Class 11 Economics Chapter 9 — Use of Statistical Tools (ASSEB)
Welcome to HSLC Guru! This English-medium guide for ASSEB Class 11 Economics — Statistics for Economics, Chapter 9: Use of Statistical Tools brings together a clear chapter summary, complete textbook question answers, additional MCQs, fill in the blanks, true or false statements, and a handy glossary. The chapter shows how the statistical tools learnt in earlier chapters are actually applied to study real economic problems through structured projects.
Chapter Summary
Chapter 9 ties together everything covered in the Statistics for Economics textbook by showing the practical application of statistical tools to real economic problems. The earlier chapters introduced collection of data, organisation, presentation through tables and diagrams, measures of central tendency, dispersion, correlation and index numbers. This concluding chapter explains how a student can use these tools to actually investigate questions such as price changes, household consumption, employment, literacy, or migration in a small project. Statistics turns abstract economic theory into measurable evidence.
The chapter outlines the six stages of a statistical project. The first stage is identifying the problem or topic of enquiry — the topic should be relevant, specific and manageable. The second stage is choice of target group, that is, deciding the population or sample from which data will be collected (for example, households, students, shopkeepers). The third stage is collection of data using primary methods (interview, questionnaire, observation) or secondary sources (government publications, reports, websites). The fourth stage is organisation and presentation of data with the help of classification, tabulation, bar diagrams, pie charts, histograms or frequency curves. The fifth stage is analysis and interpretation using averages, dispersion, correlation and index numbers. The final stage is drawing inferences and writing the report, where conclusions are presented in clear language with limitations of the study mentioned honestly.
A standard worked illustration in this chapter is the calculation of the Consumer Price Index (CPI) for a small basket of goods consumed by a household. Suppose rice, wheat, milk, sugar and clothing are studied. The investigator records base year prices and current year prices, multiplies by quantity weights, and then applies the weighted aggregative formula CPI = (Σ p₁q₀ / Σ p₀q₀) × 100. If the index turns out to be 118, it means the cost of the same basket has risen by 18 per cent compared with the base year, indicating inflation that erodes real income. This single example uses several tools — collection, tabulation, weights, ratios and percentage change — showing how statistics directly informs economic decisions like wage revision and welfare planning.
The NCERT chapter suggests several illustrative project topics that learners can attempt: a study of the impact of a rise in price of a commodity on its consumption in a locality, a study of the pattern of family expenditure of households in a colony, a study of the educational level of women workers in a factory, a study of the cost of cultivation of a crop, a study of the changing pattern of employment among rural youth, and a study of household savings. Each topic is small enough for a school student yet wide enough to apply collection, classification, diagrams, averages and a simple index or correlation. Such projects develop the discipline of measurement, accuracy and honest reporting that lies at the heart of economics as a social science.
Beyond the worked CPI illustration, the chapter highlights how different statistical tools serve different objectives. Measures of central tendency such as the arithmetic mean, median and mode summarise data in a single representative figure. Measures of dispersion like range, mean deviation and standard deviation reveal how spread out the values are around the centre. Correlation studies whether two variables, such as price and demand or income and consumption, move together. Index numbers translate complex price or quantity changes into simple percentages. When these tools are combined within one project, the learner sees that economics is not a collection of opinions but a discipline rooted in careful, transparent measurement of human behaviour.
Textbook Question Answers
1 Mark Questions
Q1. What is the first stage of a statistical project?
Answer: The first stage is identifying or selecting the problem of enquiry — choosing a clear, relevant and manageable topic for study.
Q2. Name the two main sources of data.
Answer: The two main sources are primary sources (data collected first-hand by the investigator) and secondary sources (data already collected and published by others).
Q3. What does CPI stand for?
Answer: CPI stands for Consumer Price Index, which measures the average change in the prices paid by consumers for a fixed basket of goods and services.
Q4. Mention any one method of collecting primary data.
Answer: The questionnaire method, in which a printed list of questions is given to respondents to obtain their answers.
Q5. What is meant by a target group in a statistical study?
Answer: A target group is the specific population or section of people from whom information is to be collected for the study.
Q6. Give one example of a secondary source of data.
Answer: Publications of the Reserve Bank of India, the Census of India report, or the Economic Survey of India.
Q7. What is a project report?
Answer: A project report is the final written document of a statistical study that presents the objective, methodology, data, analysis, findings and conclusions in an organised manner.
Q8. Name any one diagram used to present data.
Answer: A bar diagram (or pie chart, histogram, frequency polygon).
Q9. What is the base year in an index number?
Answer: The base year is the reference year with which prices or quantities of the current year are compared, and its index value is taken as 100.
Q10. Why is statistics called a tool of economics?
Answer: Because it provides quantitative methods to measure, compare and analyse economic facts that help in policy making and decision taking.
Q11. What is meant by inference in a statistical study?
Answer: Inference is the conclusion drawn from analysed data through logical reasoning about the problem under study.
Q12. Name any one method of presenting data graphically.
Answer: Histogram (or frequency polygon, ogive, line graph).
Q13. What is the full form of WPI?
Answer: WPI stands for Wholesale Price Index, which measures the change in prices at the wholesale or producer level.
Q14. What is the meaning of “weight” in an index number?
Answer: Weight refers to the relative importance assigned to each item in the index, usually based on its share in total expenditure.
Q15. Why are limitations mentioned in a project report?
Answer: Limitations are mentioned to honestly inform the reader about the boundaries of the study and to make the conclusions credible and realistic.
2-3 Marks Questions
Q1. List the six stages of a statistical project.
Answer: (i) Identifying the problem or topic, (ii) Choice of target group, (iii) Collection of data, (iv) Organisation and presentation of data, (v) Analysis and interpretation of data, and (vi) Drawing inferences and writing the report.
Q2. Distinguish between primary and secondary data with one example each.
Answer: Primary data are collected directly by the investigator for a specific purpose, e.g., a student surveying his classmates about pocket money. Secondary data are already collected and published by others, e.g., literacy figures taken from the Census of India report. Primary data are more reliable for the specific study but costly; secondary data are economical but may not perfectly fit the study’s needs.
Q3. Why is the choice of topic important in a statistical project?
Answer: The topic decides the entire direction of the project. A well-chosen topic must be relevant to the learner’s syllabus, of social or economic importance, manageable within the time and resources available, and must allow the use of statistical tools. A vague or too-broad topic leads to confusion and weak conclusions, while a sharp topic gives meaningful results.
Q4. Mention any three precautions to be taken while collecting data.
Answer: (i) The questions in the schedule or questionnaire must be clear, simple and unambiguous. (ii) The respondent’s identity and answers should be kept confidential to ensure honest replies. (iii) Investigators should be properly trained and the data collected should be cross-checked for accuracy and consistency.
Q5. Suggest any three project topics suitable for a Class 11 student.
Answer: (i) Pattern of monthly expenditure of households in a residential colony. (ii) Effect of rise in petrol price on the use of two-wheelers in a town. (iii) Study of the educational and employment status of women in a village. Each of these topics is local, manageable and allows the use of tabulation, diagrams and averages.
Q6. Why is presentation of data through diagrams useful?
Answer: Diagrams convey information at a glance, are attractive and easy to remember, allow comparison between groups and time periods, and make the report appealing to readers who are not trained statisticians. They also help in spotting trends, gaps and outliers quickly.
5-6 Marks Questions
Q1. Explain in detail the six stages of a statistical project with a suitable example.
Answer: A statistical project moves through six well-defined stages.
(i) Identifying the problem — the investigator selects a specific economic question, for example, “What is the average monthly expenditure of households in our locality on food?”
(ii) Choice of target group — here the population is, say, fifty households in a particular ward of the town.
(iii) Collection of data — a simple questionnaire is prepared asking about family size, monthly income and food expenditure, and the investigator visits each household.
(iv) Organisation and presentation — the raw data are classified into income groups, tabulated, and then shown through bar diagrams or pie charts to compare expenditure across groups.
(v) Analysis and interpretation — averages such as the mean monthly expenditure, dispersion measures and the share of food in total income are computed; correlation between income and food expenditure may also be calculated.
(vi) Drawing inferences and writing the report — a written project explains the methodology, exhibits the tables and diagrams, lists the findings (e.g., lower-income families spend a higher proportion on food, supporting Engel’s law) and mentions limitations such as small sample size. These six stages together convert a curious question into evidence-based knowledge.
Q2. Describe how the Consumer Price Index (CPI) is constructed and explain its importance.
Answer: The Consumer Price Index measures the change over time in the cost of a fixed basket of goods and services consumed by a representative household.
Steps in construction: (i) decide the target group, e.g., industrial workers; (ii) conduct a family budget enquiry to identify the items and their weights; (iii) fix a base year and collect base-year prices; (iv) collect current-year prices for the same items from the same markets; (v) apply the weighted aggregative formula CPI = (Σ p₁q₀ / Σ p₀q₀) × 100 or the family budget method CPI = ΣWR / ΣW, where R is price relative and W is weight.
Importance: CPI helps measure inflation, is the basis for granting Dearness Allowance to employees, is used in wage negotiations, in deflating money values to obtain real values, and in framing monetary and fiscal policy. Hence it is one of the most widely watched economic indicators.
Q3. Discuss the role and limitations of statistics in the study of economics.
Answer: Role of statistics: (i) it expresses economic facts in numbers, e.g., GDP, inflation, unemployment; (ii) it allows comparison across regions, classes and time; (iii) it tests economic theories such as the law of demand or Engel’s law; (iv) it helps in forecasting through trend analysis; (v) it is essential for policy formulation and evaluation.
Limitations: (i) statistics deals only with quantitative facts and cannot directly study qualitative aspects like honesty or motivation; (ii) it studies aggregates and averages, not individuals — an average can hide wide inequality; (iii) results are true only on the average and may mislead in specific cases; (iv) data can be misused or manipulated by selective presentation; (v) the conclusions are only as good as the data — poor collection means poor results. A wise use of statistics, therefore, requires both technical skill and ethical care.
Q4. