# A Brief Introduction to Statistics | Definition, Scope and Limitations

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**Introduction to Statistics:**

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`In the modern world of computers and information technology, the importance of statistics is very well recognized by all the disciplines. Statistics has originated as a science of statehood and found applications slowly and steadily in Agriculture, Economics, Commerce, Biology, Medicine, Industry, planning, education and so on. As on date there is no other human walk of life, where statistics cannot be applied.`

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`In the modern world of computers and information technology, the importance of statistics is very well recognized by all the disciplines. Statistics has originated as a science of statehood and found applications slowly and steadily in Agriculture, Economics, Commerce, Biology, Medicine, Industry, planning, education and so on. As on date there is no other human walk of life, where statistics cannot be applied.`

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Introductory statistics online course |

### Origin and Growth of Statistics:

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The word ‘Statistics’ and ‘Statistical’ are all derived from the Latin word Status, means a political state. The theory of statistics as a distinct branch of scientific method is of comparatively recent growth. Research particularly into the mathematical theory of statistics is rapidly proceeding and fresh discoveries are being made all over the world.
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The word ‘Statistics’ and ‘Statistical’ are all derived from the Latin word Status, means a political state. The theory of statistics as a distinct branch of scientific method is of comparatively recent growth. Research particularly into the mathematical theory of statistics is rapidly proceeding and fresh discoveries are being made all over the world.
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### What is Statistics:

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Statistics is concerned with scientific methods for collecting, organizing, summarizing, presenting and analysing data as well as deriving valid conclusions and making reasonable decisions on the basis of this analysis. Statistics is concerned with the systematic collection of numerical data and its interpretation.
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The word ‘statistic’ is used to refer to
1. Numerical facts, such as the number of people living in particular area.
2. The study of ways of collecting, analyzing and interpreting the facts.
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Statistics is concerned with scientific methods for collecting, organizing, summarizing, presenting and analysing data as well as deriving valid conclusions and making reasonable decisions on the basis of this analysis. Statistics is concerned with the systematic collection of numerical data and its interpretation.
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The word ‘statistic’ is used to refer to
1. Numerical facts, such as the number of people living in particular area.
2. The study of ways of collecting, analyzing and interpreting the facts.
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### Statistics Definition:

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Statistics is defined differently by different authors over a period of time. In the olden days statistics was confined to only state affairs but in modern days it embraces almost every sphere of human activity. Therefore a number of old definitions, which was confined to narrow field of inquiry, were replaced by more definitions, which are much more comprehensive and exhaustive. Secondly, statistics has been defined in two different ways – Statistical data and statistical methods. The following are some of the definitions of statistics as numerical data.
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1. Statistics are the classified facts representing the conditions of people in a state. In particular they are the facts, which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement.
2. Statistics are measurements, enumerations or estimates of natural phenomenon usually systematically arranged, analysed and presented as to exhibit important interrelationships among them.
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Statistics is defined differently by different authors over a period of time. In the olden days statistics was confined to only state affairs but in modern days it embraces almost every sphere of human activity. Therefore a number of old definitions, which was confined to narrow field of inquiry, were replaced by more definitions, which are much more comprehensive and exhaustive. Secondly, statistics has been defined in two different ways – Statistical data and statistical methods. The following are some of the definitions of statistics as numerical data.
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1. Statistics are the classified facts representing the conditions of people in a state. In particular they are the facts, which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement.
2. Statistics are measurements, enumerations or estimates of natural phenomenon usually systematically arranged, analysed and presented as to exhibit important interrelationships among them.
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### Statistics Definitions by A.L. Bowley:

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Statistics are numerical statement of facts in any department of inquiry placed in relation to each other. - **A.L. Bowley**

Statistics may be called the science of counting in one of the departments due to Bowley, obviously this is an incomplete definition as it takes into account only the aspect of collection and ignores other aspects such as analysis, presentation and interpretation.

Bowley gives another definition for statistics, which states ‘statistics may be rightly called the scheme of averages’.

This definition is also incomplete, as averages play an important role in understanding and comparing data and statistics provide more measures.

