## What is Statistics?

Since all branches use statistics, there are number of definitions of statistics, each based on the way one looks at the application of the statistics. Some of the definitions appealing to the managerial perspective are listed below.

Thus, statistics is a science of collection, organisation, presentation, analysis and interpretation of data, so that it helps a manager to take effective and knowledgeable decisions under given circumstances.

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## Importance of Statistics

Whatever be the field of application, complete information can seldom be obtained due to cost and time factors. In real life, partial information forms the basis of most of our decisions. Statistical techniques enable us to:

- Identify what information or data is worth collecting
- Decide when and how judgments may be made on the basis of partial information, and
- Measure the extent of doubt and risk associated with the use of partial information and stochastic processes.

The key distinction between normative (or judgmental) techniques and statistical techniques is of estimate of level of confidence in the decision. Statistical methods are explicit in nature and provide clearly defined measures of error.

On the other hand, normative techniques based on the judgment and rule of thumb, although help in effective decision-making but fail to specify an estimate of error.

## Classification of Statistics

Statistical methods are broadly divided into five categories. These categories are not mutually exclusive. These are often found to be overlapping.

### Descriptive Statistics

When statistical methods are used, a problem is always formulated in terms of ‘population’ or ‘universe’, which is defined as all the elements about which conclusions or decisions are to be made. In statistics, there is a specific meaning to the word’s population and universe.

We shall discuss exact definitions subsequently. For example, if we want to find customer satisfaction, all our customers represent the population. If information or data is taken from each and every element of the population, we are dealing with ‘Descriptive Statistics’.

In research vocabulary, such a process is called ‘Census’. This includes methods for collection, collation, tabulation, summarization and analysis of the data on entire population.

Averages, trends, index numbers, dispersion and skewness, help in summarizing and describing the main features of the statistical data. This is primarily to present the data in the form easily understandable to the decision-maker. One example is the national census conducted every 10 years.

### Analytical Statistics

This deals with establishing relationship between two or more variables. This includes methods like correlation and regression, association of attributes, multivariate analysis, etc., which help establishing relationship between variables.

This facilitates comparison, interpolation, extrapolation and relationships. In these cases, we require multiple samples on different populations or same population, for example, sales of a product before and after launch of promotion campaign.

### Inductive Statistics

Decision making in most business situations requires estimates about future trends and forecast. Inductive statistics include methods that help in generalizing the trends based on the random observations.

This process provides estimation indirectly on the basis of partial data or method of forecasting based on past data, for example, the future share price of a share based on the inflow of funds by FII.

### Inferential Statistics

Another way, in which conclusions or decisions are made, is by using a portion of the population or sample from the universe. The sample data is analyzed. Then based on the sample evidence, conclusions are generalized about the target population.

Exit poll during elections is an example of a sample survey. This method is referred to as ‘Statistical Inference’. Hypotheses and significance tests form an important part of inferential statistics.

### Applied Statistics

It is the application of statistical methods and techniques used for solving real-life problems. Quality control, sample surveys, inventory management, simulations, quantitative analysis for business decision-making, etc., form a part of this category.

## Role of Statistics

Role of statistics is defined below in different areas.

### Role of Statistics in Business

Today, statistics is not restricted to information about the state but extends to almost every realm of the business. Statistics is concerned with scientific methods of collecting, organizing, summarizing, and analyzing data.

What is even more important is drawing valid conclusions and making effective decisions based on such analysis.

The success of a business to a large extent depends on the accuracy and precision of the forecast. Statistics is an indispensable tool for production control and market research.

Statistical tools are extensively used in business for time and motion study, consumer behavior study, investment decisions, performance measurements and compensations, credit ratings, inventory management, accounting, quality control, distribution channel design, etc.

Hence, understanding statistical concepts and knowledge of using statistical tools is essential for today’s managers.

### Role of Statistics in Decision Making

Very often, people consider decision-making just as an act of selection among alternatives. However, there are two more phases in decision-making. Noble Laureate Sir Herbert A Simon identified the phases of decision-making as:

**Information gathering:**Searching the environment for information, is called intelligence activity.**Generation of alternatives:**Inventing, developing, and analyzing possible courses of action, called the design activity.**Selection of alternatives:**Selecting a particular course of action from those available, is called the decision activity.

