Collection of DataClass 11 Statistics For Economics NCERT Solutions
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Q1EXERCISES
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?
(ii)
How often do you use computers?
(iii)
Which of the newspapers do you read regularly?
(iv)
Rise in the price of petrol is justified.
(v)
What is the monthly income of your family?
Solution
Here are four appropriate multiple-choice options for each question:
(i) Which of the following is the most important when you buy a new dress?
(a) Price
(b) Brand
(c) Quality of fabric
(d) Colour and design
(ii) How often do you use computers?
(a) Daily
(b) 2-3 times a week
(c) Occasionally
(d) Never
(iii) Which of the newspapers do you read regularly?
(a) The Times of India
(b) The Hindu
(c) Hindustan Times
(d) Any other (please specify)
(iv) Rise in the price of petrol is justified.
(a) Strongly agree
(b) Agree
(c) Disagree
(d) Strongly disagree
(v) What is the monthly income of your family?
(a) Less than Rs 20,000
(b) Rs 20,001 - Rs 50,000
(c) Rs 50,001 - Rs 1,00,000
(d) More than Rs 1,00,000
Q2EXERCISES
Frame five two-way questions (with 'Yes' or 'No').
Solution
Five two-way questions with 'Yes' or 'No' answers are:
- Do you have a library card for the city library? (Yes/No)
- Is your school located within 3 kilometers of your home? (Yes/No)
- Have you ever participated in a school sports event? (Yes/No)
- Do you think online classes are as effective as physical classes? (Yes/No)
- Do you use public transport to commute to school? (Yes/No)
Q3EXERCISES
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.
Solution
(i)
True. As discussed in the chapter, data can be obtained from primary sources (collected firsthand by the researcher) and secondary sources (collected by other agencies).
(ii)
False. For a literate population spread over a large area, a mailing (questionnaire) survey is more suitable as it is less expensive and can reach remote areas. Telephone surveys have limitations as many people may not own telephones.
(iii)
False. Data collected for the first time by an investigator or researcher is called primary data.
(iv)
True. In non-random sampling, the investigator uses their convenience or judgment to select the sample, which introduces a bias in the selection process.
(v)
False. Sampling errors can be minimised by taking a larger sample. Non-sampling errors, which arise from issues like incorrect recording of data or non-response, are difficult to minimise even with a large sample.
Q4EXERCISES
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?
(ii)
If plastic bags are only 5 per cent of our garbage, should it be banned?
(iii)
Wouldn't you be opposed to increase in price of petrol?
(iv)
Do you agree with the use of chemical fertilisers?
(v)
Do you use fertilisers in your fields?
(vi)
What is the yield per hectare in your field?
Solution
Yes, there are problems with some of these questions based on the principles of good questionnaire design.
(i) How far do you live from the closest market?
- Problem: This question is ambiguous. The term 'far' is subjective and can be interpreted differently by different people.
- Improvement: The question should be precise, asking for a specific unit of measurement, such as "What is the distance in kilometers between your home and the closest market?"
(ii) If plastic bags are only 5 per cent of our garbage, should it be banned?
- Problem: This is a leading question. By stating that plastic bags are "only 5 per cent" of the garbage, it gives a clue to the respondent and suggests that the ban may not be necessary, thus influencing the answer.
- Improvement: A better question would be neutral, like "Do you think plastic bags should be banned?"
(iii) Wouldn't you be opposed to increase in price of petrol?
- Problem: This question uses a double negative ("Wouldn't you be opposed"). This can confuse the respondent and may lead to a biased response.
- Improvement: The question should be phrased directly and positively, such as "Do you support the increase in the price of petrol?" or "Are you opposed to the increase in the price of petrol?"
(iv) Do you agree with the use of chemical fertilisers?
- Problem: While this is a direct question, it might be too general. A respondent might agree with its use in some cases but not others. It is a simple two-way question that may not capture the complexity of the issue.
- Improvement: It could be followed by more specific questions or changed to a multiple-choice format to capture nuances.
(v) Do you use fertilisers in your fields?
- Problem: This question is good. It is a clear, precise, and direct two-way question without any ambiguity or bias.
(vi) What is the yield per hectare in your field?
- Problem: This question is also good. It is specific and clear, assuming it is directed at a respondent who is a farmer and would have this information.
Q5EXERCISES
You want to do a research on the popularity of Vegetable Atta Noodles among children. Design a suitable questionnaire for collecting this information.
Solution
Questionnaire: Popularity of Vegetable Atta Noodles
Instructions: Please tick the most appropriate option. Your responses will be kept confidential and used for research purposes only.
