Class XI:Statistics [Ch-3 Census and Sample Methods of Collection of Data]

Concepts of ‘Census’ and ‘Sample’

Census Method

Census method is that method in which data is collected covering every item of the universe or population relating to the problem under investigation.

SUITABILITY OF CENSUS METHOD

Senses method is suitable particularly for such statistical investigations which have (1) small size of population, (2) widely diverse items in the population, (3) requirement of intensive examination of different items, and (4) high degree of accuracy and reliability. 

Merits

Principal merits of census are as under:

1. Reliable and Accurate:

Results based on census methods are accurate and highly reliable. This is because each and every item of the population is studied.

2. Less biassed:

Results based on census methods are less biassed. It is because of the absence of investigator’s directly regarding the selection of sample items.

3. Extensive Information:

Information collected through the census method is quite exhaustive and therefore, more meaningful because all the items of a universe are examined. For example, population census in India gives exhaustive information relating to the number of people in different parts of the country, their age and sex composition, education, status, occupation, and the like.

4. Study of  Diverse Characteristics:

By using census methods, one can study diverse characteristics of the universe.

5. Study of Complex Investigation:

When items in a universe are of complex nature and it is necessary to study each item, only the census method can produce the desired result. Data on a country's population is collected by this method.

6. Indirect Investigation:

Census methods can be successfully used in indirect investigations related to unemployment, poverty, corruption, etc.

Demerits

However, there are certain demerits of census method as under

1. Costly:

The Census method is very costly and is, therefore, generally not used for ordinary investigations. Only the Government or some big institutions can afford to use this method and that too for specific purposes only.

2. Large Manpower:

Census method requires a lot of manpower. Training a large number of enumerators becomes essential, which is a very difficult process.

3. Not Suitable for Large Investigations:

If the universe comprises a large number of items, then it may not be possible to cover each and every item. The Census method becomes particularly inoperative in such situations.

Sample Method

Sample method is that method in which data is collected about the sample on a group of items taken from the population for examination and conclusions are drawn on their basis.

SUITABILITY OF THE SAMPLE METHOD

Sample method is particularly suitable when: (1) the size of the population is very large, (2) a very high degree of accuracy is not needed, (3) intensive examination of diverse items is not required, and (4) when different units of the universe are broadly similar to each other.

Merits of the Sample Method

Some of the principal merits of the sample method are as under:

1. Economical:

Sample method of investigation is economical because only some units of the population are studied.

2. Time Saving:

In this method, only a limited number of items are investigated. As such the process of investigation is time-saving, not time-consuming.

3. Identification of Error:

Because only a limited number of items are covered, errors can be easily identified. To that extent the sampling method shows better accuracy.

4. Large Investigations:

Sample method is more feasible in situations of large investigations than the census method which generally involves unaffordable cost.

5. Administrative Convenience:

There is an administrative convenience in handling a limited number of items. More capable and efficient investigators can be appointed.

6. More Scientific:

According to R. Fisher, Sample Method is more scientific because the sample data can be conveniently investigated from various angles.

Demerits of the Sample Method

Yet there are some demerits of the sample methods as under:

1. Partial:

It is only a partial investigation of the universe. The investigator’s bias in the selection of the sample is not ruled out. Accordingly, the results may be biassed as well.

2. Wrong Conclusions:

If the selected sample does not represent the characteristics of the universe, the study may end up with wrong conclusions.

3. Difficulty in Selecting Representative Sample:

It is not very easy to select a sample which would represent the characteristics of the entire population.

4. Difficulty in Framing a Sample:

Sometimes the universe may be so diverse that it becomes difficult to frame a sample.

5. Specialised Knowledge:

Sampling involves a set of technical procedures. One must have the technical knowledge of choosing a representative sample from the universe. Persons who are well-versed with all the techniques of sampling are not easily available.

Essentials of a Sample

1. Representative:

A sample must represent all the characteristics of the universe. It is possible only when each unit of the universe stands equal chances of being selected in the sample.

2. Independent:

All units of a sample must be independent of each other.

3. Homogeneity:

If more than one sample are selected from a universe, these samples should be homogeneous (and not contradictory) to each other.

4. Adequacy:

The number of items in the sample should be fairly adequate so that some reliable conditions are drawn covering the characteristics of the universe as a whole.

Methods of Sampling

1. Random Sampling

Random sampling is that method of sampling in which each and every item of the universe has an equal chance of being selected in the sample.

2. Purposive or Deliberate Sampling 

Purposive sampling is that method in which the investigator himself makes the choice of the sample items which in his opinion are the best representative of the universe.

3. Stratified or Mixed Sampling

According to this method of sampling, the population is divided into different strata having different characteristics and some of the items are selected from each strata, so that the entire population gets represented.

4. Systematic Sampling

According to this method, units of the population are numerically, geographically and alphabetically arranged. Every nth item of the numbered items is selected as a sample item.

5. Quota Sampling

In this method, the population is divided into different groups of classes according to different characteristics of the population.

6. Convenience Sampling

In this method, sampling is done by the investigator in such a manner that suits his convenience.

Class XI:Statistics [Ch-2 Collection of Data]

Collection

Collection of data is the first step in the process of statistical study. 

Data can be collected from two sources

1. Primary Source of Data

2. Secondary Source of Data

1. Primary Source of Data

It implies collection of data from its source of origin. It offers you first hand quantitative information relating to your statistical study. 

2. Secondary Source of Data

It implies collection of data from some agency or institution which already happens to collect the data. It does not offer you first hand data.

Difference Between Primary and Secondary Data

Basis	Primary Source of Data	Secondary Source of Data
Originality	It is original.	It is not original.
Objective	It is related to the specific objective of the investigator.	It is not as per the specific objective of the investigator.
Cost	Costlier than secondary sources in terms of money and time.	It is cheaper than the primary source in terms of time and money.

Methods of Collecting Primary Data

These are some popular methods of collecting primary data

Personal Investigations 

1. Direct personal investigation

2. Indirect oral investigation

3. Information from local sources or correspondents

Information Through Questionnaires and Schedules

1. Making questionnaires surveys

2. Enumerators method 

Method	Meaning	Merits	Demerits
Direct Personal Investigation	Data are personally collected by the investigator from the respondent.	High degree of original data. Accurate and reliable.	Difficult to cover a wide area. It is a very costly method.
Indirect Oral Investigation	Information will be collected from a person to our expected to have the necessary information about the person regarding whom the information is regarded.	Wide coverage, less expensive and sometimes correct information.	Doubtful and less accurate.
Information from Local Sources or Correspondence	Investigator appoints local persons or corresponce at different places.	Economy and wide coverage.	Less accurate, delay in collection and loss of originality.
Questionnaire Method	It is a tool of research when an answerer sends his answer through mail to the researchers.	Simple is not limited to access to technology such as phone or internet.	Can have a low response rate if the person viewing the questionnaire is junk mail.
Enumerator Method	Under this method the enumerator himself fills the schedules after seeing information from the informants.	It is economical, because we do not have to collect all the data. Instead of getting data from 5000 farmers, we get it from 50-100 only.	Methods, such as purposive sampling may not provide a simple, that is representative.

Qualities of a Good Questionnaire

1. Number of questions should be limited and related to the purpose only.

2. The language of the questions should be similar.

3. Questions must be placed in a proper order.

4. No undesirable questions.

5. Questions should not include complex calculations.

6. Instruction should be clear.

7. It should be pretested or cross verified.

8. Requests for the return should be mentioned.

Explain the Various Types of Questionnaire

1. Structured Questionnaire

It is a document that consists of a set of standardized questions with a fixed scheme, which specifies the exact wording and order of the questions, for gathering information from respondents.

2. Under-structure Questionnaires

The questionnaire in this case has a basic structure and some branching questions but nothing that limits the responses of a respondent.

Telephonic Interview

The investigator seeks the desired information from the respondent over the telephone.

Merits

Original accurate and reliable data collected at less expenses.

Demerits

Response ratio is very less.

Class XI:Statistics [Ch-1 Introduction]

Introduction

What Is Statistics?

Statistics, in itself, is the collection and analysis of numerical data to arrive at specific inference.

1. Singular Statistics

The statistician Stephen Senn has defined it as ‘the science of quantitative reasoning’- of ways of thinking about and working with numerical facts and ideas.

2. Plural Statistics

A ‘statistic’ is a numerical fact, or a piece of numerical information or data, and collection of such things are called ‘statistic’ plural.

Scope Of Statistics

Statistics are numerical statements of facts capable of analysis and interpretation as well as study of the methods used in collection, organisation, presentation, analysis, and interpretation of numerical data.

Basic Relationship Between Economics And Statistics

When we study the basic problems facing a country, such as poverty, inequalities of income etc these studies require that we know more about Economic facts. Statistics help in the collection, organisation, presentation, analysis and interpretation of these economic facts.

Features Of Statistics 

1. It Consists Of Aggregates Of Facts:

In the plural sense, statistics refers to data, but data to be called statistics must consist of aggregate of certain facts.

For a data may amount to statistics it must be in the form of a set or aggregate of certain facts, viz. 50, 65, 70 Kgs. weight of students in a class or profits of a firm over different times etc. is liable to be affected by multiplicity of causes.

2. It Is Affected By Many Causes:

It is not easy to study the effects of one factor only by ignoring the effects of other factors. Here, the overall effect is taken and not of one factor only as in other natural sciences.

3. It Should Be Numerically Expressed:

A data to be called statistics should be numerically expressed so that counting or measurement of data can be made possible. Thus these data must contain numerical figures so that those may be called as numerical statements of facts.

4. It Must Be Enumerated Or Estimated Accurately:

As stated above, the statements should be precise and meaningful. If it is infinite or very large, even enumeration of data is impossible and a reasonable standard of accuracy may not be achieved. Example- we may measure the height of buildings in metres but we cannot measure the length of small things like bricks in the same unit of metre.

5. It Should Be Collected In A Systematic Manner:

Another characteristic of statistics is that the data should be collected in a systematic manner. A proper plan should be made and trained investigators should be used to collect data so that they may collect statistics.  So to get correct results the data must be collected in a precise manner.

6. It Should Be Collected For A Predetermined Purpose:

Before we start the collection of data, we must be clear with the purpose for which we are collecting the data. We may need some more relevant data to achieve the required purpose, which we would miss in the event of its ignorance.

If some person in the government duty is counting the vehicles passing through a road in a unit time is statistics, but same work done by any other person not related to this field, is not statistics because the former is doing it for the Government which wants to make it a four lane road-if needed.

7. It Should Be Capable Of Being Placed In Relation To Each Other:

Last but not least, the characteristics of the statistics. If the figures collected are not comparable, in that case, they lose a large part of their significance.

For example- Heterogeneous data like sale of Rs. 20,000 result of 80% cases and mileage of 80 kms can never be placed in relation to each other and compared for analysis and interpretation which is the ulterior motive of the science of statistics.