Statistics – Meaning, Definitions, Nature, scope, importance, functions, applications, types and Limitations

In this article we will discuss the basic aspects of business statistics  – Statistics – Meaning, Definitions, Nature, scope, importance, functions, applications, types, and Limitations

1.1 Introduction of Statistics:

In the modern world of computers and information technology, the importance of statistics is very well recognized by all 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 of date, there is no other human walk of life, where statistics cannot be applied.

1.2    Origin and Growth of Statistics:

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 the 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.

Meaning and Definitions of Statistics

The meaning and Definitions of Statistics are given below:

1.3    Meaning of Statistics:

Meaning of statistics -Statistics is concerned with scientific methods for collecting, organising, summarising, 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. 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, analysing and interpreting the

1.4    Definitions of Statistics:

Definitions of ststistics – 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 enquiry 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. Followings are some defnitions given by various statisticians

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 phenomena usually systematically arranged, analyzed and presented as to exhibit important inter-relationships among

1.4.1       Definitions by A.L. Bowley:

Statistics are numerical statements 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 the 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.

1.4.2       Definition by Croxton and Cowden:

Statistics may be defined as the science of collection, presentation analysis, and interpretation of numerical data from 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:

1. Collection of Data: It is the first step and this is the foundation upon which the entire data 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 the correct method.
2. Presentation of data: The mass data collected should be presented in a suitable, concise form for further The collected data may be presented in the form of tabular or diagrammatic or graphic form.
3. Analysis of data: The data presented should be carefully analysed for making inference from the presented data such as measures of central tendencies, dispersion, correlation, regression ,
4. Interpretation of data: 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

1.4.3       Definition by Horace Secrist:

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.

Apart from meaning and definitions of statistics we are going to describe about Nature, scope, importance, functions, applications, types, and Limitations

Nature of Statistics – Science

What is the nature of statistics? Is it a science or an art? This is a debatable topic. Let’s look at both.        

Nature of statistics as science – Science, by definition, is a systematic body of knowledge which studies the cause and effect relationship and endeavors to find out generalization. In simpler terms, it explains the facts. Further, the primary features of science are:

• It is a systematic study of any subject
• It takes a fact and tries to establish the relationship between cause and effect
• Also, the lawsof science are universal in nature

If we take the various statistical methods in consideration, we can define statistics as a science in which we study:

• Numerous methods of collecting, editing, classifying, tabulating and presenting facts using graphs and diagrams
• Several ways of condensing data regarding various social, political, and economic problems

This is done to establish a relationship between various facts. Also, it helps in analyzing and interpreting problems and forecast them too.

However, unlike the pure sciences like physics, chemistry, etc., statistics is not an exact science. We can call it a science of scientific methods. Statistics help other sciences to derive their own laws.

Further, statistical knowledge is not for its own sake but for the sake of other knowledge. Tippet defines statistics as, “A science, where the statistical method is a part of the general scientific methods and based on the same fundamental ideas and processes.”

Nature of Statistics – Art

Nature of statistics as an Art – If Science is knowledge, Art is action or the actual application of science. While Science teaches us to know, Art teaches us to do. Further, Art has the following characteristics:

• It is a group of actions which solve a problem
• It does not describe the facts but examines the merits and demerits and suggests ways to achieve the objective

Based on these characteristics, we can define statistics as an art of applying the science of scientific methods. As an art, statistics offer a better understanding and solution to problems in real life as it offers quantitative information.

While there are several statistical methods, the successful application of the methods is dependent on the statistician’s degree of skill and experience.

According to Tippet, “Statistic is both a science and an art. It is a science in that its methods are basically systematic and have general application and art in that their successful application depends, to a considerable degree, on the skill and special experience of the statistician, and on his knowledge of the field of application.”

After the clarification of basic concepts of statistics like meaning, definitions, Nature, scope, importance, functions, applications, types, and Limitations, we are further describing the scope and limitations of statistics. 