Statistics are numerical statement of facts in any department of inquiry placed in relation to each other. -A.L. Bowley

Statistics may be called the science of counting in one of the departments due to Bowley, obviously this is an incomplete definition as it takes into account only the aspect of collection and ignores other aspects such as analysis, presentation and interpretation.

Bowley gives another definition for statistics, which states ‘statistics may be rightly called the scheme of averages’.

This definition is also incomplete, as averages play an important role in understanding and comparing data and statistics provide more measures.

#### Definition by Croxton and Cowden: What is the definition of statistical data?

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Statistics may be defined as the science of collection, presentation analysis and interpretation of numerical data from the logical analysis. It is clear that the definition of statistics by
Croxton and Cowden is the most scientific and realistic one.
According to this definition there are four stages:
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Statistics may be defined as the science of collection, presentation analysis and interpretation of numerical data from the logical analysis. It is clear that the definition of statistics by
Croxton and Cowden is the most scientific and realistic one.
According to this definition there are four stages:
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### 1. Collection of Data:

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It is the first step and this is the foundation upon which the entire data set. Careful planning is essential before collecting the data. There are different methods of collection of data such as census, sampling, primary, secondary, etc., and the investigator should make use of correct method.

It is the first step and this is the foundation upon which the entire data set. Careful planning is essential before collecting the data. There are different methods of collection of data such as census, sampling, primary, secondary, etc., and the investigator should make use of correct method.

### 2. Presentation of data:

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The mass data collected should be presented in a suitable, concise form for further analysis. The collected data may be presented in the form of tabular or diagrammatic or graphic form.
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The mass data collected should be presented in a suitable, concise form for further analysis. The collected data may be presented in the form of tabular or diagrammatic or graphic form.
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### 3. Analysis of data:

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The data presented should be carefully analyzed for making inference from the presented data such as measures of central tendencies, dispersion, correlation, regression etc.,
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The data presented should be carefully analyzed for making inference from the presented data such as measures of central tendencies, dispersion, correlation, regression etc.,
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### 4. Interpretation of data:

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The final step is drawing conclusion from the data collected. A valid conclusion must be drawn on the basis of analysis. A high degree of skill and experience is necessary for the interpretation.
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The final step is drawing conclusion from the data collected. A valid conclusion must be drawn on the basis of analysis. A high degree of skill and experience is necessary for the interpretation.
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#### Definition by Horace Secrist:

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Statistics may be defined as the aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other. The above definition seems to be the most comprehensive and exhaustive.
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Statistics may be defined as the aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other. The above definition seems to be the most comprehensive and exhaustive.
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### Functions of Statistics:

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There are many functions of statistics. Let us consider the following five important functions.
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There are many functions of statistics. Let us consider the following five important functions.
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### Condensation:

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Generally speaking by the word ‘to condense’, we mean to reduce or to lessen. Condensation is mainly applied at embracing the understanding of a huge mass of data by providing only few observations. If in a particular class in Chennai School, only marks in an examination are given, no purpose will be served. Instead if we are given the average mark in that particular examination, definitely it serves the better purpose. Similarly the range of marks is also another measure of the data. Thus, Statistical measures help to reduce the complexity of the data and consequently to understand any huge mass of data.
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Generally speaking by the word ‘to condense’, we mean to reduce or to lessen. Condensation is mainly applied at embracing the understanding of a huge mass of data by providing only few observations. If in a particular class in Chennai School, only marks in an examination are given, no purpose will be served. Instead if we are given the average mark in that particular examination, definitely it serves the better purpose. Similarly the range of marks is also another measure of the data. Thus, Statistical measures help to reduce the complexity of the data and consequently to understand any huge mass of data.
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### Comparison:

