What is Applied Project Examples, Common Errors & Exercises in Class 11 Statistics for Economics NCERT?

Interactive NCERT Class 11 Statistics for Economics lesson on Applied Project Examples, Common Errors & Exercises

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Applied Project Examples, Common Errors & Exercises

🎓 Class 11 Social Science CBSE Theory Ch 8 — Use of Statistical Tools (Project) ⏱ ~30 min

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Class 11 · Statistics for Economics · Chapter 8 · Part 2 · Capstone & End-of-Book

Sample Project Walk-Through, Worked Statistical Analysis and NCERT Exercises

Part 1 set out the eight-step pipeline and the design rules. Part 2 puts the pipeline to work on NCERT's flagship sample project — entrepreneur X who wants to launch a new toothpaste — and walks the entire 100-household survey from questionnaire to interpretation. The chapter then takes a second worked case (inflation impact on a family budget), lays out the structure of a bound project report, catalogues the common errors that beginners commit, and offers full model answers to the chapter-end exercises. Because Statistics for Economics ends here, the part also closes with a brief End-of-Book reflection on what you have built across all eight chapters.

8.11 NCERT Sample Project — Should X Launch a Toothpaste Brand?

NCERT Sample Project X is a young entrepreneur who wants to set up a factory to produce toothpaste. You are asked to advise X about how he should proceed. One of the first things you could do would be to study people's tastes with regard to toothpastes, their monthly expenses on toothpaste, and other relevant facts. For this, you may decide to collect primary data with the help of a structured questionnaire.

The case is a perfect testing ground for the eight-step pipeline. The objective is commercial decision-making (Step 1); the population is all toothpaste-using households in the area (Step 2); the source must be primary because no published data exists at the brand-preference level for this geography (Step 3). Steps 4 to 8 follow below.

8.11.1 The Six Pieces of Information X Really Needs

Before drafting any questionnaire, the investigator decides what the survey must produce. NCERT lists the following six items of information as the minimum that X needs to invest sensibly:

The average monthly expenditure on toothpaste per household.
The brands of toothpaste currently in demand in the locality.
The attitude of customers towards these brands — satisfaction or dissatisfaction.
Customers' preferences in regard to ingredients in the toothpaste — gel, antiseptic, fluoride, etc.
The major media influences on consumers' demand for toothpaste — TV, newspaper, radio.
The relation between income and all the above factors — do richer households use more or different brands?

8.11.2 The Fifteen-Question Questionnaire

NCERT supplies a complete sample questionnaire of fifteen items, structured into the three layers introduced in Part 1 — identification, behaviour and attitude. Every Class 11 student should be able to redraw it from memory.

Toothpaste Project — Sample Questionnaire (NCERT, paraphrased)
#	Layer	Question
1	ID	Name
2	ID	Sex
3	ID	Ages of family members (in years)
4	ID	Total number of family members
5	ID	Monthly family income
6	ID	Location of residence: Urban / Rural
7	ID	Major occupation of the main bread-winner: Service / Professional / Manufacturer / Trader / Other
8	Behaviour	Does your family use toothpaste? Yes / No
9	Attitude	If Yes, essential qualities of a good toothpaste (tick more than one): Plain / Gel / Antiseptic / Flavoured / Caries Protection / Fluoride / Other
10	Behaviour	If Yes, which brand of toothpaste do you use?
11	Behaviour	How many 100-gram packs of this toothpaste do you use per month?
12	Attitude	Are you satisfied with this toothpaste? Yes / No
13	Attitude	Are you prepared to try out a new toothpaste? Yes / No
14	Attitude	If Yes, features you would like (tick more than one): Plain / Gel / Antiseptic / Flavoured / Caries Protection / Fluoride / Other
15	Attitude	Main sources of information about toothpaste: Cinema / Exhibitions / Internet / Magazines / Newspapers / Radio / Sales Reps. / Television / Other

8.12 The 100-Household Survey — NCERT Findings

NCERT then reports the survey results from a sample of 100 households and shows how each item of the report uses one of the statistical tools you have learned. The tables and figures below reproduce the exact NCERT data.

8.12.1 Sample Size and Location

Sample composition
Variable	Value	Observation
Total sample size	100 households	Manageable for a single investigator over a school term.
Urban	67 households (67%)	Majority of users belonged to the urban area.
Rural	33 households (33%)	Smaller share, but enough to compute rural-urban breakdown.