-
What is your age?
- (a) 5-8 years
- (b) 9-12 years
- (c) 13-15 years
-
Do you like eating instant noodles?
- (a) Yes
- (b) No
-
How often do you eat instant noodles?
- (a) Every day
- (b) 2-3 times a week
- (c) Once a week
- (d) Occasionally
-
Have you heard of 'Vegetable Atta Noodles'?
- (a) Yes
- (b) No (If No, please end the survey here)
-
Have you ever tasted 'Vegetable Atta Noodles'?
- (a) Yes
- (b) No
-
How would you rate the taste of 'Vegetable Atta Noodles'?
- (a) Excellent
- (b) Good
- (c) Average
- (d) Poor
-
Which feature of 'Vegetable Atta Noodles' do you like the most?
- (a) Taste
- (b) The idea of having vegetables and atta
- (c) Quick to cook
- (d) Any other (please specify) ______________
-
Would you ask your parents to buy 'Vegetable Atta Noodles' again?
- (a) Yes
- (b) No
Thank you for your time!
Q6EXERCISES
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?
Solution
Based on the definitions provided in the chapter:
-
Population: The population (or universe) in statistics refers to the totality of the items under study. In this case, the study is about the cropping pattern in a specific village. Therefore, the population is all 200 farms in the village.
-
Sample Size: A sample is a group or section of the population from which information is obtained. In this study, information was collected from a smaller group of farms. Therefore, the sample size is the 50 farms that were surveyed.
Q7EXERCISES
Give two examples each of sample, population and variable.
Solution
Here are two examples for each term based on the chapter:
Population:
- All the students enrolled in Class 11 in all schools of a city.
- The total number of agricultural labourers in the state of Punjab.
Sample:
- A group of 500 students selected from different schools in the city to study their academic performance.
- A selection of 1,000 agricultural labourers from various districts of Punjab to understand their economic condition.
Variable:
- The marks obtained by students in their final examination. (The value of marks varies from student to student).
- The monthly income of a household. (The value of income varies from one household to another).
Q8EXERCISES
Which of the following methods give better results and why?
(a)
Census
(b)
Sample
Solution
Neither method is universally better; the choice depends on the purpose of the survey, available resources (time and money), and the required level of accuracy.
Census Method:
- Advantages: It provides complete and accurate information because every single item of the population is studied. It is free from sampling error and provides detailed data for various characteristics.
- Disadvantages: It is extremely expensive, time-consuming, and requires a large number of enumerators, making it impractical for most studies.
Sample Method:
- Advantages: It is less expensive, requires less time, and allows for more detailed and intensive data collection from a smaller group. If the sample is representative, it can provide reasonably accurate and reliable information.
- Disadvantages: It is subject to sampling error (the difference between the sample result and the true population result). There is also a risk of bias if the sample is not selected properly.
Conclusion:
A Sample survey often gives 'better' results in a practical sense because it provides a good balance of accuracy, cost, and time. For many economic and social studies where a quick and reliable estimate is needed, a well-designed sample survey is preferred over a census.
Q9EXERCISES
Which of the following errors is more serious and why?
(a)
Sampling error (b) Non-Sampling error
Solution
Non-sampling error is more serious than sampling error.
Reasoning:
-
Sampling Error: This error arises because the study is based on a sample instead of the entire population. It is the difference between the sample estimate and the actual population parameter. The magnitude of sampling error can be predicted and reduced by increasing the sample size. A larger sample is generally more representative of the population, thus minimizing this error.
-
Non-Sampling Error: These errors are related to the process of data collection and processing. They include errors in data acquisition (incorrect responses), non-response errors (when individuals in the sample do not respond), and sampling bias (flaws in the sampling plan). These errors are more serious because they are difficult to detect and control. Crucially, increasing the sample size does not reduce non-sampling errors. In fact, a large survey might even increase them due to the difficulty in training and supervising many enumerators. Even a census can suffer from non-sampling errors, leading to fundamentally incorrect conclusions.
Q10EXERCISES
Suppose there are 10 students in your class. You want to select three out of them. How many samples are possible?
Solution
To find the number of possible samples of 3 students from a group of 10, we need to calculate the number of combinations. The formula for combinations is:
C(n, k) = n! / (k! * (n-k)!)
Where:
- n = total number of items (population) = 10
- k = number of items to choose (sample size) = 3
Calculation:
C(10, 3) = 10! / (3! * (10-3)!)
C(10, 3) = 10! / (3! * 7!)