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Classification and tabulation are the two methods that are used to condense the data. They help us to compare data collected from different sources. Grand totals, measures of central tendency measures of dispersion, graphs and diagrams, coefficient of correlation etc provide ample scope for comparison. If we have one group of data, we can compare within it. If the rice production (in Tonnes) in Tanjore district is known, then we can compare one region with another region within the district. Or if the rice production (in Tonnes) of two different districts within Tamilnadu is known, then also a comparative study can be made. As statistics is an aggregate of facts and figures, comparison is always possible and in fact comparison helps us to understand the data in a better way.
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Classification and tabulation are the two methods that are used to condense the data. They help us to compare data collected from different sources. Grand totals, measures of central tendency measures of dispersion, graphs and diagrams, coefficient of correlation etc provide ample scope for comparison. If we have one group of data, we can compare within it. If the rice production (in Tonnes) in Tanjore district is known, then we can compare one region with another region within the district. Or if the rice production (in Tonnes) of two different districts within Tamilnadu is known, then also a comparative study can be made. As statistics is an aggregate of facts and figures, comparison is always possible and in fact comparison helps us to understand the data in a better way.
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### Forecasting:

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By the word forecasting, we mean to predict or to estimate beforehand. Given the data of the last ten years connected to rainfall of a particular district in Tamilnadu, it is possible to predict or forecast the rainfall for the near future. In business also forecasting plays a dominant role in connection with production, sales, profits etc. The analysis of time series and regression analysis plays an important role in forecasting.
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By the word forecasting, we mean to predict or to estimate beforehand. Given the data of the last ten years connected to rainfall of a particular district in Tamilnadu, it is possible to predict or forecast the rainfall for the near future. In business also forecasting plays a dominant role in connection with production, sales, profits etc. The analysis of time series and regression analysis plays an important role in forecasting.
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### Estimation:

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One of the main objectives of statistics is drawn inference about a population from the analysis for the sample drawn from that population. The four major branches of statistical inference are
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1. Estimation theory
2. Tests of Hypothesis
3. Non Parametric tests
4. Sequential analysis
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In estimation theory, we estimate the unknown value of the population parameter based on the sample observations. Suppose we are given a sample of heights of hundred students in a school, based upon the heights of these 100 students, it is possible to estimate the average height of all students in that school.
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One of the main objectives of statistics is drawn inference about a population from the analysis for the sample drawn from that population. The four major branches of statistical inference are
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1. Estimation theory
2. Tests of Hypothesis
3. Non Parametric tests
4. Sequential analysis
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In estimation theory, we estimate the unknown value of the population parameter based on the sample observations. Suppose we are given a sample of heights of hundred students in a school, based upon the heights of these 100 students, it is possible to estimate the average height of all students in that school.
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### Tests of Hypothesis:

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A statistical hypothesis is some statement about the probability distribution, characterizing a population on the basis of the information available from the sample observations. In the formulation and testing of hypothesis, statistical methods are extremely useful. Whether crop yield has increased because of the use of new fertilizer or whether the new medicine is effective in eliminating a particular disease are some examples of statements of hypothesis and these are tested by proper statistical tools.
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A statistical hypothesis is some statement about the probability distribution, characterizing a population on the basis of the information available from the sample observations. In the formulation and testing of hypothesis, statistical methods are extremely useful. Whether crop yield has increased because of the use of new fertilizer or whether the new medicine is effective in eliminating a particular disease are some examples of statements of hypothesis and these are tested by proper statistical tools.
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### Scope of Statistics:

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Statistics is not a mere device for collecting numerical data, but as a means of developing sound techniques for their handling, analyzing and drawing valid inferences from them. Statistics is applied in every sphere of human activity – social as well as physical – like Biology, Commerce, Education, Planning, Business Management, Information Technology, etc. It is almost impossible to find a single department of human activity where statistics cannot be applied. We now discuss briefly the applications of statistics in other disciplines.
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Statistics is not a mere device for collecting numerical data, but as a means of developing sound techniques for their handling, analyzing and drawing valid inferences from them. Statistics is applied in every sphere of human activity – social as well as physical – like Biology, Commerce, Education, Planning, Business Management, Information Technology, etc. It is almost impossible to find a single department of human activity where statistics cannot be applied. We now discuss briefly the applications of statistics in other disciplines.
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### Statistics and Industry:

