience and patience for the creation of beauty leading to perfection.

Statistics is Both a Science and an Art

According to Toppett “It is both a science and an art. It is a science in that its methods are basically systematic and have general application, and an art in that their successful application depends to a considerable of the statistician and his knowledge of the field of application, e.g., Economics.”

Division of Statistics

The subject matter f the statistics may be classified into the following main divisions:

(a)          Theoretical Statistics

Mathematical theory which is the basis of the science of statistics is called theoretical statistics. The basis of theoretical statistics often called Theory of Probability and deals with the chance variation of the observations.

(b)          Statistical Methods

Statistical methods are the devices by which complex and numerical data are analysed in such a way that way become intelligible and lead to correct conclusions. The important statistical methods are:

  1. Collection of data,
  2. Classification of data,
  3.  Tabulation of data,
  4.  Presentation of data,
  5.  Analysis of data,
  6.  Interpretation of data,
  7.  Forecasting.

(c)           Applied Statistics

This division of the science of statistics deals with the application of rules and principles developed in theoretical statistics to specific problems in different disciplines. For example, Statistical Quality Control, Sample Survey, Design of Experiments, Analysis of Time-Series, Index Numbers etc. The two sub-divisions of applied statistics are as follows:

  1. Descriptive Applied Statistics. The branch of applied statistics which deals with the existing facts of historical importance that are of great interest is known as Descriptive Applied Statistics.
  2. Scientific Applied Statistics. The branch of applied statistics which deals with the establishment of definite laws, rules and doctrines is known as Scientific Applied Statistics subject matter of Applied Statistics.

(d) Business Statistics

A new branch of statistics called Business Statistics under Applied Statistics has been developed. This branch has been expending so rapidly due to the use of statistical methods in business. Every business passes through four phases: prosperity, decline, depression and recovery. Statistical methods are very helpful in forecasting about these phases.

Now-a-days various problems regarding business are studied, analysed and solved through statistical methods.

Importance and Scope of Statistics

The science of statistics is growing in importance every day. It is now being used in almost every field of human activity. Its application has become so wide that no branch of human knowledge from the graphic arts to astrophysics and from numerical composition to missile guidance escapes its approach. Statistics provides tools and techniques for research workers in analysis of problems in both natural and social sciences. There is hardly and field whether it be economics, commerce, industry, trade, biology, sociology, psychology medicine, physics, chemistry, education, astronomy meteorology, administration, insurance, banking or planning where statistical methods are not applicable. That is why it is said that, “Sciences without statistics bear no fruit, statistics without sciences has no root”. In the absence of statistics, most of our problems would have remained unsolved and our knowledge would have limited.

To be more specific we may discuss the application (or relationship) of statistics in (or with) various fields.

Statistics in State:

 Earlier statistics was used by the rulers to assess their military and economic strength. State Government collects information on the economic conditions of the people and resources available. Facts are necessary to plan the use of resources and to assess from time to time the achievement of the objective. All these require collection and analysis of statistics on a regular basis.

Statistics and Economics.

Statistical techniques have proved immensely useful in the solution of a variety of economic problems such as production, consumption, distribution of income and wealth, expenditure and poverty etc. Presently, statistics serves as the base for the mathematical approach to Economics. Some of the uses of statistics in economics are as follows:

  1. Measures of gross national product and input-output analysis have greatly advanced overall economic knowledge and opened up entirely new fields of study.
  2. Financial statistics are basis in the field of money and banking, short-term credit, consumer finance and public finance.
  3. Statistical studies of business cycles, long term growth and seasonal fluctuations serve to expand our knowledge of economic instability and to modify older theories.
  4. Studies of competition, oligopoly and monopoly require statistical comparison of market prices,
    cost and profits of individual firms.
  5. Statistical surveys of prices are essential in studying the theories of prices, pricing policy and price
    trends as well as their relationship to the general problem of inflation.
  6. Operational studies of public utilities require both statistical and legal tools of analysis.
  7. Analysis of population, land economics and economic geography are basically statistical in their approach.
  8. In solving various economic problems such as poverty, unemployment, disparities in the distribution of income and wealth, statistical data and statistical methods play a vital role.

Statistics and Physical Sciences:

 Currently, the physical sciences seem to be making increasing use of statistics, especially in astronomy, chemistry, engineering, geology, meteorology and certain branches of physics.

Statistics and Natural Sciences:

 Statistical techniques have proved to be extremely useful in the study of all natural sciences like astronomy, biology, medicine, meteorology, zoology, botany etc. For example, in diagnosing the correct disease the doctor has to rely heavily on actual data like temperature of the body, pulse rate, blood pressure. Similarly, in judging the efficiency of a particular drug for causing a certain disease experiments have to be conducted and success or failure would depend upon the number of people who are cured after using the drug. In fact, it is difficult to find any scientific activity where statistical data and statistical methods are not used.

