# GSEB Solutions Class 11 Statistics Chapter 1 Collection of Data Ex 1

Gujarat Board Statistics Class 11 GSEB Solutions Chapter 1 Collection of Data Ex 1 Textbook Exercise Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Statistics Chapter 1 Collection of Data Ex 1

Section – A

Choose the correct option from those given below each question:

Question 1.
Who used the German word ‘Statistik’ for the first time?
(a) John Graunt
(b) William Patty
(c) Gottfried Achen Wall
(d) Gauss
(c) Gottfried Achen Wall

Question 2.
Who was one of the giants of initial results of probability theory among the following?
(a) John Graunt
(b) Laplace
(c) Fisher
(d) J. Neyman
(b) Laplace

Question 3.
Who was the founder of mathematical statistics ?
(a) Karl Pearson
(b) Laplace
(c) Mahalanobis
(d) Gosset
(a) Karl Pearson

Question 4.
Out of the following, which one is an example of primary data?
(a) Data collected from the records of Municipality.
(b) Data collected from a published journal of an industry.
(c) Data collected from website.
(d) Data collected by NSSO.
(d) Data collected by NSSO.

Question 5.
Which one of the following is an Example of qualitative data?
(a) Income category
(b) Production (in tons)
(c) Age of workers (in year)
(d) Height of persons (in meter)
(a) Income category

Question 6.
Which one of the following is true for secondary data?
(a) Should never be used.
(b) Use after careful verification.
(c) It is not necessary to check while using it.
(d) Secondary data itself is a primary data.
(b) Use after careful verification

Question 7.
Which one of the following is true for primary data?
(a) Primary data is always more reliable as compared to secondary data.
(b) Primary data is less reliable as compared to secondary data.
(c) Primary data depends on whether the data is collected carefully or not.
(d) Primary data can be obtained from the government publications.
(a) Primary data is always more reliable as compared to secondary data.

Question 8.
Which of the following statements is true ?
(a) The data collected by direct inquiry may be more accurate.
(b) The data collected by direct inquiry may be less accurate.
(c) The data collected by direct inquiry may not be reliable.
(d) The data obtained through e-mail is known as the data obtained by direct inquiry.
(a) The data collected by direct inquiry may be more accurate.

Question 9.
Which of the following is a proper method of getting supplementary information about the personal characteristics of the respondents?
(a) Questionnaire by post
(b) Direct inquiry
(c) Indirect inquiry
(d) From the news papers
(b) Direct inquiry

Question 10.
Which method will be costly when the number of respondents are more and spread over the large area?
(a) Questionnaire by post
(b) Indirect inquiry
(c) Direct inquiry
(d) By telephone
(c) Direct inquiry

Section – B

Answer the following questions in one sentence:

Question 1.
Who was the founder of Indian Statistical Institute?
The founder of Indian Statistical Institute was the well-known Indian Statistician Prof. P. C. Mahalanobis.

Question 2.
Define population.
A set of all the units under study is called a population. For example, in population census all the citizens of the country is population.

Question 3.
Define sample.
A set of units selected from the population on the basis of some definite criterion is called sample. For example, a set of randomly selected 90 students from a group of 900 students of a school is sample.

Question 4.
Define qualitative data.
A set of observations on the attribute is called qualitative data. For example, the data of education level of workers of a factory.

Question 5.
Define quantitative data.
A set of observations on the numerical variable is called quantitative data. For example, the data on monthly wages of workers of a factory.

Question 6.
Define primary data.
The data originally collected by any authorised agency or investigators for the first time is called primary data. For example, the data of Indian population collected by NSSO every ten years is primary data.

Question 7.
Define secondary data.
When an authorised agency or investigator uses the data collected by any other agency or investigator, then such data is called secondary data for the users. For example, if the data of population census used by any agency or investigator for their study, then the data becomes secondary for them.

Question 8.
State the methods of collecting primary data.
The methods of collecting primary data are:

• Direct method of inquiry
• Indirect method of inquiry and
• Method of the questionnaire.

Section – C

Question 1.
State the definition of statistics given by Croxton and Cowden.
The definition of statistics given by Croxton and Cowden is as under:
“Statistics is the science which deals with the collection, analysis and interpretation of numerical data.”

Question 2.
What is data?
The set of all the observations obtained by inspecting a variable characteristic defined on population units or sample units is called data.

Question 3.
What is questionnaire?
A list of questions relevant to the object of the study keeping the space between the questions for the answers is called a questionnaire.