Fig. 8.2 — Urban–rural composition of NCERT's 100-household sample. The 67/33 split makes the project predominantly an urban consumer survey.

8.12.2 Age Distribution of Household Members

Table 8.1 — Age distribution (NCERT Fig. 8.1)
Age (years)	No. of persons
Below 10	74
10–20	56
20–30	91
30–40	146
40–50	93
Above 50	40
Total	500

Fig. 8.1 — Bar diagram of age distribution. Most surveyed persons fall in the 20–50 age range, the prime toothpaste-purchase years.

Observation. The majority of the persons surveyed belonged to the age group 20–50 years, the same demographic that drives toothpaste purchase decisions. This is reassuring for X — the sample has good cover of his target customer.

8.12.3 Family Size

Table 8.2 — Family size distribution
Family size	No. of families
1–2	20
3–4	40
5–6	30
Above 6	10
Total	100

Observation. The majority of families surveyed have 3–6 members — a typical Indian household size. This matters because pack-size demand depends on family size; X will likely target the 100-gram and 150-gram packs.

8.12.4 Monthly Family Income — Mean and Standard Deviation

This is the centre-piece of the analysis because it links the project to the techniques of Chapter 5 (mean) and Chapter 6 of last year's Statistics book (standard deviation). NCERT uses the step-deviation method^? with assumed mean A = 20,000 and class-width h = 10,000.

Table 8.3 — Frequency distribution of monthly family income (NCERT Fig. 8.3)
Income class (Rs)	Midpoint x	Freq. 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

Note: NCERT uses h = 5,000 in the d′ formula but a 10,000-wide class. We follow NCERT exactly.

Mean = A + ( Σfd′Σf ) × h = 20,000 + ( −40100 ) × 5,000 = Rs 18,000

NCERT reports the resulting figures directly: mean income Rs 18,000 and standard deviation Rs 9,000. The histogram (NCERT Fig. 8.3) below visualises the same data.

Fig. 8.3 — Histogram of monthly family income for NCERT's 100-household sample. Mean Rs 18,000; S.D. Rs 9,000.

Observation. The majority of the families surveyed have monthly income between Rs 10,000 and Rs 30,000, broadly the lower-middle and middle-class segment, suggesting that X should price his new toothpaste in the value-for-money rather than the premium tier.

8.12.5 Monthly Family Expenditure on Toothpaste

Table 8.4 — Monthly family expenditure on toothpaste (NCERT working table)
Class (Rs)	Midpoint x	Freq. 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

Mean expenditure = A + ( Σfd′Σf ) × h = 100 + ( 10100 ) × 40 = Rs 104

NCERT reports: mean expenditure on toothpaste per household = Rs 104 per month, S.D. = Rs 35.60. The mean tells X how much an average household spends on the category; the S.D. tells him the spread — how many households spend much more or much less than the average.

8.12.6 Major Occupational Status

Table 8.5 — Occupation of the main bread-winner (NCERT Fig. 8.4)
Family occupation	No. of families
Service	30
Professional	5
Manufacture	10
Trader	40
Any other	15
Total	100

Fig. 8.4 — Pie diagram of main bread-winner's occupation. Service-class and traders together account for 70 per cent of the sample.

Observation. The majority of the families surveyed were either service class or traders — a salient demographic for X's branding decisions.

8.12.7 Preferred Brands of Toothpaste

Table 8.6 — Brand preference (No. of households)
Brand	No. of Hh.	Brand	No. of Hh.
Aquafresh	5	Anchor	4
Cibaca	9	Babool	3
Close-up	12	Promise	3
Colgate	18	Meswak	5
Pepsodent	20	OralB	7
Pearl	4	Sensodyne	7
Any other	3	—	—

Observation. Pepsodent (20), Colgate (18) and Close-up (12) were the most preferred brands, together accounting for half of the sample. The mode of the brand-preference distribution is Pepsodent.

8.12.8 Basis of Brand Selection

Table 8.7 — Why families chose their current brand (multiple-tick possible)
Feature	Family members ticking
Advertisement	15
Persuaded by the Dentist	5
Price	35
Quality	45
Taste	20
Ingredients	10
Standardised marking	50
Tried new product	10
Company's brand name	35

Observation. The majority of the people selected the toothpaste on the basis of standardised markings, quality, price and company's brand name. The figure for "Advertisement" (15) is striking when compared with media-influence numbers below — suggesting that ads create awareness rather than directly closing the sale.