Most important task of a manager is to take decisions in a given situation that helps an organization to achieve its goals. Management is a process of converting information into action – this we call decision-making.

Decision-making is a deliberate thought process based on available data developing alternatives to choose from so as to find the best solution to the problem at hand.

Statistics and statistical tools play a very vital role during all these three phases of decisions. There are two basic approaches of decision-making, namely, quantitative (or mathematical) and qualitative (or rational, creative, and judgmental).

In the first approach statistics and mathematics play a dominant role. Even in the second approach statistics plays a role in the collection and presentation of data to help decision-makers’ intuition. The extent to which statistical and mathematical tools can be used depends upon the situation.

These can be briefly classified as:

**Decision-making under certainty:**These are deterministic situations amenable to mathematical tools to the fullest extent.**Decision-making under risk:**These are stochastic situations amenable to statistical tools to a large extent with the supplement of rational decision-making.**Decision-making under uncertainty:**These are amenable to judgmental and creative approaches.

It is observed that middle-level and senior-level managers primarily deal with decision-making under risk or in a few cases decision-making under uncertainty. Thus, knowledge of statistical and mathematical computational tools is necessary, if not mandatory, for efficient and effective decision-making.

It is not required to apply all advanced statistical tools in every situation. Certain tools may not be applicable in some cases.

Simple statistics like average, weighted average, percentage, and standard deviation, and index would reveal a great deal of information in many decision-making scenarios. The exploratory investigation may, however, require some advanced tools.

### Role of Statistics in Research

Statistical analysis is a vital component in every aspect of research. Social surveys, laboratory experiments, clinical trials, marketing research, human resource planning, inventory management, quality management, etc., require statistical treatment before arriving at valid conclusions.

Today, with the availability of computers, we can very effectively apply statistical techniques in every field of knowledge. The findings of any research have to be justified in the light of statistical logic.

In business situations, the use of statistical tools in marketing research, operations research, forecasting, factor analysis, human resource development, etc., could immensely benefit managers to gain a competitive advantage, improve productivity and reduce costs.

Thus, every manager must be aware of statistical tools and should have the knowledge to use them.

## Functions of Statistics

The functions of statistics are described below:

**Condensation**: Statistics compresses a mass of figures to small meaningful information, for example, average sales, BSE index (SENSEX), and growth rate. It is impossible to get a precise idea about the profitability of a business from a record of income and expenditure transactions.

The information on Return on Investment (ROI), Earnings per Share (EPS), profit margins, etc., however, can be easily remembered, understood, and used in decision-making.**Comparison**: Statistics facilitates comparing two related quantities, for example, the Price to Earning Ratio (PE Ratio) of Reliance Industries stood at 17.5 as compared to the industry figure of 13 showing the confidence of investors.**Forecast**: Statistics helps in the forecast by looking at trends. These are essential for planning and decision-making. Predictions based on gut feeling or hunch could be harmful to the business.

For example, to decide the refining capacity for a petrochemical plant, we need to predict the demand for petrochemical product mix, supply of crude, cost of crude, substitution products, etc., over the next 15 to 25 years, before committing an investment.**Testing of hypotheses**: Hypotheses are statements about the population parameters based on our past knowledge or information that we would like to check its validity in the light of current information. Inductive inference about the population based on the sample estimates involves an element of risk.

However, sampling keeps the costs of decision-making low. Statistics provides a quantitative base for testing our beliefs about the population.**Preciseness**: Statistics present facts precisely in quantitative form. A statement of facts conveyed in exact quantitative terms is always more convincing than vague utterances. For example, ‘increase in profit margin is less in the year 2006 than in the year 2005’ does not convey a definite piece of information.

On the other hand, statistics present the information more definitely like “profit margin is 10% of the turnover in year 2006 against 12% in the year 2005”.**Expectation**: Statistics provides the basic building block for framing suitable policies. For example, how much raw material should be imported, how much capacity should be installed, or manpower recruited, etc., depends upon the expected value of the outcome of our present decisions.

### Laws of Statistics

There are two fundamental laws of statistics. These are:

#### The Law of Statistical Regularity

This law states, “A moderately large number of items, chosen at random from a large group, are almost sure on average to possess the characteristics of the large group.”