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Statistics is widely used in many industries. In industries, control charts are widely used to maintain a certain quality level. In production engineering, to find whether the product is conforming to specifications or not, statistical tools, namely inspection plans, control charts, etc., are of extreme importance. In inspection plans we have to resort to some kind of sampling – a very important aspect of Statistics.
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Statistics is widely used in many industries. In industries, control charts are widely used to maintain a certain quality level. In production engineering, to find whether the product is conforming to specifications or not, statistical tools, namely inspection plans, control charts, etc., are of extreme importance. In inspection plans we have to resort to some kind of sampling – a very important aspect of Statistics.
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### Statistics and Commerce:

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Statistics are lifeblood of successful commerce. Any businessman cannot afford to either by under stocking or having overstock of his goods. In the beginning he estimates the demand for his goods and then takes steps to adjust with his output or purchases. Thus statistics is indispensable in business and commerce.
As so many multinational companies have invaded into our Indian economy, the size and volume of business is increasing. On one side the stiff competition is increasing whereas on the other side the tastes are changing and new fashions are emerging. In this connection, market survey plays an important role to exhibit the present conditions and to forecast the likely changes in future.
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Statistics are lifeblood of successful commerce. Any businessman cannot afford to either by under stocking or having overstock of his goods. In the beginning he estimates the demand for his goods and then takes steps to adjust with his output or purchases. Thus statistics is indispensable in business and commerce.
As so many multinational companies have invaded into our Indian economy, the size and volume of business is increasing. On one side the stiff competition is increasing whereas on the other side the tastes are changing and new fashions are emerging. In this connection, market survey plays an important role to exhibit the present conditions and to forecast the likely changes in future.
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### Statistics and Agriculture:

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Analysis of variance (ANOVA) is one of the statistical tools developed by Professor R.A. Fisher, plays a prominent role in agriculture experiments. In tests of significance based on small samples, it can be shown that statistics is adequate to test the significant difference between two sample means. In analysis of variance, we are concerned with the testing of equality of several population means.
For an example, five fertilizers are applied to five plots each of wheat and the yields of wheat on each of the plots are given. In such a situation, we are interested in finding out whether the effect of these fertilizers on the yield is significantly different or not. In other words, weather the samples are drawn from the same normal population or not. The answer to this problem is provided by the technique of ANOVA and it is used to test the homogeneity of several population means.
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Analysis of variance (ANOVA) is one of the statistical tools developed by Professor R.A. Fisher, plays a prominent role in agriculture experiments. In tests of significance based on small samples, it can be shown that statistics is adequate to test the significant difference between two sample means. In analysis of variance, we are concerned with the testing of equality of several population means.
For an example, five fertilizers are applied to five plots each of wheat and the yields of wheat on each of the plots are given. In such a situation, we are interested in finding out whether the effect of these fertilizers on the yield is significantly different or not. In other words, weather the samples are drawn from the same normal population or not. The answer to this problem is provided by the technique of ANOVA and it is used to test the homogeneity of several population means.
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### Statistics and Economics:

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Statistical methods are useful in measuring numerical changes in complex groups and interpreting collective phenomenon. Nowadays the uses of statistics are abundantly made in any economic study. Both in economic theory and practice, statistical methods play an important role.
Alfred Marshall said, “Statistics are the straw only which I like every other economists have to make the bricks”. It may also be noted that statistical data and techniques of statistical tools are immensely useful in solving many economic problems such as wages, prices, production, distribution of income and wealth and so on. Statistical tools like Index numbers, time series Analysis, Estimation theory, Testing Statistical Hypothesis are extensively used in economics.
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Statistical methods are useful in measuring numerical changes in complex groups and interpreting collective phenomenon. Nowadays the uses of statistics are abundantly made in any economic study. Both in economic theory and practice, statistical methods play an important role.
Alfred Marshall said, “Statistics are the straw only which I like every other economists have to make the bricks”. It may also be noted that statistical data and techniques of statistical tools are immensely useful in solving many economic problems such as wages, prices, production, distribution of income and wealth and so on. Statistical tools like Index numbers, time series Analysis, Estimation theory, Testing Statistical Hypothesis are extensively used in economics.
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### Statistics and Education:

