NCERT Solutions for Class 11 Economics Chapter 8: Use of Statistical Tools
These Class 11 Economics Chapter 8 solutions cover Use of Statistical Tools from the NCERT book Statistics for Economics (updated for the 2026–27 session). This is a project-based chapter — it teaches you how to apply everything you learnt in earlier chapters (collection, organisation, presentation, central tendency, dispersion and correlation) to a real survey. Below you get the full steps for designing a project, a walkthrough of the textbook’s sample toothpaste project (with the mean and standard deviation worked out step by step), all 12 suggested projects reproduced verbatim with guided model answers, plus extra practice, MCQs, Assertion–Reason and FAQs.
Class 11 Economics Chapter 8 – Overview
Chapter 8, Use of Statistical Tools, is the concluding, application-oriented chapter of Statistics for Economics. Instead of introducing new theory, it shows how the statistical tools you already studied — collection of data (Chapter 2), organisation and tabulation (Chapter 3), diagrammatic and graphic presentation (Chapter 4), measures of central tendency (Chapter 5), measures of dispersion (Chapter 6) and correlation (Chapter 7) — come together in a single project. You learn the sequence of steps for making a project: identifying a problem or area of study, choosing a target group, collecting data (primary/secondary), organising and presenting it, analysing and interpreting it, drawing a conclusion, and listing a bibliography. The chapter gives a list of suggested project topics and a fully worked sample project on toothpaste, where survey data are tabulated, shown as bar diagrams, pie diagrams and histograms, and summarised using the mean and standard deviation. The aim is to make you capable of independently designing a survey, processing the data and writing a clear, evidence-based report.
Steps in Designing a Project & Key Terms
1. Identifying a problem / area of study: Be clear about what you want to study (e.g. sale of a car or mobile phone, household water problems, consumer awareness). The objective drives every later step.
2. Choice of target group: Identify the people on whom you focus — for cars, middle- and higher-income groups; for soap, all rural and urban consumers; for safe drinking water, both urban and rural population. The target group decides how questions are framed.
3. Collection of data: Decide between primary (first-hand — questionnaire or interview schedule, by personal interview, mail/post, phone or email) and secondary data (already available; used when time, money and manpower are short). A postal questionnaire needs a covering letter stating the purpose. If sampling is used, the sampling method must be suitable.
4. Organisation and presentation of data: Process the information by tabulating it and presenting it with suitable diagrams — bar diagrams, pie diagrams, histograms, etc. (Chapters 3 and 4).
5. Analysis and interpretation: Use Measures of Central Tendency (e.g. mean), Measures of Dispersion (e.g. standard deviation) and Correlation to find the average, the variability and any relationship among variables (Chapters 5, 6 and 7).
6. Conclusion: Draw meaningful conclusions from the analysis; where possible, predict future prospects and give suggestions on growth and policy.
7. Bibliography: List the details of all secondary sources used — magazines, newspapers, research reports, etc.
Primary vs secondary data: Primary data are collected first-hand for the present study; secondary data already exist (collected by someone else for another purpose) and are used only if they suit the requirement.
Questionnaire vs interview schedule: A questionnaire is filled in by the respondent; an interview schedule is filled in by an enumerator who asks the questions. A structured questionnaire uses closed-ended questions with given options.
Sampling vs census: In the census method every unit of the population is studied; in the sample survey method only a representative subset (the sample) is studied. Random sampling gives every unit an equal chance of selection.
Sample Project (Toothpaste) – Worked Out
The textbook gives a sample project in which X, a young entrepreneur, wants to set up a toothpaste factory and you are asked to advise him. Primary data are collected from 100 households using a questionnaire, then organised, presented and analysed. Two of the tables require the mean and standard deviation, computed by the step-deviation method. Here is the working that the textbook’s figures come from.
Important formulas (step-deviation method)
where A = assumed mean, d′ = (X − A)/c, c = common class width, f = frequency, X = class midpoint.
