GSEB Class 11 Statistics Solutions Chapter 1 Collection of Data

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
Answer: (c) Gottfried Achen Wall
In simple words: Gottfried Achen Wall was the individual credited with initially employing the German term 'Statistik'.
🎯 Exam Tip: Knowing the historical figures associated with key statistical terms can be crucial for foundational knowledge questions.

 

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
Answer: (b) Laplace
In simple words: Laplace made significant early contributions to the field of probability theory.
🎯 Exam Tip: Recognizing pioneering figures in specific mathematical and statistical fields is important for historical context and theoretical understanding.

 

Question 3. Who was the founder of mathematical statistics?
(a) Karl Pearson
(b) Laplace
(c) Mahalanobis
(d) Gosset
Answer: (a) Karl Pearson
In simple words: Karl Pearson is widely recognized as the individual who established the field of mathematical statistics.
🎯 Exam Tip: Identifying the founders of academic disciplines helps in understanding the origins and evolution of statistical methods.

 

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.
Answer: (d) Data collected by NSSO.
In simple words: Primary data refers to information gathered directly for a specific research purpose, such as data collected by the National Sample Survey Organisation (NSSO).
🎯 Exam Tip: Differentiating between primary and secondary data sources is fundamental in statistics; primary data is original and collected firsthand.

 

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)
Answer: (a) Income category
In simple words: Qualitative data describes characteristics that cannot be measured numerically, like classifying income into categories (e.g., low, medium, high).
🎯 Exam Tip: Understand that qualitative data pertains to attributes or characteristics that are descriptive, while quantitative data involves numerical measurements.

 

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.
Answer: (b) Use after careful verification
In simple words: Secondary data, which is collected by others, should always be thoroughly checked for accuracy and relevance before being utilized in a study.
🎯 Exam Tip: Always exercise caution and verify the source and methodology of secondary data to ensure its reliability and suitability for your research.

 

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.
Answer: (a) Primary data is always more reliable as compared to secondary data.
In simple words: Information gathered firsthand directly for a specific purpose is inherently more trustworthy than data collected by others.
🎯 Exam Tip: The direct control over data collection methods makes primary data generally more credible and relevant to a specific inquiry.

 

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.
Answer: (a) The data collected by direct inquiry may be more accurate.
In simple words: Data acquired through direct inquiry often boasts higher accuracy because of the immediate interaction between the investigator and the source.
🎯 Exam Tip: Direct interaction in data collection allows for clarification and real-time validation, enhancing accuracy compared to indirect methods.

 

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
Answer: (b) Direct inquiry
In simple words: To gather additional detailed personal information about respondents, direct inquiry is the most suitable method, allowing for immediate interaction and follow-up.
🎯 Exam Tip: Direct inquiry is invaluable for collecting sensitive or nuanced personal details, as it permits interaction and ensures comprehension of the questions.

 

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
Answer: (c) Direct inquiry
In simple words: When a large number of respondents are geographically dispersed, directly contacting each one for an inquiry becomes the most expensive method due to travel and labor costs.
🎯 Exam Tip: For extensive geographical coverage and numerous respondents, direct inquiry methods are typically resource-intensive and financially demanding.

 

Section - B

Answer the following questions in one sentence:

 

Question 1. Who was the founder of Indian Statistical Institute?
Answer: The esteemed Indian Statistician Prof. P. C. Mahalanobis was the founder of the Indian Statistical Institute.
In simple words: Prof. P. C. Mahalanobis established the Indian Statistical Institute.
🎯 Exam Tip: Remember Prof. P. C. Mahalanobis as the key figure in the establishment of ISI, a significant institution in Indian statistics.

 

Question 2. Define population.
Answer: A population is defined as the complete collection of all units under investigation in a study. For instance, in a population census, all citizens of a country constitute the population.
In simple words: A population is the entire group of items or individuals that a study is interested in.
🎯 Exam Tip: Clearly distinguish between 'population' as the whole group and 'sample' as a subset when answering definitions.