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Statistics is widely used in education. Research has become a common feature in all branches of activities. Statistics is necessary for the formulation of policies to start new course, consideration of facilities available for new courses etc. There are many people engaged in research work to test the past knowledge and evolve new knowledge. These are possible only through statistics.
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Statistics is widely used in education. Research has become a common feature in all branches of activities. Statistics is necessary for the formulation of policies to start new course, consideration of facilities available for new courses etc. There are many people engaged in research work to test the past knowledge and evolve new knowledge. These are possible only through statistics.
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### Statistics and Planning:

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Statistics is indispensable in planning. In the modern world, which can be termed as the “world of planning”, almost all the organizations in the government are seeking the help of planning for efficient working, for the formulation of policy decisions and execution of the same.
In order to achieve the above goals, the statistical data relating to production, consumption, demand, supply, prices, investments, income expenditure etc and various advanced statistical techniques for processing, analyzing and interpreting such complex data are of importance. In India statistics play an important role in planning, commissioning both at the central and state government levels.
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Statistics is indispensable in planning. In the modern world, which can be termed as the “world of planning”, almost all the organizations in the government are seeking the help of planning for efficient working, for the formulation of policy decisions and execution of the same.
In order to achieve the above goals, the statistical data relating to production, consumption, demand, supply, prices, investments, income expenditure etc and various advanced statistical techniques for processing, analyzing and interpreting such complex data are of importance. In India statistics play an important role in planning, commissioning both at the central and state government levels.
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### Statistics and Medicine:

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In Medical sciences, statistical tools are widely used. In order to test the efficiency of a new drug or medicine, t - test is used or to compare the efficiency of two drugs or two medicines, t - test for the two
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samples is used. More and more applications of statistics are at present used in clinical investigation.
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In Medical sciences, statistical tools are widely used. In order to test the efficiency of a new drug or medicine, t - test is used or to compare the efficiency of two drugs or two medicines, t - test for the two
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samples is used. More and more applications of statistics are at present used in clinical investigation.
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**Statistics and Modern applications**:

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Recent developments in the fields of computer technology and information technology have enabled statistics to integrate their models and thus make statistics a part of decision making procedures of many organizations. There are so many software packages available for solving design of experiments, forecasting simulation problems etc.
SYSTAT, a software package offers mere scientific and technical graphing options than any other desktop statistics package. SYSTAT supports all types of scientific and technical research in various diversified fields as follows
1. Archaeology: Evolution of skull dimensions
2. Epidemiology: Tuberculosis
3. Statistics: Theoretical distributions
4. Manufacturing: Quality improvement
5. Medical research: Clinical investigations.
6. Geology: Estimation of Uranium reserves from ground water.
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Recent developments in the fields of computer technology and information technology have enabled statistics to integrate their models and thus make statistics a part of decision making procedures of many organizations. There are so many software packages available for solving design of experiments, forecasting simulation problems etc.
SYSTAT, a software package offers mere scientific and technical graphing options than any other desktop statistics package. SYSTAT supports all types of scientific and technical research in various diversified fields as follows
1. Archaeology: Evolution of skull dimensions
2. Epidemiology: Tuberculosis
3. Statistics: Theoretical distributions
4. Manufacturing: Quality improvement
5. Medical research: Clinical investigations.
6. Geology: Estimation of Uranium reserves from ground water.
```

### Limitations of statistics:

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Statistics with all its wide application in every sphere of human activity has its own limitations. Some of them are given below.
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Statistics with all its wide application in every sphere of human activity has its own limitations. Some of them are given below.
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### 1. Statistics is not suitable to the study of qualitative phenomenon:

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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 inquiry, 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.

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 inquiry, 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:

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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 inquiry.

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 inquiry.

### 3. Statistical laws are not exact:

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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.
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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.
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### 4. Statistics table may be misused:

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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 un traced 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’.
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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 un traced 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’.
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### 5. Statistics is only, one of the methods of studying a problem:

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`Statistical method 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.`

`Statistical method 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.`

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