Question 4.
What is unpublished data?
Some of the statistical data may not be published. Such data may be collected on request from the unpublished internal records of private and public organizations. Also some data may be drawn from the research papers, articles and essays, etc. Such data is called unpublished data.

Question 5.
What is a variable characteristic?
A characteristic that varies from unit to unit of a population or a sample is called a variable characteristic. It can be either numerical or non-numerical. The variable characteristic which is non-numerical is called an attribute and that which is numerical is called numeric variable.

Question 6.
What is an attribute ?
An attribute is a qualitative variable which is non-numerical. For example, profession, marital status, level of education, sex, honesty, habit of smoking, etc. are attributes which are non-numerical means cannot be expressed in numbers.

Section – D

Question 1.
What is the role of Prof. P. C. Mahalanobis in the development of statistics in India?
The well-known Indian Statistician Prof. P. C. Mahalanobis founded the Indian Statistical Institute – ISI at Kolkata in 1931.
He started the first post-graduate course in statistics at Kolkata University in 1941.

• National Sample Survey-NSS (now known as National Sample Survey Organisation – NSSO) proposed by
• Mahalanobis was started in 1950 and the data collection started in India.
• In 1953 using operations search system in ISI he had framed outline of second five year plan.
• Thus his contribution in the development of statistics in India was significant.

Question 2.
State the difference between qualitative and quantitative data.

 Qualitative Data Quantitative Data 1. The set of observations collected on qualitative variable is called qualitative data. 1. The set of observations collected on the numerical variable is called quantitative data. 2. For example the data relevant to the attributes such as sex, standard of study of the students studying in a school is qualitative data. 2. For example, the data relevant to numeric variables such as age, weight, height, etc. of students studying in a school is quantitative data. 3. The observations of qualitative data are non -numerical mean they cannot be expressed in numbers. 3. The observations of quantitative data are numerical means they are in numbers.

Question 3.
Give some examples of primary data.
Some examples of primary data are as follows:

• The data of Population Census of India obtained by NSSO.
• The data on Indian agriculture obtained by IASR.
• The data of post graduate students obtained by Gujarat University.
• The financial data of India obtained by RBI.
• The data on Textile Industries of Gujarat obtained by ATIRA.

Question 4.
Discuss the method of questionnaire.
A list of logically arranged questions relevant to the object of the study and keeping the space between the questions for answers is called a questionnaire.

• The method of obtaining information using such type of questionnaire is called a method of questionnaire.
• This method is quite useful when the field of inquiry is very vide.
• There are two ways of collecting information by questionnaire:
1. By post and
2. By enumerators.
• The success of this method of collecting information depends on the construction of questionnaire.
• Since there is considerable saving of time and cost in this method, it is the most economical method of inquiry.
• This method of questionnaire may be used in direct inquiry as well as indirect inquiry.

Question 5.
Discuss questionnaire by post.
In questionnaire by post, a questionnaire is sent to respondents by post.

• A letter of request is sent along with the questionnaire, requesting the respondent to send the questionnaire daily filled within the stipalated time.
• A blank envelope is sent along with the questionnaire to all the respondents bearing the address of enumerator and a proper postal stamp to get it return in given period of time.
• Since the answers to the questionnaire are to be given by respondent themselves, the questions in questionnaire should be clear, short, simple, relevant and self explanatory.
• To collect data from educated and responsible persons this method of questionnaire by post is very convenient and useful.

Question 6.
Discuss questionnaire by enumerators.
In the method of questionnaire by enumerators, enumerators themselves contact the respondents personally and fill the questionnaire.

• In this method if enumerators are enthusiastic, polite, honest and efficient in their work, correct answers to the questions are obtained by providing relevant and supplementary information to the respondents.
• The enumerators are instructed to create friendly atmosphere without entering into any contro¬versy or showing any disrespect towards the respondents.
• Whether respondents are educated or uneducated by this method it become easy to collect data.

Question 7.
Describe the method of collecting secondary data from unpublished sources.
Some statistical data obtained by private and public organisation or researchers are not published. Such data is called unpublished secondary data.

• Unpublished data may be collected on request from the records of private and public organisation.
• From research papers, articles and essays some unpublished data can be obtained.

Question 8.
Discuss some applications of statistics.
At present statistics has been accepted as an independent part of scientific methods. As its scope becomes wide, statistics is not only useful for quantitative data but also useful for qualitative data.