 

Question 3. Define sample.
Answer: A sample comprises a subset of units chosen from a larger population based on a specific criterion. For example, if 90 students are randomly selected from a school's total of 900 students, those 90 students form a sample.
In simple words: A sample is a smaller, representative group chosen from a larger population for study.
🎯 Exam Tip: Emphasize that a sample is a 'subset' and is selected using a 'definite criterion' to ensure it represents the population.

 

Question 4. Define qualitative data.
Answer: Qualitative data consists of observations regarding an attribute, rather than numerical values. For example, the education level of workers in a factory represents qualitative data.
In simple words: Qualitative data describes characteristics or qualities that cannot be measured numerically.
🎯 Exam Tip: Focus on the non-numerical, descriptive nature of qualitative data, often relating to categories or attributes.

 

Question 5. Define quantitative data.
Answer: Quantitative data refers to a collection of observations based on a numerical variable. An example would be the monthly wages of workers in a factory.
In simple words: Quantitative data involves numerical measurements that can be counted or quantified.
🎯 Exam Tip: Highlight the numerical aspect of quantitative data, indicating that it can be counted or measured.

 

Question 6. Define primary data.
Answer: Primary data is information collected for the first time by an authorized agency or investigator. An example is the Indian population data gathered by the NSSO every ten years.
In simple words: Primary data is original information collected directly by the researcher for their specific study.
🎯 Exam Tip: Emphasize the 'first-time collection' and 'original' aspects to correctly define primary data.

 

Question 7. Define secondary data.
Answer: Secondary data refers to information that has been previously collected by one agency or investigator and is subsequently used by another. For example, if population census data is utilized by a different agency for their research, it becomes secondary data for that agency.
In simple words: Secondary data is existing information that was collected by someone else for a different purpose, and is now being reused.
🎯 Exam Tip: Key aspects of secondary data are its 'pre-existing' nature and its use by an entity other than the original collector.

 

Question 8. State the methods of collecting primary data.
Answer: The primary methods for gathering initial data include:
- Direct method of inquiry
- Indirect method of inquiry and
- Method of the questionnaire.
In simple words: Primary data can be collected using direct questioning, indirect questioning, or through questionnaires.
🎯 Exam Tip: Remember these three core methods as they form the basis for direct data acquisition in statistical studies.

 

Section - C

Answer the following questions:

 

Question 1. State the definition of statistics given by Croxton and Cowden.
Answer: The definition of statistics provided by Croxton and Cowden is as follows: "Statistics is the science which deals with the collection, analysis and interpretation of numerical data."
In simple words: Croxton and Cowden defined statistics as the science that involves gathering, analyzing, and understanding numerical information.
🎯 Exam Tip: When citing specific definitions, accuracy of the quotation is paramount. Ensure all components (collection, analysis, interpretation, numerical data) are included.

 

Question 2. What is data?
Answer: Data is the collection of all observations obtained by examining a variable characteristic, which is defined on units within a population or a sample.
In simple words: Data consists of all the observations or measurements collected about a specific characteristic from a group being studied.
🎯 Exam Tip: Understand data as the raw facts or figures derived from observations, serving as the foundation for statistical analysis.

 

Question 3. What is questionnaire?
Answer: A questionnaire is a structured list of questions, relevant to the study's objective, with designated spaces for recording answers.
In simple words: A questionnaire is a set of written questions used to collect information from people for a study.
🎯 Exam Tip: Highlight that a questionnaire is a 'list of questions' that are 'relevant' and provide 'space for answers'.

 

Question 4. What is unpublished data?
Answer: Unpublished data consists of statistical information that has not been formally released to the public. This data can be acquired by requesting access to internal records from private and public organizations, or from sources like research papers, articles, and essays that haven't been widely published.
In simple words: Unpublished data is information that has been collected but not yet formally released or made public, often found in internal records or non-public research.
🎯 Exam Tip: Note that unpublished data is often available upon request and originates from sources not widely disseminated, such as private organizational records or specific research documents.