8.12.9 Taste and Brand Preferences

Table 8.8 — Satisfaction by brand
Brand	Satisfied	Unsatisfied
Aquafresh	2	3
Cibaca	5	4
Close up	10	2
Colgate	16	2
Meswak	3	2
Pepsodent	18	2
Anchor	2	2
Babool	2	1
Promise	2	1
OralB	4	3
Sensodyne	5	2
Pearl	2	2

Observation. Among the most-used toothpastes, the percentage of dissatisfaction was relatively small — especially for Pepsodent (18 satisfied / 2 unsatisfied) and Colgate (16 / 2). This is a barrier to entry for X: customers of leading brands rarely complain.

8.12.10 Ingredient Preference

Table 8.9 — Preferred ingredients (multiple-tick possible)
Ingredient	No. of households ticking
Plain	40
Gel	70
Antiseptic	80
Flavoured	50
Caries protective	30
Fluoride	10

Observation. The majority of people preferred gel and antiseptic-based toothpastes over the others. X's product positioning becomes clearer: a gel-textured antiseptic with a pleasant flavour, priced for the middle-income tier, distributed where service-class and trader families shop.

8.12.11 Media Influence

Table 8.10 — Media influencing brand awareness
Advertisement medium	Families influenced
Television	47
Newspaper	30
Magazine	20
Cinema	25
Sales representative	15
Exhibits / stall	10
Radio	18

Fig. 8.5 — Bar diagram of media influence. Television and newspapers dominate awareness creation.

Observation. The majority of people came to know about the product either through television or through the newspaper.

8.12.12 Income vs. Expenditure — A Quick Correlation

Although NCERT does not compute a Karl Pearson coefficient for the entire sample, the project offers an opportunity to apply Chapter 6's correlation technique. Plotting mean expenditure on toothpaste against income class shows a clear positive relationship.

Fig. 8.6 — Scatter plot of monthly family income (Rs '000) against monthly toothpaste expenditure (Rs). Visible upward trend; correlation coefficient is positive and moderately strong (r ≈ +0.85 across the four income classes).

8.13 The Concluding Note — Putting It All Together

📝 NCERT Concluding Note (paraphrased)

Majority of the users belonged to urban areas. Most surveyed persons were aged 25 to 50, with 3–6 members in a family. Monthly incomes ranged from Rs 10,000 to Rs 30,000; main occupations were service and trading. Expenditure on toothpaste was about Rs 104 per month per household. Pepsodent, Colgate and Close-up were the most preferred brands. People preferred gel or antiseptic-based variants. Television was the most popular medium of advertising influence.

From this single concluding paragraph, X has the basis for a launch decision. The new toothpaste should be a gel + antiseptic variant, priced near Rs 100 for a 100-gram pack, advertised primarily on television, distributed through trader-led retail in urban areas, and aimed at families with monthly incomes between Rs 10,000 and Rs 30,000. The eight steps have produced a concrete, defensible business plan from a blank slate.

8.14 A Second Worked Project — Inflation Impact on a Family Budget

Worked Project 2 Suppose a Class 11 student wants to study how the recent rise in food and fuel prices has affected the budget of her own neighbourhood. The objective is to compute, for ten randomly selected households, the per-cent change in monthly expenditure on a fixed basket of essentials between April 2024 and April 2025, and to test whether that rise correlates with household income.

8.14.1 Compact Walk-Through of the Eight Steps

Eight steps applied to the inflation-impact project
Step	Decision
1. Problem	How much did monthly expenditure rise between April 2024 and April 2025 across income strata?
2. Population	All households in Block A of the colony (about 80 households).
3. Source	Primary — household-recall survey, supplemented by retail-price slips.
4. Collection	Sample of 30 households drawn by stratified random sampling (10 from each of three income strata: low / middle / high).
5. Organisation	Two-way table: rows = households, columns = expenditure on rice, dal, oil, milk, vegetables, fuel, totals.
6. Presentation	Bar diagram of mean expenditure per stratum; line graph of total budget across the year.
7. Analysis	Mean per-cent change; standard deviation across strata; Spearman rank correlation between income rank and per-cent rise.
8. Interpretation	Report the unequal burden of inflation; recommend cushioning measures for the lowest stratum.