C(10, 3) = (10 × 9 × 8 × 7!) / ((3 × 2 × 1) × 7!)
C(10, 3) = (10 × 9 × 8) / (6)
C(10, 3) = 720 / 6
C(10, 3) = 120
Therefore, 120 different samples are possible.
Q11EXERCISES
Discuss how you would use the lottery method to select 3 students out of 10 in your class.
Solution
The lottery method is a simple way to ensure that every student has an equal chance of being selected. The procedure would be as follows:
-
Assign Numbers: First, assign a unique number from 1 to 10 to each of the 10 students in the class.
-
Prepare Slips: Take 10 identical slips of paper. They must be identical in size, shape, and colour to avoid any bias. Write one unique number (from 1 to 10) on each slip.
-
Mix the Slips: Fold all the slips in the same manner so that the numbers are not visible. Place them in a box or a bowl.
-
Shuffle Thoroughly: Mix the slips in the box thoroughly to ensure that they are randomly distributed.
-
Draw the Sample: Without looking, draw three slips from the box one by one. The students whose numbers correspond to the numbers on the three drawn slips will form the random sample.
Q12EXERCISES
Does the lottery method always give you a random sample? Explain.
Solution
Yes, the lottery method always gives a random sample, provided it is executed correctly.
Explanation:
The fundamental principle of random sampling is that every individual unit in the population must have an equal and independent chance of being selected in the sample. The lottery method is designed to fulfill this condition.
- Equal Chance: By using identical slips of paper and mixing them thoroughly, each slip has an equal probability of being drawn. Since each slip corresponds to one student, every student has an equal chance of being selected.
- Independence: The selection of one student does not influence the selection of another (in the case of drawing without replacement, it only affects the probability for the subsequent draws, but the initial chance is equal for all).
If there is any bias in the process, such as using non-identical slips or not mixing them properly, the sample would not be truly random. However, when the procedure is followed without any bias, the lottery method is a classic and effective way of drawing a random sample.
Q13EXERCISES
Explain the procedure for selecting a random sample of 3 students out of 10 in your class by using random number tables.
Solution
Using random number tables is another method to ensure a random selection. The procedure is as follows:
-
List and Assign Numbers: First, make a list of all 10 students in the class. Assign a unique number to each student, from 0 to 9.
-
Refer to a Random Number Table: Take a standard table of random numbers. These tables consist of digits (0-9) arranged randomly in rows and columns.
-
Choose a Starting Point: Close your eyes and place your finger anywhere on the random number table to select a starting point (a specific row and column).
-
Select Numbers: From the starting point, decide on a direction to read the numbers (e.g., move down the column, or across the row). Since our assigned numbers are single digits (0-9), we will read single digits from the table.
-
Identify the Sample: Read the digits one by one in the chosen direction. The first three unique digits between 0 and 9 will be selected. For example, if you read the digits 7, 2, 9, 3, 2, ..., you would select the numbers 7, 2, and 9. You would ignore the second '2' because it is a repeat and you need three unique students.
-
Match with Students: The three students whose assigned numbers match the three selected random numbers will form your random sample.
Q14EXERCISES
Do samples provide better results than surveys? Give reasons for your answer.
Solution
This question seems to contain a misunderstanding. A sample is a part of a survey; a survey is the method of collecting data, which can be conducted either on a sample (a sample survey) or on the entire population (a census survey). The question should likely be interpreted as: "Do sample surveys provide better results than census surveys?"
In many situations, sample surveys can provide 'better' results than census surveys for the following reasons:
-
Greater Accuracy and Quality: Because a sample survey deals with a smaller number of units, it is possible to hire highly trained and skilled investigators. This allows for more detailed information to be collected and better supervision, which helps in reducing non-sampling errors (like errors in recording data or misinterpretation of questions). In a large census, it is harder to maintain high quality control.
-
Lower Cost: Collecting data from a small fraction of the population is significantly cheaper than collecting data from every single unit. This makes research possible when financial resources are limited.
-
Faster Results: A sample survey can be completed much more quickly than a census. This is crucial when information is needed urgently for decision-making.
-
Feasibility: In cases where the population is very large or infinite, conducting a census is practically impossible. A sample survey is the only feasible option.
-
In-depth Enquiry: With a smaller group, it is possible to ask more complex and detailed questions, leading to a richer and more in-depth understanding of the issue being studied.
While a census is free from sampling error, it is prone to significant non-sampling errors, high costs, and long delays. Therefore, for many practical purposes, a well-designed representative sample survey often provides more reliable, timely, and cost-effective results.