• Industrial statistics and a branch of statistics Operations Research – OR was used in the military projects during the second world war.
• In India, OR is used for national planning and survey and OR technique is used to formulate five year plans.
• OR technique can be useful for government to maximise the per capita income with minimum resources.
• In industry, by using OR technique, decisions regarding the optimum allocations of limited resources can be made and it can be planned to maximise the returns.
• To meet the market demand in future, OR technique is useful to decide the size of inventery.
• Thus, considering the use of statistics in recent times, its importance cannot be ignored.

Section – E

Question 1.
State the difference between primary and secondary data. Answer:

 Primary data Secondaiy data 1. Primary data are collected for the first time and hence original. 1. Secondary data are not original but it is the collected data reused by others 2. Primary data are collected on the units under inquiry. 2. Secondary data are obtained from the primary data. 3. Primary data are original and hence the nature of primary data is quite extensive. Usually such data are in raw form. Hence, they are required to be classified and tabulated. 3. Secondary data may be in organised and tabulated form, i.e., they are usually in classified form. 4. Since primary data are independently collected, large amount of resources, manpower and monetary cost are involved for their collection. 4. Secondary data are cost effective in terms of time, energy and money.

Question 2.
Discuss the method of collecting primary data by direct inquiry.
In the method of direct inquiry an investigator himself or an enumerator appointed by him visits personally to the field and collects the necessary information.

• For example, if an investigator wants to collect the data about the reading habit of students, then he visits personally to the students of a school or college and collects the information by asking the relevant question. The information thus obtained is called the information by direct inquiry.
• In this method it requires more time to collect the information. Hence, it is used when the field of inquiry is limited.
• The information collected by this method may be considered reliable. But it is affected by the bias and prejudice of the enumerator and hence the data may have different impression in practice.

Question 3.
Discuss the method of collecting primary data by indirect inquiry.
When the field of inquiry is very large and there is a lack of time for personal contact with the respondents, the information to be obtained is of complex nature and the cost associated with direct inquiry is high, than an investigator or an enumerator appointed by him collects the information with the help of the third party acquainted with the inquiry.

1. Thus, a method of inquiry in which instead of direct inquiry, enumerator collects the information with the help third party or agency, is called the method of indirect inquiry.
2. For example, an investigator or enumerator may collect the information on reading habit of students from the librarian of a school or a college instead of meeting the students personally.
3. The method of indirect inquiry is quite popular in practice. But the reliability of information obtained by this method depends on the ability, honesty and experience of the enumerators.

Question 4.
Discuss the method of collecting secondary data.
There are mainly two sources of collecting secondary data:

1. Published and
2. Unpublished.

In published form the secondary data are obtained from the following sources:
1. Government Publications:
Government publications is the main source of secondary data. The central and state governments collect certain data for their administrative use and publish them regularly in the interest of public information. On results of population census, index number of wholesale prices, statistics of imports and exports, vital statistics, agricultural statistics, statistics related to five-year plans, etc. are easily available from government publications, published by Central Statistical Organisation (CSO), National Sample Survey Organisation (NSSO), Indian Council of Agricultural Research (ICAR). Statistical Buletin of RBI, Statistical Abstract of Gujarat State, Social Economic Review of Gujarat, etc.

2. Semi-government Publications:
Semi-government organisations like the Life Insurance Corporation of India, State Electricity Boards, City Municipalities, etc. regularly publish various data in their publications.

3. Publications of International Institutes:
Information can be obtained by the publications of International organisations like United Nations Organisation (UNO), International Monetary Fund (IMF), International Labour Organisation (ILO), World Health Organisation (WHO), etc.

4. Reports of Research Organisations:
Research institutions such as Ahmadabad Textile Industry’s Research Association (ATIRA), Physical Research Laboratory (PRL), Ahmadabad; Tata Research Centre; Management Associations, etc. provide useful data in their reports and publications.

5. Local Self-government Institutions and Autonomous Educational Institutions:
Municipal Corporations and Jilla Panchayats, Agricultural Universities and other Universities supply secondary data through their reports and publications.

6. Publications of Business and Commerce Organisations:
Federations of Chamber of Commerce, Worker’s unions, Various business organisations, Nationalized banks, etc. publish data on regular basis which can be used as secondary data.

7. Newspapers and Periodicals:
Different periodicals and newspapers are important sources of secondary data. Economic and Political Weekly (EPW), Commerce, Eastern Economist, Business India, Business Today, Economic Times, Financial Express, etc. are the important periodicals which publish secondary data in a well organised manner.