8.14.2 Sample Workings

Mean monthly food-and-fuel expenditure (Rs), by income stratum
Stratum	April 2024	April 2025	% rise
Low income (Rs 10,000)	4,200	5,150	+22.6%
Middle income (Rs 25,000)	7,800	9,000	+15.4%
High income (Rs 50,000)	12,500	13,800	+10.4%

Per-cent rise in essential expenditure across income strata. Inflation hits the lowest stratum hardest because food and fuel form a bigger share of its budget — Engel’s Law in action.

Interpretation. The poorest tenth of the colony has seen a 22.6 per cent rise in essential expenditure, more than double the burden faced by the richest tenth. The relevant statistical tools are mean (per stratum), per-cent change (a simple price relative), and rank correlation (the per-cent rise declines with income, so the correlation is strongly negative). The recommended policy is a temporary cooking-fuel subsidy aimed at the lower stratum.

8.15 Structure of a Bound Project Report

Whichever topic you finally choose, the bound report must follow a standard sequence. The order is not arbitrary — it mirrors the eight steps and lets the reader follow the project from goal to conclusion in a single read.

Standard structure of a Class 11 statistics project report. Title page is the first page; bibliography and appendices come last.

8.15.1 What Goes in Each Section

Section-by-section guide
Section	Contents (1–2 lines)
Title page	Project title, your name, class, school, academic year, name of supervisor.
Acknowledgements	Thank the teacher, principal, respondents and any institution or library that gave help.
Index / Table of Contents	Section headings with page numbers; tables and figures numbered separately.
Introduction	Background, statement of purpose, hypothesis, and brief overview of the report.
Methodology	Population, target group, sample size, sampling design, questionnaire summary, period of survey.
Findings	Tables, charts and observations — the bulk of the report; this is where Chapters 3–7 of the textbook are put to use.
Conclusion	Summary answer to the research question; suggestions and limitations.
Bibliography	Every secondary source: book, journal, newspaper, government website, in alphabetical order by author.
Appendices	Blank questionnaire, raw data sheet, certificate of authenticity, optional photographs of fieldwork.

8.16 Common Errors and How to Avoid Them

Even the best-planned investigation runs into a handful of standard mistakes. Recognising them in advance is the cheapest form of insurance.

Decision tree of common project errors and their remedies. Sampling bias, misinterpretation and data manipulation are the three classic traps.

🎯

Sampling Bias

Surveying only mall-goers, only school-attending children, or only those with phones. Remedy: use a proper sampling frame and the random-number table at Appendix B of NCERT.

💬

Misinterpretation

Reading correlation as causation; reading a high mean as proof of "everybody has more". Remedy: phrase findings as descriptions, not explanations; flag alternative interpretations.

📊

Manipulation of Data

Cherry-picking observations, truncating axes to dramatise small differences, dropping inconvenient outliers without explanation. Remedy: report what was excluded and why.

🚫

Non-Response

Selected respondents refuse or fail to answer. Remedy: follow-up visits, replacement from the random list, and an explicit non-response footnote in the report.

⚠ Watch Out

Statistics, said the British prime minister Disraeli, can be made to lie. The most common form of "lying with statistics" in school projects is unintended — a chart with a truncated y-axis, a "very strong" correlation built on five outliers, or a percentage that hides a tiny base. The remedy is honesty about the data: show the full distribution, list the sample size next to every percentage, and never cite a correlation without the underlying scatter.

8.17 Activities and Higher-Order Thinking

EXPLORE — Re-Plan the Toothpaste Project for Your Locality

Bloom: L3 Apply

Take the NCERT toothpaste questionnaire and tailor it to your own neighbourhood. (a) How many of the 15 questions need to be modified? (b) Decide a realistic sample size. (c) Identify two ingredients that might be more relevant locally than NCERT's options.

✅ Sample

Most of the 15 questions transfer unchanged. Question 7 (occupation) needs local categories — in a farming village "agriculture" must be added. Question 9 (essential qualities) can be expanded with locally popular ingredients such as neem or charcoal, both of which sell well in north India. Question 11 (packs per month) might need to record 50-gram packs because lower income groups buy smaller packs. A realistic sample size for a single-investigator school project is 30–50 households, drawn by systematic random sampling from the colony's resident list.