(a) Monthly family income — Mean and S.D.
| Income class | Midpoint X | f | d′ = (X−20000)/5000 | fd′ | fd′² |
|---|---|---|---|---|---|
| 0 – 10,000 | 5,000 | 20 | −3 | −60 | 180 |
| 10,000 – 20,000 | 15,000 | 40 | −1 | −40 | 40 |
| 20,000 – 30,000 | 25,000 | 30 | 1 | 30 | 30 |
| 30,000 – 40,000 | 35,000 | 10 | 3 | 30 | 90 |
| Total | 100 | −40 | 340 |
(b) Monthly expenditure on toothpaste — Mean and S.D.
| Expenditure class (Rs) | Midpoint X | f | d′ = (X−100)/40 | fd′ | fd′² |
|---|---|---|---|---|---|
| 0 – 40 | 20 | 5 | −2 | −10 | 20 |
| 40 – 80 | 60 | 20 | −1 | −20 | 20 |
| 80 – 120 | 100 | 40 | 0 | 0 | 0 |
| 120 – 160 | 140 | 30 | 1 | 30 | 30 |
| 160 – 200 | 180 | 5 | 2 | 10 | 20 |
| Total | 100 | 10 | 90 |
Reading the sample report
The sample report presents many tables and diagrams — age distribution, family size, income, expenditure, occupation, preferred brand (Pepsodent, Colgate and Close-up were most preferred), basis of selection (standardised marking, quality, price, brand name), ingredient preference (gel and antiseptic), and media influence (television was the most effective medium). The concluding note ties these together: most users were urban, aged about 25–50, in families of 3–6 members, with monthly income of Rs 10,000–30,000, spending about Rs 104 per month on toothpaste, strongly influenced by advertisements (mainly TV). This shows how a complete project moves from raw survey data to a clear, decision-useful conclusion.
Suggested List of Projects – Full Guided Answers
This chapter has no numbered exercise; instead the NCERT textbook gives a Suggested List of Projects. All 12 project tasks below are reproduced verbatim from the textbook. For each, a guided model answer outlines the objective, target group, data to collect, statistical tools to apply and the kind of conclusion expected. You are free to choose any topic dealing with an economic issue.
1. Consider yourself as an advisor to Transport Minister who aims to bring about a better and coordinated system of transportation. Prepare a project report.
2. You may be working in a village cottage industry. It could be a unit manufacturing dhoop, agarbatti, candles, jute products, etc. You want to start a new unit of your own. Prepare a project proposal for getting a bank loan.
3. Suppose you are a marketing manager in a company and recently you have put up advertisements about your consumer product. Prepare a report on the effect of advertisements on the sale of your product.
4. You are a District Education Officer, who wants to assess the literacy levels and the reasons for dropping out of school children. Prepare a report.
5. Suppose you are a Vigilance Officer of an area and you receive complaints about overcharging of goods by traders i.e., charging a higher price than the Maximum Retail Price (MRP). Visit a few shops and prepare a report on the complaint.
6. Consider yourself to be the head of Gram Panchayat of a particular village who wants to improve amenities like safe drinking water to your people. Address your issues in a report form.
7. As a representative of a local government, you want to assess the participation of women in various employment schemes in your area. Prepare a project report.
8. You are the Chief Health Officer of a rural block. Identify the issues to be addressed through a project study. This may include health and sanitation problems in the area.
9. As the Chief Inspector of Food and Civil Supplies department, you have received a complaint about food adulteration in the area of your duty. Conduct a survey to find the magnitude of the problem.
10. Prepare a report on Polio immunisation programme in a particular area.
11. You are a Bank Officer and want to survey the saving habits of the people by taking into consideration income and expenditure of the people. Prepare a report.
12. Suppose you are part of a group of students who wants to study farming practices and the problems facing farmers in a village. Prepare a project report.
Extra Practice Questions
Short Answer Type Questions
Q1. List the steps involved in making a project.
Q2. Distinguish between primary and secondary data with reference to a project.
Q3. Why is the choice of target group important in a project?
Q4. What is a bibliography and why is it needed in a project?
Q5. Name the statistical tools used at the ‘analysis and interpretation’ stage of a project.
Long Answer Type Questions
Q1. Explain, with an example, all the steps you would follow to design a statistical project.
Q2. Using the sample toothpaste project, explain how the mean and standard deviation are calculated by the step-deviation method.
Q3. ‘Diagrams and statistical averages make a project report meaningful.’ Discuss.
