1. Frame at least four appropriate multiple-choice options for following questions:
(i) Which of the following is the most important when you buy a new dress?
Ans. Price, Quality, Design, Brand
(ii) How often do you use computers?
Ans. Daily, Weekly, Occasionally, Never
(iii) Which of the newspapers do you read regularly?
Ans. The Hindu, Times of India, Dainik Bhaskar, None
(iv) Rise in the price of petrol is justified.
Ans. Strongly agree, Agree, Disagree, Strongly disagree
(v) What is the monthly income of your family?
Ans. Below ₹10,000, ₹10,000–₹30,000, ₹30,000–₹50,000, Above ₹50,000
2. Frame five two-way questions (with ‘Yes’ or ‘No’).
Do you use the internet daily?
Do you like online classes?
Do you save money regularly?
Do you read newspapers daily?
Do you think prices are rising?
3. State whether the following statements are True or False.
(i) There are many sources of data.
(ii) Telephone survey is the most suitable method of collecting data, when the population is literate and spread over a large area.
(iii) Data collected by investigator is called the secondary data.
(iv) There is a certain bias involved in the non-random selection of samples.
(v) Non-sampling errors can be minimised by taking large samples.
Ans. (i) True
(ii) False
(iii) False
(iv) True
(v) False
4. What do you think about the following questions? Do you find any problem with these questions? Describe.
(i) How far do you live from the closest market?
Ans. – This question is vague because it does not specify the unit of distance, so it may create confusion.
(ii) If plastic bags are only 5 per cent of our garbage, should it be banned?
Ans. – This is a leading question as it suggests an answer and influences the respondent.
(iii) Wouldn’t you be opposed to increase in price of petrol?
Ans. – This question uses double negative, which may confuse respondents and affect accuracy.
(iv) Do you agree with the use of chemical fertilisers?
Ans. – This question is clear, simple and appropriate, so it has no major problem.
(v) Do you use fertilisers in your fields?
Ans. – This question is clear but lacks specific options, which may reduce accuracy of responses.
(vi) What is the yield per hectare in your field?
Ans. This question may be difficult because respondents may not know exact data, leading to inaccurate answers.
5. You want to do a research on the popularity of Vegetable Atta Noodles among children. Design a suitable questionnaire for collecting this information.
Ans. – To study the popularity of Vegetable Atta Noodles among children, a questionnaire should be carefully prepared. According to the theory, the questionnaire should not be too long and must be easy to understand. Questions should be clear, precise and arranged from general to specific. Both closed-ended and open-ended questions can be used. For example: Do you like Vegetable Atta Noodles? (Yes/No), How often do you eat it? (Daily/Weekly/Occasionally), Why do you prefer it? (Taste/Health/Price). The questionnaire should avoid ambiguous, leading and double negative questions. Proper design of questionnaire helps in collecting reliable and accurate data.
6. In a village of 200 farms, a study was conducted to find the cropping pattern. Out of the 50 farms surveyed, 50% grew only wheat. What is the population and the sample size?
Ans. Population = Total 200 farms (complete group under study)
Sample = 50 farms (selected part of population)
7. Give two examples each of sample, population and variable.
Ans. In statistics, population or universe refers to the totality of items under study, while a sample is a smaller representative part selected from it. For example, all students in a school form the population, while 20 selected students form a sample. A variable is a characteristic which can take different values, such as income, marks or age.
8. Which of the following methods give better results and why?
(a) Census
Ans. Census and sample are two methods of data collection. Census or complete enumeration
includes every unit of the population and provides complete information, but it is expensive
and time-consuming.
(b) Sample
Ans. On the other hand, a sample survey studies only a representative part of the population. According to the theory, a good sample can provide reasonably accurate information at lower cost and in less time. It also allows more detailed study. Therefore, sample surveys are generally preferred in practical situations because they are economical, quicker and easier to manage while still giving reliable results.
9. Which of the following errors is more serious and why?
(a) Sampling error (b) Non-Sampling error
Ans. Non-sampling errors are more serious than sampling errors. Sampling error refers to the difference between the sample estimate and the population value and can be reduced by increasing the sample size. However, non-sampling errors arise due to reasons like bias, non-response, and errors in data collection. According to the theory, these errors cannot be easily minimised even by large samples or census. They may occur due to carelessness or misunderstanding. Therefore, non-sampling errors affect the accuracy of data more seriously and are difficult to control.
10. Suppose there are 10 students in your class. You want to select three out of them. How many samples are possible?
Ans. To find the number of samples of 3 students from a class of 10 students, we use combinations. The formula is 10C3, which gives the number of possible samples. When calculated, it equals 120. This means there are 120 different possible samples of 3 students from 10.
11. Discuss how you would use the lottery method to select 3 students out of 10 in your class.
Ans. In the lottery method, names of all individuals are written on slips and mixed thoroughly. Then required number of slips are selected randomly. This method ensures that each unit gets an equal chance of selection, which is the main feature of random sampling.
12. Does the lottery method always give you a random sample? Explain.
Ans. The lottery method gives a random sample if it is conducted properly. In this method, every unit of the population has an equal chance of being selected, which is the basic principle of random sampling. If slips are mixed properly and selection is done without bias, the sample will be fair and representative. However, if there is any carelessness or influence during selection, randomness may be affected. Therefore, the method depends on proper execution. When used correctly, it is a simple and effective way to obtain a representative sample.
13. Explain the procedure for selecting a random sample of 3 students out of 10 in your class by using random number tables.
Ans. To select a random sample using random number tables, first assign numbers to all units of the population. Then select numbers randomly from the table. Ignore numbers that are not relevant. The required number of valid numbers is selected as the sample. According to the theory, this method ensures that each unit has an equal chance of selection. It helps in avoiding bias and provides a fair and representative sample. It is a scientific method of sampling.
14. Do samples provide better results than surveys? Give reasons for your answer
Ans. Sample surveys are often more useful than complete census surveys in practical situations. Census involves studying the entire population, which is costly and time- consuming. A sample survey studies only a part of the population but can still give reliable results if the sample is representative. According to the theory, sample surveys save time, cost and effort and allow detailed study. They are easier to manage and more practical. Therefore, sample surveys are generally preferred because they are efficient and economical while still providing useful information.