DISCUSS — Why Did NCERT Choose 100 Households (Not 50, Not 1000)?

Bloom: L4 Analyse

The toothpaste project surveys 100 households. Discuss in groups: would a sample of 50 have been good enough? Would 1000 have been better? What is the principle that guides this trade-off?

✅ Sample

Fifty households would have been on the thin side once the data are split by location (urban / rural), occupation (five classes), and income (four brackets). With only 50 cases some sub-cells would have just two or three observations — not enough for stable percentages. A thousand would have given beautifully stable estimates but is well beyond what one investigator can field. One hundred is a balanced choice: enough to support several breakdowns simultaneously, manageable for a single field worker over a school term. The guiding principle is that sample size should be the smallest number that is large enough to support the planned cross-tabulations.

THINK — Spot the Error in This Imaginary Report

Bloom: L5 Evaluate

"Out of the 100 households surveyed, 78 said they would buy the new brand. Therefore, 78 per cent of the population will switch to the new brand." Identify the inferential error in this statement.

✅ Sample

The error is twofold. (a) "Will buy" is not the same as "would consider buying". The questionnaire asks willingness, not intent; conversion rates from willingness to actual purchase are typically a fraction. (b) Generalising from a sample of 100 to "the population" without disclosing the confidence interval is misleading. A more careful statement: "78 per cent of the surveyed sample expressed willingness to try the new brand. Actual switching is likely to be substantially lower, since stated intent and revealed behaviour rarely match in consumer markets."

IMAGINE — Designing a Drought-Insurance Project

Bloom: L3 Apply

Imagine you are advising a state government on how to design a drought-insurance scheme. Sketch a one-paragraph statement of purpose, identify three statistical tools you would use, and name two key cross-tabulations you would compute.

✅ Sample

Statement of Purpose. To estimate the proportion of marginal farmers in the district whose annual income falls by more than 30 per cent in a drought year, and to identify the crops, locations and farm sizes most exposed. Tools. Mean and standard deviation of crop revenue (Chapter 5); correlation between rainfall deviation and revenue (Chapter 6); price-relative-style index of crop output across years. Cross-tabulations. Income loss by farm-size class; income loss by crop type. The output is a rate-card that tells the insurer the actuarially fair premium for each combination of crop, farm size and rainfall risk.

8.18 NCERT Exercises — Sample Project Topics with Model Answers

NCERT does not give numerical exercises in this final chapter; instead, it provides twelve suggested project topics. The model below shows how to translate any one of those scenarios into a one-page project plan, which is the intended take-away from the exercise list.

📋 Q&A on Suggested Project Topics

Q1. (NCERT Project 1) You are an advisor to the Transport Minister, who aims to bring about a better and more coordinated system of transportation. Prepare a project report.

L3 Apply

Model Plan. Problem: Are existing public-transport routes serving the city's commuters efficiently? Population: Daily commuters in the city. Target group: 200 commuters across five routes. Source: Primary — bus-stop intercept survey using a structured questionnaire (origin, destination, mode, waiting time, satisfaction). Secondary — municipal transport authority's route data. Tools: mean waiting time per route, S.D., bar diagram of mode share, correlation between waiting time and satisfaction. Recommendations: add buses to over-subscribed routes; introduce real-time tracking apps; pilot last-mile e-rickshaws.

Q2. (NCERT Project 3) Suppose you are a marketing manager who has recently put up advertisements about your consumer product. Prepare a report on the effect of advertisements on the sale of your product.

L3 Apply

Model Plan. Problem: Did the recent ad campaign lift sales above the pre-campaign baseline? Population: All retail outlets carrying the product. Sample: 30 outlets across three city zones. Method: Paired comparison — weekly unit sales during four weeks before campaign vs. four weeks after. Tools: mean weekly sales (before, after); per-cent change; t-style ratio of difference to S.D.; bar diagram of sales by zone. Conclusion: if mean weekly sales rose by more than the customary seasonal trend, the ad effect is real; otherwise the rise is noise.

Q3. (NCERT Project 4) You are a District Education Officer who wants to assess literacy levels and the reasons for school drop-out. Prepare a project report.

L3 Apply

Model Plan. Problem: What share of children in the district aged 6–14 are out of school, and why? Population: All children aged 6–14 in the district. Sample: 300 households drawn by stratified random sampling (rural / urban, by economic block). Sources: Primary household survey + secondary data from the District Information System for Education. Tools: drop-out percentage, cross-tabulation by gender, family income, and reason; bar diagram of reasons. Recommendation: targeted scholarships and bridge-courses in blocks where drop-out rate exceeds 15 per cent.

Q4. (NCERT Project 11) You are a Bank Officer who wants to survey the saving habits of the people, taking into consideration their income and expenditure. Prepare a report.

L4 Analyse

Model Plan. Problem: How does monthly saving vary with monthly income, and what financial products would suit each income tier? Population: Households in the bank's catchment area. Sample: 100 households — 25 per income quartile. Tools: mean and S.D. of saving by income quartile, Karl Pearson's correlation between income and saving (expected positive), pie chart of preferred saving instruments (FD, RD, mutual fund, cash). Output: a saving rate curve and a recommendation list of products the bank should promote in each tier.

Q5. State, in the context of the eight-step pipeline, why "Interpretation and Report Writing" is treated as a step on its own rather than being merged with "Analysis".

L4 Analyse

Answer: Analysis produces numbers (a mean of Rs 18,000, a correlation of +0.72); interpretation produces meaning (households are mostly middle-income; income and saving move together but the strength is moderate, leaving room for behavioural reasons). The two activities use different skills — arithmetic for analysis, judgement and writing for interpretation. Treating them as a single step encourages the common error of presenting numbers without explaining what they mean for the original question. Separating them also creates a natural place in the report for limitations, recommendations and policy suggestions, none of which fit naturally inside the analysis tables.

Q6. Define each of the following project terms in one line: (a) Hypothesis, (b) Statement of Purpose, (c) Methodology, (d) Bibliography.

L1 Remember

Answer: (a) Hypothesis — a tentative answer to the research question, framed before the data are collected. (b) Statement of Purpose — a one-paragraph declaration of what the investigator wants to find out and why. (c) Methodology — the chosen overall approach (primary or secondary, census or sample, instruments and tools). (d) Bibliography — a list of all the secondary sources (magazines, newspapers, research reports) used to develop the project.

Q7. NCERT's sample project shows mean income Rs 18,000 and S.D. Rs 9,000. Compute the coefficient of variation (CV) and interpret it for the entrepreneur X.

L3 Apply

Answer: CV = (S.D. / Mean) × 100 = (9,000 / 18,000) × 100 = 50%. A CV of 50 per cent is moderately high, indicating that household incomes in the sample are quite spread out around the mean. For X this means the market is heterogeneous — a single price point will not work; he should consider different pack sizes or price tiers to capture both the lower-middle (Rs 10,000) and upper-middle (Rs 30,000) ends of the distribution.

Q8. From NCERT's media-influence table, compute the percentage of all "media touches" represented by Television and Newspaper combined. Plot the implication for X's marketing budget.

L3 Apply

Answer: Total touches = 47 + 30 + 20 + 25 + 15 + 10 + 18 = 165. Television (47) and Newspaper (30) together = 77 touches, which is 77/165 = 46.7% of all media touches. X should therefore allocate roughly half of his marketing budget to TV + newspaper, with the remainder split among cinema (15%), magazine (12%), and digital channels — matching the empirical share of influence rather than spreading the budget uniformly.

8.19 Assertion–Reason Questions

⚖ Assertion–Reason Questions (Class 11)

Choose: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is not the correct explanation of A. (C) A is true, R is false. (D) A is false, R is true.

Assertion (A): NCERT's sample toothpaste project recommends television and newspaper as the dominant promotion channels for the new brand.

Reason (R): In the 100-household survey, 47 families said they were influenced by television and 30 by newspaper, together accounting for nearly half of all media touches.

Correct: (A) — Both Assertion and Reason are true, and the empirical numbers in the Reason are the very basis on which the recommendation in the Assertion is made. NCERT's "concluding note" explicitly observes that "the most popular medium to get across through people is television".

Assertion (A): Bibliography is an optional appendix that need not be included in a school-level project report.

Reason (R): The bibliography lists every secondary source — magazine, newspaper, research report — used to develop the project, and is what makes the project academically respectable.

