*By statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other*.” - Horacesecrist

^{th}or 1/20

^{th}) can be ignored; when measuring the distance from Chennai to Kanyakumari, fraction of a kilometer can be easily ignored. No hard and fast rule can be laid down for all cases. Hence mathematical accuracy cannot be attained in statistical studies.

*“Statistics is the science of estimates and probabilities”***.**

*“Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data”***: The first step of an investigation is the collection of data. Careful collection is needed, because further analysis is based on this. There are different methods of collection of data (Census, sampling, primary, secondary etc.) and they must be reliable. If the collected data are faulty, results will also be faulty. Therefore, the investigator must take special care in collection.**

__Collection of data__**: The collected data are generally in an unintelligible form and need to be classified and tabulated before they can be analyzed. For example, the investigator is interested to know the average income of 1000 families of a village. The mass data collected should be difficult to understand and analyze. Therefore, the collected data are to be presented in tabular or diagrammatic or graphic form. The data presented in a systematic order will facilitate further analysis.**

__Presentation of data__**: After the presentation of data, the next step is to analyse the presented data. Analysis includes condensation, summarization, conclusion, etc. though the means of measures of central tendencies, dispersion, skewness, kurtosis, correlation, re-gression, etc.**

__Analysis of data__**: Figures do not speak for themselves. The duty of the statistician is not complete with mere collection and analysis of data. But, valid conclusions must be drawn on the basis of analysis. A high degree of skill and experience is necessary for the interpretation. Correct interpretation leads to valid conclusion.**

__Interpretation of data__**:**

__Functions of Statistics__- Statistics
helps in developing sound methods of collecting data so that the data
collected can be used to draw the valid inference regarding the desired
objectives.
- It
presents the information in numerical form.
- It
helps in simplifying the complex data by way of classification /
tabulation / graphical representation.
- The
tabular / graphical representation of data and other complex statistics
help in comparison.
- Statistics
can be used to study the relationship between two or more factors. The use of such relationship can be made
in estimating one factor when other/s are known.
- The
data regarding a characteristic for a series of past periods can be used
to forecast its value for a future period.
- The
powerful function of forecasting leads us to the need of planning and thus
facilitates in formulating policies and helps in planning to implement
these policies.

**:**

__Limitations of Statistics__

__SOURCES OF DATA__**from where to get the data or what the sources of data are.**

**POPULATION**:

**SAMPLE**:

**VARIATE**:

**ATTRIBUTE**:

**PARAMETER:**

**for mean,**

**for standard deviation etc.**

**STATISTIC**:

- The
purpose or the objective of the collection must be precisely defined. The type of data to be included, the
characteristics to be considered, the sources from where the data is to be
obtained and the steps to be followed to collect the data – every step
should be worked out in advance.
- The
scope of the enquiry with respect to the time, the places to be covered
should be decided first. There are
different types of enquiries like official or non-official, regular or
ad-hoc, direct or indirect etc. The
proper type which suites the purpose and the scope should be decided.
- The
measurement of values of a variable is done in a particular unit which is
called Statistical unit. For
example, for incomes of employees, the unit is a rupee. For heights of persons, centimeter
etc. Along with the unit, the
degree of accuracy also should be decided.

**METHODS OF COLLECTING PRIMARY DATA**

**DIRECT PERSONAL INVESTIGATION:**Here the investigator meets the informants personally and collects the information by asking questions. The questions should be simple, short and should be so formed as to get brief and unambiguous answers. The enumerator must be trained, specially hired for the job. His observation should be keen and he should be well acquainted with the local conditions. He should possess sufficient knowledge of tastes and preferences of the informants. The investigator should be polite and courteous yet he should be firm, determined to get answers tactfully from the respondents.

**INDIRECT ORAL INVESTIGATION**: If the persons, directly concerned with the investigation are not willing to supply the necessary information, then it is obtained by questioning witnesses who are supposed to know the situation, to have knowledge about the persons concerned or the problem involved.

**QUESTIONNAIRES AND SCHEDULES**: In this method, a list of questions is prepared and it is sent by post to various informants. Usually, a sample of informants is selected from the concerned population. Sometimes the schedules are filled in by the enumerators who question the people and write down the necessary information. If the questionnaire is sent by mail, then a forwarding letter, explaining the objective of the survey and requesting co-operation, should accompany the form. The advantage in this method is that the respondents can write the answers of the questions as per their convenience and would not hesitate to give some confidential information asked in the questionnaire. This method has a wide coverage, it is quick and inexpensive. But still, the response is not very good. If possible, there should be some incentive like a small prize, lucky number draw, concession at some shops etc. to get better response. Every questionnaire must be accompanied by an addressed and stamped envelope.

**REQUISITES OF A GOOD QUESTIONNAIRE OR A SCHEDULE:**

**EDITING OF THE PRIMARY DATA**

- The
data should be consistent. That is,
the answers obtained should not contradict one another.
- The
answers should be complete and uniform in all respects. If some, important questions are left
unanswered then the respondent should be contacted again to complete the
questionnaire.
- The
answers should be checked for accuracy.
Inaccuracy due to mathematical errors is to be corrected.
- The
data must be checked for homogeneity of answers. For example, if one respondent has
mentioned the gross pay and if the other has mentioned net pay after tax
deduction, then these cannot be compared.

**SECONDARY DATA**

**Census**and if it is collected only for a sample then it is called a

**Sample Survey.**