# STATISTICS

MEANING AND SCOPE OF STATISTICS

MEANING OF STATISTICS:
There is an ever-growing number of people in various disciplines who are finding it more than useful to have knowledge of statistics. The field of statistics has widespread applications, and is offered by a number of disciplines such as business, engineering, social sciences, all the sciences, education, health, environmental science, among others.
Because of the varied number of users, many have different conception of the discipline. Many authors have defined the word “statistics” differently based on mathematical derivation and detail of statistical methods or reflection of a particular philosophical or conceptual emphasis. Whatever the conception, statistics has two broad functions.
The first of these functions is description, the summarizing of information in such a manner as to make it more usable. The second function is induction, which involves either making generalizations about some population on the basis of a sample drawn from it or formulating general laws on the basis of repeated observations.
The word statistics in its plural form means facts, data, and observations, especially those expressed numerically. Examples include births, deaths, marriages. number of road accidents, inflation rates, unemployment figures, business performance, movement of exchange rate, enrolment figures in schools etc. It also includes random estimates of some population parameters, for example, mean income per worker, variance of distance traveled, proportion of female workers in a company, etc.

The word statistics in its singular form connotes a branch of knowledge, a discipline In this sense, statistics may be defined as the scientific method that deals with the collection, collation, classification,presentation, analysis and interpretation of numerical data with a view to making decisions in the face of uncertainty.As a body of knowledge, statistics may be divided into two parts.

Descriptive (Applied) Statistics, which deals with the method of illustrating the mass of data in order to provide more precise information that are capable of being readily assimilated or used in decision-making.

Mathematical Statistics, which is concerned with methods of refined analysis based on the theory of probability and attempts to draw precise general conclusions.

PURPOSE OF STATISTICS

The broad objectives of statistical methods are estimation, prediction and decision-making. To this end, statistics serves the following general purposes:

(i) Problem solving, in government, industry, commerce, etc especially those which are capable of being expressed numerically.

(ii) Information (Record) purposes generally in public and private organizations.

(iii) Experimental needs in engineering, medicine and other sciences.

(iv) Research needs of a social, economic, political, or religious nature.

SCOPE OF STATISTICS

The methods of statistics are useful in understanding, judging and interpreting information on over-widening range of human activities, especially where numerical information exist. For Statistical methods to apply. the phenomenon must satisfy two conditions:

(i) It must be capable of being quantified either through a counting or measurement process.

(ii) The changes observed in the phenomenon being studied are caused by several forces acting simultaneously. Thus output, sales, accident, crime and other figures are of interest because they are determined by a number of factors.

Depending upon the type of materials desired (and the problem at hand) some of the areas on which data may be collected include:

(i) Population - Size, composition, distribution, etc

(ii) Vital events - Data derived chiefly from censuses and registration of births, deaths and illnesses. These could then be supplemented by surveys and case studies.

(iii) Economics and business - Data are generally collected from market reports, annual or other reports of industries, tax returns, etc.

(iv) Education - School health records, intelligence and achievement tests, and other school records.

(v) Public Health - Hospital records, private medical clinics, local health authorities, surveys, etc.

(vi) Social Events - Studies relating to living conditions, earnings, expenditure on vital programmes, opinions, etc

(vii) Other areas on which data are collected are migration (immigration and emigration), external trade, transportation, agriculture, insurance, environment to mention a few.

METHODOLOGY

Statistical Methods involve three functional processes:(l) Data collection, (2) Summarization of data, and (3) Analysis, interpretation and generalizations based on data.

I. Data Collection: Data may be collected directly from the field by the investigator through direct personal interviews, mail questionnaires, or any of the other methods. These constitute primary data, and the source a primary source. If on the other hand, data collected by another individual or agency for an expressed purpose are adopted by the investigator for his current problem, the data are secondary data and the source a secondary source to the investigator. Whatever the source and no matter the experience(s) under study, data for statistical purposes must be accurate, collected in sufficiently large numbers, timely and representative of the experiences to which they relate.