Statistics in Social Sciences:

 Some specific areas of applications of statistics in social sciences are as follows:

  1. Regression and correlation analysis technique are used to study and isolate all those factors associated with each social phenomenon which bring out the changes in data with respect to time, place, and object.
  2. Sampling techniques and estimation theory are indispensable methods for conducting any social   survey pertaining to any strata of society, and drawing valid inferences.
  3. In sociology, statistical methods are used to study mortality rates, fertility trends, population growth, and other aspects of vital statistics.

Statistics and Computers:

Computers and information technology, in general, have had a fundamental effect on most business and service organizations. Computers help in processing and maintaining past records of operations involving payroll calculations, inventory management, railway/airline reservations etc. Use of computers hardware, however, presupposes that the user it’s able to interpret the computer outputs that are generated.

Limitations of Statistics

Although statistics is so much useful in the modern world and although it has grown enormously in recent years it is misunderstood by many. It is misunderstood by those who believe in the popular notion that by statistics you can prove anything. The reasons of this misunderstanding are as follows.

  1. It is not useful for individual case.
    1. It cannot study qualitative phenomenon.
    2. Its results are true only on an average.
    3. The statistical results are subject to bias.
    4. It can be misused. Statistical results may be misleading if quoted without context.
    5. Results may be misleading if quoted without context.

Misuse of Statistics

By misuse of statistics we mean the improper use of statistical tools by unscrupulous people with an improper statistical bend of mind and misinterpretation of data.

Misuse of statistics occurs when a statistical argument asserts a falsehood. In the period since statistics began to play a significant role in society, they have often been misused. In some cases, the misuse was accidental. In others, it was purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.

The false statistics trap can be quite damaging to the quest for knowledge. For example, in medical science, correcting a falsehood way take decades and cost lives.

Misuses can be easy to fall into professional scientists, even mathematicians and professional statisticians; can be tooled by even some simple methods, even if they are careful to check everything. Scientists have been known to fool themselves with statistics due to lack of knowledge of probability theory and lack of standardization of their tests.

The misuse of statistics is the main cause to discredit this science and has led to the public distrust in statistics. The various ways in which statistics are often misused are:

  1. Inappropriate comparison of data.
  2. Deliberate manipulation of statistics by selfish persons to achieve their personal ends.
  3. Mathematical manipulations such as wrong use of percentages.
  4. Quoting figures without proper context.      
  5. Ignorance of limitations of statistics. Misuse of statistics can be avoided by:
    Use of sufficient and appropriate data.
  6. Use of statistics by experts.
  7. Logical use of statistical techniques.
  8. Keeping eternal vigilance.
  9. Keeping in mind the limitations of statistics.

In brief, to avoid misuse of statistics, the statistical data should be handled only by those who are aware of their use limitations and dangers and are free from prejudice. Utmost care and precautions should be taken for the interpretations of data in all manifestations.

Distrust of Statistics

Distrust of statistics is the lack of confidence in statistical methods and statements. The following are some derogatory remarks against statistics:

  1. Statistics can prove or disprove anything.
  2. Statistics is like clay of which one can make a God or Devil, one likes.
  3. Statistics are like bikinis. They reveal what is interesting and conceal what is vital.
  4. There are three kinds of lies—Lies, Damn Lies and Statistics.

Reasons for Distrust in Statistics

The causes of distrust in statistics are as follows:

  1. Defective data.
  2. Insufficient data.
  3. Non-comparable data.
  4. Innocence of the figures.
  5. Misinterpretation of Data.
  6. Inappropriate statistical methods.
  7. Absence of an objective lest.

Methods of Removing Distrust of Statistics

  1. Statistics should be used by a person who knows statistical techniques.
  2. There should be patience and self-restraint in the person who collects data and who use them.
  3. Statistical data should be obtained and analysed with independent conversation.
  4. Statistical limits should be kept in mind while interpreting the data.
  5. Precautions should be taken at each step.

The subject of Statistics, as it seems, is not a new discipline but it is as old as the human society itself. Statistical methods and principles have found applications in many fields, business, the social sciences, engineering and the natural and physical sciences. In fact, modern age is the age of statistics. H.G. Well’s prediction that, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”, has become valid in the context of today’s competitive business environment where many organizations find themselves data-rich but information-poor. Thus for decision-makers it is important to develop the ability to extract meaningful information from raw data to make better decisions. It is possible only through the careful analysis of data guided by statistical thinking.

Almost every aspect of natural phenomenon and human and other activity is now subjected to measurement and interpretation in terms of statistics. Through application of appropriate statistical methods, current performance may be measured, significant relationships may be studied, past experience may be analysed and probable future trends appraised. To acquire knowledge and to express it precisely statistical methods and statistics, have a vital role to play.