 

Question 5. What is a variable characteristic?
Answer: A variable characteristic is an attribute that exhibits differences from one unit to another within a population or sample. It can be either numerical or non-numerical; a characteristic that is non-numerical is termed an attribute, while a numerical one is called a numeric variable.
In simple words: A variable characteristic is a feature that changes or varies among different individuals or items in a study.
🎯 Exam Tip: Emphasize that a variable characteristic is something that "varies" among units and can be either qualitative (attribute) or quantitative (numeric variable).

 

Question 6. What is an attribute?
Answer: An attribute represents a qualitative variable that is non-numerical. Examples include profession, marital status, education level, gender, honesty, and smoking habits. These are characteristics that cannot be numerically expressed.
In simple words: An attribute is a descriptive quality or characteristic that cannot be measured with numbers, like a person's profession or marital status.
🎯 Exam Tip: Focus on the 'qualitative' and 'non-numerical' nature of an attribute, providing clear examples that illustrate these qualities.

 

Section - D

Answer the following questions:

 

Question 1. What is the role of Prof. P. C. Mahalanobis in the development of statistics in India?
Answer: The renowned Indian Statistician Prof. P. C. Mahalanobis played a pivotal role in advancing statistics in India.
He established the Indian Statistical Institute (ISI) in Kolkata in 1931 and initiated the country's first post-graduate course in Statistics at Kolkata University in 1941.
- The National Sample Survey-NSS (now known as National Sample Survey Organisation - NSSO) was proposed by Mahalanobis and began data collection in India in 1950.
- In 1953, he formulated the outline for the second five-year plan using an operations research system at ISI.
- Consequently, his contributions were immensely significant in fostering the development of statistics across India.
In simple words: Prof. P. C. Mahalanobis was key to developing statistics in India, founding the Indian Statistical Institute (ISI) and initiating major data collection and planning efforts like the NSSO and contributions to five-year plans.
🎯 Exam Tip: When discussing contributions of individuals, mention key institutions they founded, major projects they initiated, and their lasting impact on the field.

 

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

Qualitative Data	Quantitative Data
1. This data comprises observations collected on a qualitative variable.	1. This data consists of observations collected on a numerical variable.
2. For instance, information pertaining to attributes like gender or students' study standards in a school constitutes qualitative data.	2. For example, data related to numerical variables such as age, weight, or height of students in a school represents quantitative data.
3. Observations in qualitative data are non-numerical, meaning they cannot be expressed with numbers.	3. Observations in quantitative data are numerical, meaning they are expressed as numbers.

In simple words: Qualitative data describes characteristics that aren't numbers, like colors or types, while quantitative data involves numbers that can be measured or counted, like age or height.
🎯 Exam Tip: Use clear examples for both types of data to illustrate the core difference: qualitative for descriptive attributes and quantitative for measurable numerical values.

 

Question 3. Give some examples of primary data.
Answer: Some illustrations of primary data include:
- Population Census data for India, gathered by NSSO.
- Data on Indian agriculture, obtained by IASR.
- Information about postgraduate students, collected by Gujarat University.
- Financial data for India, acquired by RBI.
- Data concerning Textile Industries in Gujarat, gathered by ATIRA.
In simple words: Primary data examples include original census data, agricultural surveys, university student data, financial records collected directly, and industrial research data.
🎯 Exam Tip: When listing examples, ensure they clearly demonstrate data collected directly by the stated agency for its specific purpose, highlighting its original nature.

 

Question 4. Discuss the method of questionnaire.
Answer: A questionnaire is a systematically arranged list of questions pertinent to a study's objective, providing adequate space for respondents to write their answers.
- The process of gathering information using such a structured questionnaire is known as the questionnaire method.
- This technique is particularly effective when the scope of the inquiry is extensive.
- Information can be collected via a questionnaire through two main approaches: 1. By post and 2. By enumerators.
- The efficacy of this method heavily relies on how well the questionnaire is constructed.
- It is considered the most economical data collection method as it significantly saves time and cost.
- The questionnaire method can be employed in both direct and indirect inquiries.
In simple words: The questionnaire method uses a prepared list of questions to collect data, which is useful for broad studies and can be sent by post or administered by interviewers; its success depends on good design and it's generally cost-effective.
🎯 Exam Tip: Emphasize the questionnaire's structured nature, its utility for wide inquiries, the two modes of delivery, and its cost-effectiveness in examinations.