Scope of Statistics

The scope of statistics – Statistics has an extremely wide scope. There is hardly any sphere of human activity where statistics do not show. Be it social sciences or management, all disciplines use statistics in some form. Broadly speaking, the scope of statistics is confined to two main aspects:

1. The Divisions or Classification of Statistics
2. The Application of Statistics

Let’s look at the classification of statistics next. We will talk about its applications in our next article.

Division or Classification of Statistics

Statistics is broadly classified into a few major categories as given below:

Descriptive Statistics

Descriptive statistics is all about numerical data. This data represents the observations which are obtained either through counting or some other measurement process.

The data can define an entire population or universe. Also, a sampling procedure helps in deriving the data. In some cases, the data represents the raw material of any subsequent statistical processing and have the potential to answer specific questions or solve a specific problem itself.

Descriptive statistics also includes techniques like the collection and tabulation of data, averages or measures of the central tendency, dispersion, index number, skewness, etc. These techniques help in the summarization and description of the primary features of the data. Further, it pays a lot of attention to the characteristics of data which a user might otherwise overlook due to its sheer size.

Applied Statistics

Applied Statistics concerns itself with the application of statistical methods and techniques to specific problems in real life. Some such techniques are sample surveys, quantitative analysis for business decisions, quality control, etc.

To give you an example, if a business wants to forecast the demand of a particular product in the market, then the statistician uses methods like extrapolation or least square. This is applied statistics.

Inferential Statistics

Statistics has some methods and techniques for drawing conclusions and statistical inferences about certain parameters of the population based on the estimates from the sample.

This is inferential statistics. Similarly, the hypothesis regarding the characteristics of the sample is tested based on the population’s parameters.

There are numerous tests for this purpose. These tests lay down the possibility of being true in individual cases. Further, the conclusions or statistical inferences are not just guesses. Logical thought and fundamental theories of science and mathematics back these conclusions.

Basic terminology of Statistics :

• Population –
  It is actually a collection of set of individuals or objects or events whose properties are to be analyzed.
• Sample –
  It is the subset of a population.

After the clarification of basic concepts of statistics like meaning, definitions, Nature, scope, importance, functions, applications, types, and Limitations, we are further describing the types of statistics

 Types of Statistics:

The following are mainly 2 types of statistics – descriptive and inferential

1. Descriptive Statistics:
   Descriptive statistics uses data that provides a description of the population either through numerical calculation or graph or table. It provides a graphical summary of data. It is simply used for summarizing objects, etc. There are two categories in this as following below.

In the descriptive Statistics, the Data is described in a summarized way. The summarization is done from the sample of the population using different parameters like Mean or standard deviation. Descriptive Statistics are a way of using charts, graphs, and summary measures to organize, represent, and explain a set of Data. 

• Data is typically arranged and displayed in tables or graphs summarizing details such as histograms, pie charts, bars or scatter plots.
• Descriptive Statistics are just descriptive and thus do not require normalization beyond the Data collected.
• (a). Measure of central tendency –
  Measure of central tendency is also known as summary statistics that is used to represents the center point or a particular value of a data set or sample set.
  In statistics, there are three common measures of central tendency as shown below:
• (i) Mean :
  It is measure of average of all value in a sample set.
  For example,
• (ii) Median :
  It is measure of central value of a sample set. In these, data set is ordered from lowest to highest value and then finds exact middle.
  For example,
• (iii) Mode :
  It is value most frequently arrived in sample set. The value repeated most of time in central set is actually mode.
  For example,

• (b). Measure of Variability –
  Measure of Variability is also known as measure of dispersion and used to describe variability in a sample or population. In statistics, there are three common measures of variability as shown below:
  • (i) Range :
    It is given measure of how to spread apart values in sample set or data set.

Range = Maximum value – Minimum value

• (ii) Variance :
  It simply describes how much a random variable defers from expected value and it is also computed as square of deviation.

S²= ∑ⁿ_i=1 [(x_i – ͞x)² ÷ n]   

In these formula, n represent total data points, ͞x represent mean of data points and x_i represent individual data points.