For example, it is difficult to predict the failure of an individual machine or an accident on expressway but not difficult to indicate what percentage of a large number of machines might suffer from a breakdown in a given period.

Similarly, the average number of accidents on expressways would remain stable over a fairly long period of time unless the conditions have changed drastically.

#### The Law of Inertia of Large Number

It states, ‘Other things being equal, as the sample size increases the result tends to be more reliable and accurate.’ As the sample size increases, the possibility of the effect of extreme values in data reduces due to the compensation on both sides.

Thus, as the sample size increases chances of stability of results enhance, and confidence in our estimate of the population increases. In the limiting case if the sample size reaches the population size we can exactly describe the characteristics of the population.

## Limitations of Statistics

Statistical techniques, because of their flexibility and economy, have become popular and are used in numerous fields. But statistics is not a cure-all technique and has limitations. It cannot be applied to all kinds of situations and cannot be made to answer all queries. The major limitations are:

- Statistics deals with only those problems, which can be expressed in quantitative terms and are amenable to mathematical and numerical analysis. These are not suitable for qualitative data such as customer loyalty, the integrity of employees, emotional bonding, motivation, initiative, etc.
- Statistics deals only with the collection of data and no importance is attached to an individual item.
- Statistical results are only approximate and not mathematically correct. There is always a possibility of random error.
- Statistics, if used wrongly, can lead to misleading conclusions, and therefore, should be used only after a complete understanding of the process and conceptual base.

### Common Statistical Issues

There are different types of statistical issues faced by a researcher. These are broadly classified into the following groups.

**Data collection and recording stage:**These include sampling plan, data collection, and data representation.**Computing basic statistics:**These include proportions, computing central tendency, variation, and skewness, measuring the consistency of data, frequency distribution, and cross-tabulation.**Statistical tests of hypotheses:**These include a comparison of means, comparison of proportions, and comparison of variances.**Associations and relationship:**These include testing of dependence between attributes, correction and regression, and non-parametric methods.**Multivariate method:**These include factor analysis, cluster analysis, discriminant analysis, probit and logit analysis, path analysis, profile analysis, multivariate ANOVA, and analysis of factorial experiments.

Each of these requires a fundamental understanding of its statistical origin and purpose.

### Distrust of Statistics

Many managers have doubts about using the result of statistical analysis for decision-making, particularly if the analysis goes against their intuition. Some of them also relate it to their past experience when statistical analysis has misled them.

The problem of misleading could be due to the incorrect use of data. This happens due to a lack of understanding of statistical principles or intentional fudging of the figures with ulterior motives. As Kings says, “Statistics are like the clay of which one can make a god or devil as one pleases”.

According to Bowley, “Statistics only furnishes tools, necessary though imperfect, which are dangerous in the hands of those who do not know its use and its deficiencies”. It is often quoted by managers that “figures don’t lie, liars figure”.

The distrust of statistics among managers is the result of bad experiences, a lack of understanding, hence faith in method, complex and voluminous data overwhelming the thinking, or simply the attitude of liking subjective judgments based on gut feelings.

### Misuse of Statistics

More dangerous than distrust is a misuse of statistics to draw convenient conclusions to satisfy selfish or ulterior motives. Arguments and analyses supported by facts, figures, charts, graphs, index numbers, etc. are indeed very appealing and convincing.

They can be used to intimidate opposing views. Hence, statistics is open to manipulation. Very common examples are charges people make on successive governments of fudging the figures to show how good their government is as compared to the previous government.

Business houses using statistics to mislead the public to manipulate the share prices is not uncommon. The misuse, whether through ignorance or manipulation is a result of one or more of the following reasons.

- Bias in sampling due to shortcuts, convenience, selectivity, or purposeful manipulation.
- The inadequate sample size is too less to represent the underlying characteristics of the population. Statistical inference requires a minimum specified size of the sample.
- Changing definitions, weights, and attributes, of the sampling method, after the commencement of data collection.
- Establishing absurd correlations or associations just because independent data appears moving together.
- Comparing and drawing a causal relationship between unrelated variables based on association.
- Changing hypotheses after collecting and analyzing the data.