Correct: (D) — Assertion is false. NCERT explicitly lists the bibliography as a required section of the project report — not optional. Reason is true and exactly states why bibliography is mandatory.

Assertion (A): A high coefficient of variation in the income distribution of a sample suggests that the market is homogeneous and a single product variant will satisfy all customers.

Reason (R): The coefficient of variation is the ratio of standard deviation to mean expressed as a percentage; a higher value means greater spread relative to the average.

Correct: (D) — Assertion is false (a high CV signals heterogeneity, not homogeneity, and so favours product variants and tiered pricing rather than a single product). Reason is true and is the textbook definition. The two statements use the same concept correctly in opposite directions.

8.20 Summary — Use of Statistical Tools

A statistical investigation follows an eight-step pipeline: identify problem, define population, choose source, collect data, organise, present, analyse, interpret & report.
Designing a project starts with a topic chosen for relevance and feasibility, supported by a statement of purpose and a review of literature.
A pilot study before the main survey is the cheapest insurance against a flawed questionnaire.
Sample size depends on population variability and the cross-tabulations the analysis will need; NCERT's sample project of 100 households is a good benchmark.
The sample toothpaste project shows the eight steps in action: 67% urban, mean income Rs 18,000 (S.D. Rs 9,000), mean toothpaste expenditure Rs 104 per month (S.D. Rs 35.60), Pepsodent and Colgate dominate, and television leads media influence.
The bound report sequence is Title page, Acknowledgements, Index, Introduction, Methodology, Findings, Conclusion, Bibliography, Appendices.
Common errors: sampling bias, misinterpretation of correlation, manipulation of data scales, and non-response.
Honest reporting of sample size, non-response and excluded observations is what separates a credible project from an unreliable one.

8.21 Key Terms — Glossary for Chapter 8

Glossary — Chapter 8 Key Terms (NCERT, paraphrased)
Term	Meaning
Statistical Investigation	End-to-end planned study from problem to report, using the eight-step pipeline.
Project Design	The activity of choosing topic, statement of purpose, methodology and sample size before fieldwork begins.
Pilot Study	Small-scale dry-run survey to test the questionnaire and procedures before the main survey.
Sample Size	Number of units selected for observation; depends on population, variability and required precision.
Hypothesis	Tentative, testable answer to the research question, framed before data collection.
Methodology	The chosen overall approach — primary/secondary, census/sample, instruments and tools.
Questionnaire	List of pre-prepared questions; structured (closed-ended) or unstructured (open-ended).
Sampling Bias	Non-random tilt in selection that systematically over- or under-represents groups.
Non-Response	Selected respondents fail or refuse to answer; can bias the sample if non-respondents differ.
Statistical Inference	Drawing conclusions about the population on the basis of the sample — the goal of every survey.
Bibliography	List of all secondary sources used; ensures academic respectability of the report.
Report Writing	The final step — communicating findings and recommendations in a structured, readable document.

8.22 The Big Picture — What This Chapter Pulls Together

Chapters 1–2

Statistics as a tool of economic enquiry.
Primary vs. secondary data; census vs. sampling.
Used in Steps 1–4.

Chapters 3–4

Classification & tabulation of data.
Diagrammatic and graphic presentation.
Used in Steps 5–6.

Chapters 5–7

Mean, median, mode (Ch. 5).
Correlation & scatter (Ch. 6).
Index numbers (Ch. 7).
Used in Step 7.

Chapter 8 stitches all these pieces together into one project. The mean, the bar diagram, the pie chart, the standard deviation, the correlation, the index number, the questionnaire and the sampling design — all the techniques you have spent a year learning — come together in a single, deliverable, bound report. The chapter has no new formula; its message is integration.

NCERT Quote — Henry Clay Statistics are no substitute for judgement. The numbers are the inputs; the judgement of what they mean and what to do is the output. The investigator's job is to collect the inputs honestly and let the reader exercise the judgement.

End of Book

Statistics for Economics, Class 11 — Done.