In an unpublished form the secondary data are obtained as follows ;
Some of the statistical data are collected and compiled but are not published. However, private and public institutions keep the registers for such data for their reference. Such data can be obtained on request to the concerned institutions and can be used as secondary data. Research papers of universities, private publications such as dissertations, monographs, etc. of IIM, are such kind of unpublished data.

Question 5.
Discuss origin and growth of statistics.
The origin and growth of statistics can be described as follows ;
Origin of Statistics:

• From the time of Mauryan empire (321-296 BC) the contribution of India in Statistics has been quite significant.
• During the time of Mughal Empire, Akbar (1596-’97) mentioned statistical system in Ain- I-Akbari’ written by Abul Fazal.
• The German word ‘Statistik’ was first used by Gottfried Achen Wall in 1749 for analysis of data of the state.
• By 18th century, the term ‘statistics’ was used for systematic collection of data by states.
• Statistics was formally introduce in Encyclopedia Britanic in 1797.
• In 17th and 18th century Laplace (1749- 1827) and Gauss (1772- 1855) presented the initial principles on probability.
• In the late 19th and early 20th century Karl Pearson founded Mathematical Statistics. Galton and Karl Pearson used mathematical statistics in science, Industry and Politics.
• During 1910 and 1920, Gosset and Fisher developed modern statistical science and applied in the fields such as genetics, biometry, psychology, education, agriculture, etc.
• During 1930, role of E. Pearson and J. Neyman has been significant in the development of statistics. After that advanced methods of statistics were developed day-by-day.

Growth of Statistics in India:

• Contribution of Prof. P. C. Mahalanobis has been significant in growth of statistics in India. He has founded Indian Statistical Institute – ISI in 1931 at Kolkata. He started for the first time post graduate course in Statistics at Kolkata University in 1941.
• In 1950, Mahalanobis started National Sample Survey-NSS and started data collection. (NSS has been named as National Sample Survey Organisation – NSSO at present.)
• Indian Agriculture Statistics Research Institute – LASRI has contributed a lot in the development of statistics in India.
• Among the various definitions of statistics, the definition given by Croxton and Cowden is ‘Statistics is the science which deals with the collection, analysis and interpretation of numerical data.’
• How a days, statistics is not only useful for quantitative data but also for qualitative data.
• Statistics is considered as a part of scientific methods. An important branch of statistics is Operations Research-OR, which was used in the military projects during the second world war. The use of OR in industries and for the government cannot be ignored.
• The constructive development in statistical studies has considerably increased its scope and importance.

Question 6.
A method in which an investigator himself or an enumerator appointed by him personally visits the persons from whom the information is to be obtained, asks them questions pertaining to the inquiry or survey and collects the required information, is called the method of direct inquiry.

• Since the investigator or enumerator himself collects the data by personal visit, the data obtained by this method are accurate and reliable.
• The presence of an enumerator possibly creates confidence in the person giving information. If the person giving information has a question or doubt or any embarassment, he can seek clarification from the enumerator.
• The enumerator or investigator sometimes gets supplementary information of the respondents which may be useful at the time of interpretation of the results.
• This method is much better when the information is to be obtained from a limited field of inquiry.
• The data is obtained personally hence the information about the complex questions can be obtained easily. Moreover the data pertaining to the personal information can be obtained by supplementary questions. Assurance is given that such information will not be misused.

• This method is not much effective in case of extensive and wide field of inquiry.
• This method involves considerable amount of time, energy and money because the investigators collects the data. by making personal visits to informants.
• The information collected by this method is less reliable if the enumerators are not well trained, dutiful and honest towards the object of inquiry.
• This method of inquiry is likely to be affected to a large extent by the prejudices or biases of the enumerators. .

Question 7.
A method of inquiry, in which information is obtained with the help of an organisation or agency instead of enumerators, is called the method of indirect inquiry.

• When the field of inquiry is extensive, this method is most suitable. When the object of inquiry is multiple type, this method is more suitable.
• When there are many differences of opinion among the informants, this method is more effective.
• This method involves less cost, time and energy as the data is collected indirectly.
• When the persons in charge of the inquiry and the informants are both experienced, neutral and technically qualified, the level of accuracy of the information can be enhanced.
• This method is very much useful for various departments of government to collect various type of information.

• In this method, if the individual or organisation assigned with the task of providing information may have prejudices or a biased attitude. The information becomes less reliable.
• This method becomes useless when the third party from whom the information is obtained, is dishonest, inefficient, to provide correct information.

Question 8.
Discuss the characteristics of an ideal questionnaire.
There are no stipulated norms or set rules for preparing a good questionnaire. A well designed questionnaire is known as an ideal questionnaire. Some characteristics of an ideal questionnaire are as follows:
1. Title:
An appropriate title indicating towards the object or purpose of the research should be given to the questionnaire. It should be so chosen that the respondent does not get any suspicion or dilemma in his mind about the questionnaire or its purpose.

2. Number of questions:
The number of questions in the questionnaire should be sufficient and consistent with the purpose of the inquiry. The fewer number of questions have greater chance of getting better response from the respondent.

3. Order of questions:
The order of questions should be logical so that the respondent can answer the questions quickly and spontaneously without looking back and forth at the questionnaire for reference.

4. Language of questions:
The language of questions should be simple. It should not be ambiguous, elumsy and dual in meaning.

5. Length of questions:
Questions having answers YES / NO or multiple alternative should be asked. They should also be short and clear. Very long questions or answers create boredom among the respondents and hence it is possible that correct information may not be obtained.

6. Time:
Questions concerning remote past should be avoided. Questions leading to sharpening the memory should also be avoided.

7. Confidentiality:
Asking questions concerning the personal life of the respondent should be avoided. If such questions are unavoidable, they should be framed with caution and also a guarantee must be given that they will be kept confidential.

8. Trial:
After preparing the questionnaire, it should be executed on a trial basis to check how practical it is. If required, the questions should be changed to make the questionnaire perfect.

Question 9.
In the method of questionnaire by post, a questionnaire is dispatched to respondents by post. The respondents fill up the questionnaire and send it back.

• This method is simple, quick and provides large amount of information with less cost.
• This method proves to be more efficient if the information is to be collected from educated and responsible respondents.
• An investigator can get information from the respondents of those areas where it might be difficult to reach personally or by telephone.

• This method is not quite useful if the respondents are illiterate and are lacking the sense of cooperation.
• Sometimes respondents do not bother to read or return the questionnaire.
• It is not possible to check whether the information given is correct or incorrect.
• Sometimes, because of fear of information being misused, even educated respondents with sense of understanding avoid to provide written information or ignore returning back the questionnaire.
• Because of laziness and gloom of the respondents, there may be a loss of questionnaire or delay in getting the information.
• There is lack of assistance. Therefore clarification of the instructions or giving explanation of the questions that may arise is not attended. As a result it is possible that respondent may not provide the correct information.

Question 10.
In this method, enumerators themselves contact the respondents personally and getting response to the questions and fills the questionnaire. The advantages and disadvantages of this method are as follows:

• The complete, correct and more relevant imformation can be obtained from the respondents by enumerators.
• Enumerator can get proper information from the illiterate respondents providing proper explanations.
• Loss of questionnaire or receiving incomplete questionnaire do not arise because the enumerator collects the information personally.
• For the vast field under inquiry, accurate information can be obtained within stipulated period of time.
• Doubts arising in the minds of the respondents are resolved quickly on the spot because of the presence of enumerators.

• If the data is to be collected from a large area, large number of enumerators are to be employed resulting in higher cost.
• If expert numerators are not available for the inquiry, the task of training the appointed enumerators is not easy.
• To keep close watch on the work of enumerators, it is required to appoint supervisors. This would increase the cost.
• If the respondents are not educated, polite and sensible, it is likely that they may not cooperate with the enumerators and hide correct information from them.
• Since enumerators have to settle and also adjust the convenience of time with the respondent, more delay is likely to be caused.

Question 11.
Discuss what types of precautions should be taken while using secondary data.
Certain precautions as mentioned below should be taken while using secondary data:
1. Reliability:
Before using secondary data, one should verify the level of reliability of the data. Data collected and published by government, semi-government or autonomous organisations are more reliable. The data collected by private organisations are less reliable because they collect the data to suit their own ideology or they might have some bias or prejudice present.

2. Purpose:
The purpose of collecting data should be properly examined before it is used as secondary data.

3. Method of collecting data:
The method of inquiry used in collecting data should be known. From the knowledge of method applied, one becomes familiar with its limitations also.

4. Time duration:
The time duration when the data was collected should be known because the data collected in remote past becomes irrelevant in the present circumstances.

5. Scope of data:
Before using secondary data, matters pertaining to scope of data, region for which the data are collected, definitions of terms used and the selection of units should be ascertained.

6. Limitations:
The limitation and drawbacks of the data should be known for the secondary data to be used.

7. Alternatives:
If alternative data are available, the data should be compared and then only proper data should be used as secondary data.