2. Summarization: This is second fundamental process of statistical methods. Usually four steps are involved and these are:
(i) Scrutinizing the data for accuracy, adequacy and completeness in other to eliminate (or reduce) errors.
(ii) Sorting of the mass of data into classes (or categories or groups). The idea is to logically partition raw data into mutually exclusive classes with regards to known relationships in the series at hand. Sorting may be carried out on the basis of the qualitative or quantitative characteristics of the series.
(iii) Computing the necessary statistical constants, that is summary values - averages, rates, ratios. The aim is to obtain mathematical expressions for facts embedded in the raw data.
(iv) Presentation of the data. The relationships between factors are highlighted in the form of texts, tables, graphs and summary measures. '
3. Analysis, Interpretation And Generalization: The objectives of data analysis are two fold: first, to reduce the data. Analysis ensures that most, if not all, of the information relevant to the study are preserved. Second, to assess the meaning and importance of these quantities while making due allowance for the errors attributable to disturbing influence or chance events.

Data analysis can be carried out manually by direct hand sorting or the use of score (tally) sheets (for a limited amount of data) or mechanically (for a large amount of data, large either in terms of the number of forms or number of entries per form). The invention of high-speed electronic devices has, however, greatly enhanced the mechanical analysis of data.
The study of mechanical methods is largely a matter of common sense One, however, needs some appreciation of simple mathematical principles, a certain amount of special knowledge of the various fields of enquiry and the sources of statistical information on these.
Data analysis involves drawing inferences from them. For this reason, this branch of statistics is also referred to as Inferential Statistics.
Inferences are of two types. When a general truth is referred from particular instances, we have inductive inference (inductive reasoning). When, on the other hand, inferences are drawn about an unknown part from a known whole, this is deductive inference (deductive reasoning). Inductive reasoning is based on incomplete information; deductive reasoning is based on full information on the affected circumstances.
Consider data on absenteeism expressed by the status of the absentees, ages and causes of the absenteeism. A casual observer can form any impressions based on the tabular or graphical presentations of such data. Up to this point, we are in the realm of Deductive Statistics. It is however, another thing to say whether any conclusions so drawn follow logically from the data. This can only be established after appropriate statistical tests (further analysis). Tools for such tests are in the realm ofstatistical methods (mathematical statistics) and any in fcrenccs drawn after such tests are called‘Statistieal inferences. This text does not treat statistical inference.

USES OF STATISTICS:

In general, individuals and organizations can put Statistics to the following broad uses:
(i) Decision making: Statistics being a universal guide to the unknown, have become the bases for rational decision-making.
(ii) Planning (Economic, social etc.): Accurate statistical knowledge of the exact composition of the' country's population, for instance, enables provision to be made for future demands for schools, hospitals, housing, etc.
(iii) Routine Administration: Most data are by-products of the administrative functions of government and quasi government agencies, businesses, private organizations, etc. Management nowadays depends to a great extent on statistics for the efficient discharge of its functions.

GENERAL APPLICATIONS
Specific areas of application of statistics include:
(a) Stock Control: Carrying the right amount of stock is of utmost importance as too much stock means idle capital, while two small stock means insufficient materials to work with.
(b) Market/Marketing Research: This helps gauge the market in order to take decisions affecting what to sell, in what quantities,‘ when and where.
(c) Forecasting: Business also needs data to make a better assessment of the present economic situation and When t0 forecast future prospects.
2. Industry:
The production of marketable goods of adequate quality presents numerous statistical problems. The determination of the life span of electric bulbs depends on statistical methods for the avoidance of waste. So is the determination of the breaking point of a batch of wire. The quality of mass-produced goods is more efficiently determined and controlled by means of statistical methods. The trial of new processes of production also depends on statistical methods.
3. Insurance:
The premium a client pays for an insurance policy is governed by such important factors that enable the financial risk of, say, fire in a client house to be correctly assessed. The insurance companies need to know the number of tire outbreaks that do occur in houses of similar types and the amount of damage they cause The premium to charge for insuring a motorcar required knowledge of the claims that have been made on that type of car, for the particular age, experience and occupation of the driver and previous claims records. We need Statistical methods to collect such data .
4. Government:
(a) Budgeting: Based on estimates of prospective income levels, taxes, consumption levels, etc, all of which accuracy depend on statistical techniques.
(b) Planning: The quality of economic, commercial mid industrial statistics are being continually improved for this purpose.
(c) Legislation: Based on data produced as byproducts of government activities Examples include traffic regulations, environmental protection laws.
Some other areas of general application of Statistical methods include transportation, health, agriculture and research activities.