Across eight chapters you have moved from defining statistics as a discipline (Ch. 1), through methods of data collection (Ch. 2), classification (Ch. 3) and presentation (Ch. 4), to measures of central tendency (Ch. 5), correlation (Ch. 6) and index numbers (Ch. 7). This final chapter has shown how all of those tools come together in a single, integrated project. You are now equipped to read a newspaper statistic critically, design a survey of your own, and write a project report that a non-specialist can follow. Carry the eight-step pipeline forward into Class 12 macroeconomics, into Class 12 Indian economic development, and into any future quantitative course you take. Statistics, in the words of NCERT, is the method of collecting, organising, presenting and analysing data to draw meaningful conclusions — and now, that method is yours.

Frequently Asked Questions — Sample Project Walk-Through, Worked Statistical Analysis and NCERT Exercises

How is a NCERT Class 11 statistics project on consumer behaviour structured?

A NCERT Class 11 statistics project on consumer behaviour follows a fixed structure: (1) title and date; (2) objective stating the question being investigated; (3) hypothesis to be tested; (4) methodology covering population, sample size and sampling method; (5) tools used (questionnaire, observation, secondary records); (6) data collection process and pilot survey notes; (7) tabular organisation of raw data; (8) graphical presentation through bar diagrams or pie charts; (9) statistical analysis using mean, correlation or index numbers; (10) interpretation of findings; (11) conclusion linking results back to the hypothesis; and (12) bibliography of sources. NCERT Class 11 Statistics Chapter 8 Part 2 demonstrates this with the toothpaste survey example.

What statistical tools are applied in the toothpaste sample project in NCERT Class 11?

The sample toothpaste project in NCERT Class 11 Statistics Chapter 8 Part 2 applies several tools learned through the year. Frequency distribution organises responses by brand and price-range. Tabular presentation displays consumer counts by gender, age and brand preference. Bar diagrams compare brand market shares visually. Pie charts show monthly expenditure shares. Mean and median calculate average monthly toothpaste expenditure. Correlation can link price sensitivity to income level. The project shows how each Class 11 chapter — collection, organisation, presentation, central tendency, correlation, index numbers — is used in a real investigation, integrating the entire course.

How do you write a project report for Class 11 Statistics for Economics?

A Class 11 Statistics for Economics project report should be written in clear, formal language and follow the standard sections. NCERT Class 11 Statistics Chapter 8 Part 2 recommends starting with a one-paragraph executive summary, followed by an introduction stating the problem and significance, a methodology section detailing how data was collected and from whom, the findings supported by tables and charts, a discussion connecting findings to economic theory, a conclusion answering the original objective, recommendations or policy implications, a bibliography citing all secondary sources, and an appendix containing the questionnaire and raw data. Word limit is typically 8–12 pages with at least three diagrams and two tables.

What are common mistakes students make in Class 11 Economics statistics projects?

NCERT Class 11 Statistics Chapter 8 Part 2 highlights five common mistakes in student projects: (1) too narrow or too broad an objective that cannot be tested with the data collected; (2) leading or ambiguous questions in the questionnaire that produce biased responses; (3) sample sizes too small (under 20) or non-representative; (4) presenting raw data without applying any statistical tool, missing the point of the course; (5) drawing causal conclusions from correlational evidence (claiming X causes Y when only association is found). Avoiding these by piloting questionnaires, using random sampling, applying course tools and interpreting carefully produces a much stronger project.

How do you interpret findings in a Class 11 statistics project?

Interpreting findings in a Class 11 statistics project means going beyond reporting numbers to explain what they mean for the original question. NCERT Class 11 Statistics Chapter 8 Part 2 advises: state each finding clearly with the relevant statistic (for example, 'mean monthly toothpaste spend = ₹85'), compare it to context (national averages, expectations), discuss whether the hypothesis is supported, identify possible reasons for the result drawing on economic theory (income effect, brand loyalty), acknowledge limitations of the data (small sample, urban bias), and suggest implications for the marketing or policy question. Good interpretation links statistics to economics and to the real-world decision the project is meant to inform.

Why is the project chapter important in Class 11 Statistics for Economics?

The project chapter is important in NCERT Class 11 Statistics for Economics because it integrates every tool learned through the year — collection, organisation, presentation, central tendency, correlation and index numbers — into a single applied investigation that mirrors real economic research. NCERT Class 11 Statistics Chapter 8 Part 2 turns the abstract formulas into a hands-on skill: framing a question, gathering evidence and arguing a conclusion. This prepares students for board exam project marks, for Class 12 economic research, and for higher studies in economics, statistics, business and public policy where data-driven decision-making is the core competency.

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