MCQs & Assertion–Reason
1. The very first step in designing a project is:
(a) collecting data (b) identifying a problem or area of study (c) drawing a conclusion (d) preparing a bibliography
2. Data collected first-hand for the present study are called:
(a) secondary data (b) primary data (c) tertiary data (d) processed data
3. A postal questionnaire must be accompanied by a:
(a) covering letter stating the purpose (b) photograph (c) sample product (d) cash reward
4. In the sample toothpaste project, the mean monthly expenditure on toothpaste was:
(a) Rs 18,000 (b) Rs 35.60 (c) Rs 104 (d) Rs 9,000
5. The standard deviation of monthly family income in the sample project was:
(a) Rs 18,000 (b) Rs 9,000 (c) Rs 104 (d) Rs 35.60
6. Which tool is used to study the relationship between two variables in a project?
(a) mean (b) standard deviation (c) correlation (d) range
7. A pie diagram in a project is best used to show:
(a) the components or share of a whole (b) a single value (c) the trend over time only (d) the correlation coefficient
8. The list of secondary sources used in a project is called the:
(a) questionnaire (b) bibliography (c) appendix (d) target group
9. In the sample project, the most effective medium for advertising toothpaste was:
(a) radio (b) newspaper (c) television (d) cinema
10. A method of data collection in which every unit of the population is studied is the:
(a) sample survey method (b) census method (c) random sampling (d) postal method
For each Assertion–Reason question, choose: (A) Both true and the Reason correctly explains the Assertion; (B) Both true but the Reason is not the correct explanation; (C) Assertion true, Reason false; (D) Assertion false, Reason true.
A-R 1. Assertion: The objective of the study must be identified clearly at the outset.
Reason: The objective decides the target group, the data to be collected and the tools to be used.
A-R 2. Assertion: Secondary data are always better than primary data for a project.
Reason: Secondary data are used when there is paucity of time, money and manpower and the information is easily available.
A-R 3. Assertion: The mean and standard deviation are used at the analysis stage of a project.
Reason: The mean gives the average value and the standard deviation gives the variability of the data.
A-R 4. Assertion: A bibliography should list all secondary sources used in the project.
Reason: Acknowledging sources makes the project authentic and lets readers verify the information.
A-R 5. Assertion: Diagrams have no role in a statistical project report.
Reason: Bar diagrams, pie diagrams and histograms present data clearly and make interpretation easier.
Exam Tips & Common Mistakes
How to score full marks in this chapter
Memorise the seven steps of a project in order (problem → target group → data → organisation/presentation → analysis → conclusion → bibliography) — this is the most common question. Be ready to recompute the mean and standard deviation of the sample tables by the step-deviation method, showing every column (X, d′, fd′, fd′²) and the final substitution. Know which diagram suits which data (pie for shares, bar for comparison, histogram for continuous frequency). When writing your own project, always state the objective, target group, tools and a clear, data-backed conclusion, and never forget the bibliography.
Common mistakes to avoid
- Forgetting steps or giving them out of order — the conclusion cannot come before data collection.
- Confusing primary data (first-hand) with secondary data (already available).
- Mixing up the two sample results — income S.D. is Rs 9,000 (mean Rs 18,000); toothpaste expenditure mean is Rs 104 (S.D. Rs 35.60).
- Errors in the step-deviation formula — remember to multiply by the class width c and to subtract (Σfd′/Σf)² inside the root for S.D.
- Choosing the wrong diagram (e.g. a pie diagram for a time trend).
- Leaving out the bibliography, or copying data without acknowledging the source.
Frequently Asked Questions
What is Chapter 8 of Class 11 Economics (Statistics for Economics) about?
Chapter 8, Use of Statistical Tools, is a project-based chapter that shows how to apply the statistical tools learnt earlier — data collection, tabulation, diagrams, central tendency, dispersion and correlation — to a real survey. It explains the steps for designing a project, gives a list of 12 suggested projects, and works through a sample toothpaste project.
Does Chapter 8 have a numbered exercise?
No. Instead of a numbered exercise, the chapter provides a Suggested List of Projects (12 project tasks) and a fully worked sample project. On this page all 12 project tasks are reproduced verbatim with guided model answers, and the sample project’s mean and standard deviation are solved step by step.
How are the mean and standard deviation found in the sample toothpaste project?
By the step-deviation method. For toothpaste expenditure, with assumed mean A = 100 and class width c = 40, Σfd′ = 10 and Σfd′² = 90 over 100 households, giving mean = 100 + (10/100)×40 = Rs 104 and S.D. = 40 × √(0.9 − 0.01) ≈ Rs 35.60.