 

Question 5. Discuss questionnaire by post.
Answer: In the postal questionnaire method, the questionnaire is sent to respondents via mail. Respondents then complete the questionnaire and return it by post.
Advantages:
- This method is simple, rapid, and allows for the collection of a large volume of information at a lower cost.
- It is particularly efficient when data needs to be collected from educated and responsible individuals.
- Investigators can gather information from areas that are difficult to access physically or by telephone.
Disadvantages:
- This method is less effective if respondents are illiterate or uncooperative.
- Sometimes, respondents may not bother to read or return the questionnaire.
- It is challenging to verify the accuracy of the information provided.
- Concerns about misuse of information can lead even educated respondents to avoid providing written details or returning the questionnaire.
- Respondent laziness or forgetfulness can result in questionnaire loss or delays in data retrieval.
- A lack of immediate assistance means instructions cannot be clarified, and arising questions cannot be addressed, potentially leading to incorrect information.
In simple words: The postal questionnaire method involves mailing questionnaires to respondents for them to fill out and return, offering advantages like low cost and wide reach, but it suffers from low response rates, potential inaccuracy, and lack of clarification for respondents.
🎯 Exam Tip: When discussing mailed questionnaires, balance the benefits of reach and cost-efficiency against the drawbacks of low response rates and inability to clarify queries.

 

Question 6. Discuss questionnaire by enumerators.
Answer: In the enumerator-administered questionnaire method, enumerators personally visit respondents to conduct interviews and complete the questionnaire.
- If enumerators are diligent, courteous, honest, and proficient, this method ensures accurate answers are obtained by providing relevant and supplementary information to respondents.
- Enumerators are trained to foster a friendly atmosphere, avoiding disputes or showing disrespect towards respondents.
- This method simplifies data collection, regardless of whether respondents are educated or uneducated.
- Comprehensive, accurate, and pertinent information can be gathered from respondents.
- Enumerators can effectively elicit information from illiterate respondents by offering necessary explanations.
- The risk of losing questionnaires or receiving incomplete ones is eliminated as enumerators collect the information in person.
- Accurate information can be obtained within a specified timeframe, even across a broad field of inquiry.
- Any doubts respondents might have are clarified immediately by the enumerator.
Disadvantages:
- Collecting data from a large geographical area necessitates a greater number of enumerators, leading to increased costs.
- If experienced enumerators are unavailable, training new ones for the inquiry can be challenging.
- Appointing supervisors to oversee enumerators' work is often required, which further escalates costs.
- If respondents are uneducated, impolite, or insincere, they may not cooperate or might conceal accurate information from enumerators.
- Adjusting to respondents' availability and schedules can cause delays.
In simple words: The enumerator method involves trained personnel directly administering questionnaires to respondents, which enhances data accuracy, ensures completeness, and allows for clarification, especially with diverse populations, but it can be costly and time-consuming for large areas.
🎯 Exam Tip: Highlight the enumerator's direct role in ensuring data quality and resolving respondent queries, while also noting the higher logistical and financial demands compared to postal questionnaires.

 

Question 7. Describe the method of collecting secondary data from unpublished sources.
Answer: Unpublished secondary data consists of statistical information compiled but not released publicly by private and public organizations or researchers. Such data can be acquired:
- By requesting access to records maintained by private and public organizations.
- From research papers, academic articles, and essays that remain unpublished.
In simple words: Collecting unpublished secondary data involves accessing information that hasn't been formally published, typically by requesting records from private or public organizations or by consulting specific research documents.
🎯 Exam Tip: Focus on the 'unpublished' aspect and the channels through which such data can be accessed, such as direct requests to institutions or reviewing specialized research materials.