• (iii) Dispersion :
  It is measure of dispersion of set of data from its mean.

σ= √ (1÷n) ∑ⁿ_i=1 (x_i – μ)² 

2. Inferential Statistics :
   Inferential Statistics makes inference and prediction about population based on a sample of data taken from population. It generalizes a large dataset and applies probabilities to draw a conclusion. It is simply used for explaining meaning of descriptive stats. It is simply used to analyze, interpret result, and draw conclusion. Inferential Statistics is mainly related to and associated with hypothesis testing whose main target is to reject null hypothesis.

Hypothesis testing is a type of inferential procedure that takes help of sample data to evaluate and assess credibility of a hypothesis about a population. Inferential statistics are generally used to determine how strong relationship is within sample. But it is very difficult to obtain a population list and draw a random sample.

Inferential statistics can be done with help of various steps as given below:

1. Obtain and start with a theory.
2. Generate a research hypothesis.
3. Operationalize or use variables
4. Identify or find out population to which we can apply study material.
5. Generate or form a null hypothesis for these population.
6. Collect and gather a sample of children from population and simply run study.
7. Then, perform all tests of statistical to clarify if obtained characteristics of sample are sufficiently different from what would be expected under null hypothesis so that we can be able to find and reject null hypothesis.

Types of inferential statistics –
Various types of inferential statistics are used widely nowadays and are very easy to interpret. These are given below:

• One sample test of difference/One sample hypothesis test
• Confidence Interval
• Contingency Tables and Chi-Square Statistic
• T-test or Anova
• Pearson Correlation
• Bi-variate Regression
• Multi-variate Regression

Inferential Statistics

In the Inferential Statistics, we try to interpret the Meaning of descriptive Statistics. After the Data has been collected, analyzed, and summarised we use Inferential Statistics to describe the Meaning of the collected Data. 

• Inferential Statistics use the probability principle to assess whether trends contained in the research sample can be generalized to the larger population from which the sample originally comes.
• Inferential Statistics are intended to test hypotheses and investigate relationships between variables and can be used to make population predictions.
• Inferential Statistics are used to draw conclusions and inferences, i.e., to make valid generalizations from samples.

After the clarification of basic concepts of statistics like meaning, definitions, Nature, scope, importance, functions, applications, types, and Limitations, we are further describing the functions of statistics.

1.5    Functions of Statistics:

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

1.5.1       Condensation:

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.

1.5.2       Comparison:

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 itself. 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.

1.5.3       Forecasting:

By the word forecasting, we mean to predict or to estimate before hand. 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.

1.5.4       Estimation:

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

1. Estimation theory
2. Tests of Hypothesis
3. Non Parametric tests
4. Sequential analysis

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.

1.5.5       Tests of Hypothesis:

A statistical hypothesis is some statement about the probability distribution, characterising 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.

1.6    Scope of Statistics:

       Statistics is not a mere device for collecting numerical data, but as a means of developing sound techniques for their handling, analysing 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. the following are the scope of the statistics:

1.6.1       Statistics and Industry:

       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.

1.6.2       Statistics and Commerce:

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.

1.6.3       Statistics and Agriculture:

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 yield of wheat on each of the plots are given. In such a situation, we are interested in finding out whether the effect of these fertilisers on the yield is significantly different or not. In other words, whether 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.

1.6.4       Statistics and Economics:

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 economist 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.

1.6.5       Statistics and Education:

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.

1.6.6       Statistics and Planning:

Statistics is indispensable in planning. In the modern world, which can be termed as the “world of planning”, almost all the organisations 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, analysing 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.

1.6.7       Statistics and Medicine:

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 samples is used. More and more applications of statistics are at present used in clinical investigation.

1.6.8       Statistics and Modern applications:

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 organisations. 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. Archeology: Evolution of skull dimensions
2. Epidemiology: Tuberculosis
3. Statistics: Theoretical distributions
4. Manufacturing: Quality improvement
5. Medical research: Clinical
6. Geology: Estimation of Uranium reserves from ground water

1.7    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 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
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 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 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 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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