 

Question 8. Discuss some applications of statistics.
Answer: Currently, statistics is recognized as an autonomous component of scientific methodologies. Its expansive scope makes it valuable for analyzing both quantitative and qualitative data.
- Industrial statistics and a specialized branch called Operations Research (OR) were notably utilized in military projects during the Second World War.
- In India, OR is employed for national planning and surveys, and its techniques are instrumental in formulating five-year plans.
- OR techniques can assist governments in maximizing per capita income while minimizing resource usage.
- In industry, OR techniques facilitate decisions on optimal resource allocation to maximize returns.
- OR is also useful for determining inventory sizes to meet future market demands.
- Given its widespread utility in modern times, the significance of statistics is undeniable.
In simple words: Statistics is crucial across various fields, including industrial analysis, national planning, and optimizing resource allocation, demonstrating its broad applicability in both quantitative and qualitative contexts.
🎯 Exam Tip: Provide diverse examples of statistical applications across different sectors (e.g., government, industry, military) to showcase its broad relevance and importance.

 

Question 7. Discuss advantages and disadvantages of indirect inquiry.
Answer:The method of indirect inquiry involves obtaining information from an organization or agency rather than directly from enumerators.
**Advantages:**
- This method is highly suitable when the scope of the inquiry is extensive, or if the research objective involves multiple types of data.
- It is also more effective when there are diverse opinions among the informants.
- This approach is more economical as it requires less cost, time, and energy because data is collected indirectly.
- When both the inquiry's supervisors and informants are experienced, impartial, and technically proficient, the accuracy of the information can be significantly improved.
- This method proves very useful for various government departments in gathering different types of information.
**Disadvantages:**
- Information can become less reliable if the individual or organization tasked with providing data has prejudices or a biased perspective.
- This method becomes ineffective if the third party providing the information is dishonest, inefficient, or unable to supply accurate data.
In simple words: Indirect inquiry gathers data from intermediaries, which saves resources and is good for large-scale studies, but its accuracy depends heavily on the honesty and impartiality of those third-party sources.

🎯 Exam Tip: When evaluating methods of data collection, focus on how the scope of inquiry and the reliability of sources impact the suitability of direct versus indirect methods.

 

Question 8. Discuss the characteristics of an ideal questionnaire.
Answer:While there are no strict rules for creating an ideal questionnaire, a well-designed one possesses certain key characteristics:
1. **Title:** An appropriate title, clearly indicating the study's objective, should be chosen. It should be formulated so that respondents feel no suspicion or confusion about its purpose.
2. **Number of questions:** The questionnaire should contain a sufficient number of questions, consistent with the inquiry's purpose. Fewer questions generally lead to a better response rate from participants.
3. **Order of questions:** Questions should be arranged logically to enable respondents to answer quickly and spontaneously without having to refer back and forth.
4. **Language of questions:** The language used must be simple, unambiguous, concise, and free from dual meanings.
5. **Length of questions:** Questions requiring "YES/NO" or multiple-choice answers are preferable. They should be short and clear, as excessively long questions or answers can bore respondents, potentially leading to inaccurate information.
6. **Time:** Avoid questions related to the distant past or those that demand intense memory recall.
7. **Confidentiality:** Questions about personal life should generally be avoided. If such questions are essential, they must be framed cautiously, and a guarantee of confidentiality must be provided to the respondent.
8. **Trial:** After drafting, the questionnaire should be tested on a trial basis to assess its practicality. Any necessary changes should be made to perfect it.
In simple words: An ideal questionnaire is clear, concise, logical, and easy for respondents to complete, respecting their privacy and tested beforehand for effectiveness.

🎯 Exam Tip: Remember to list practical considerations like question count and clarity, as these are crucial for maximizing response rates and data quality.

 

Question 9. Discuss advantages and disadvantages of questionnaire by post.
Answer:In the postal questionnaire method, surveys are sent to respondents via mail, who then complete and return them.
**Advantages:**
- This method is straightforward, quick, and can gather a large volume of information at a low cost.
- It is particularly effective for collecting data from educated and responsible individuals.
- Investigators can reach respondents in areas that are otherwise difficult to access personally or by telephone.
**Disadvantages:**
- This method is not very effective if respondents are illiterate or uncooperative.
- Sometimes, respondents may not bother to read or return the questionnaire.
- It is often difficult to verify the accuracy of the information provided.
- Due to concerns about data misuse, even educated and understanding respondents might avoid providing written information or delay returning the questionnaire.
- Laziness or apathy from respondents can lead to lost questionnaires or delays in receiving information.
- There is a lack of direct assistance, meaning clarifications or explanations for questions are not provided, potentially leading to incorrect information.
In simple words: The postal questionnaire method is cheap and good for reaching many people, especially educated ones, but it suffers from low response rates, difficulty in verifying answers, and no opportunity for direct clarification.

🎯 Exam Tip: Highlight the trade-off between cost-effectiveness and control over data quality and response rates when discussing postal questionnaires.

 

Question 10. Discuss advantages and disadvantages of questionnaire by enumerators.
Answer:In the enumerator-led questionnaire method, enumerators personally contact respondents, obtain their responses, and complete the questionnaire themselves.
**Advantages:**
- Complete, accurate, and more relevant information can be gathered directly from respondents by the enumerators.
- Enumerators can provide necessary explanations and secure proper information even from illiterate respondents.
- There is no loss of questionnaires or incomplete forms, as the enumerator collects the information in person.
- For extensive inquiry fields, accurate information can be obtained within a specified timeframe.
- Any doubts respondents have are resolved immediately due to the enumerator's presence.
**Disadvantages:**
- If data needs to be collected from a vast area, employing a large number of enumerators results in higher costs.
- It can be challenging to train and appoint expert enumerators for the inquiry if skilled personnel are not readily available.
- Supervisors are needed to monitor enumerators' work, which further increases costs.
- If respondents are uneducated, impolite, or lacking sensibility, they may not cooperate or might conceal accurate information from enumerators.
- Adjusting to respondents' convenience for timing can lead to significant delays.
In simple words: Using enumerators for questionnaires ensures high accuracy and completeness, even with illiterate respondents, but it is expensive, time-consuming for large areas, and relies heavily on the enumerator's skill and respondent cooperation.

🎯 Exam Tip: Emphasize how direct interaction improves data quality and accessibility but at the cost of increased resources and potential delays.

 

Question 11. Discuss what types of precautions should be taken while using secondary data.
Answer:When utilizing secondary data, several precautions should be observed:
1. **Reliability:** Before using secondary data, its reliability level should be verified. Data collected and published by government, semi-government, or autonomous organizations are generally more reliable. Data from private organizations may be less dependable if collected to suit their own agenda or if biases are present.
2. **Purpose:** The original purpose for which the data was collected must be carefully examined before it is adopted as secondary data.
3. **Method of collecting data:** Understanding the original inquiry method used to collect the data is crucial, as this knowledge helps in identifying any limitations.
4. **Time duration:** The timeframe during which the data was gathered should be known, as data collected in the distant past may not be relevant to current circumstances.
5. **Scope of data:** Before using secondary data, it is important to ascertain details regarding its scope, the geographical region it covers, the definitions of terms used, and the criteria for selecting units.
6. **Limitations:** Any inherent limitations or drawbacks of the secondary data should be understood.
7. **Alternatives:** If alternative data sources are available, the data should be compared across sources to ensure that only the most appropriate and accurate information is used.
In simple words: When using existing data, always check its source's reliability, the original reason for collection, the methods used, when it was gathered, its scope, and any limitations to ensure it fits your current needs accurately.

🎯 Exam Tip: Focus on critically evaluating the source, relevance, and methodology of secondary data to ensure its appropriateness for your specific research, as these are common pitfalls.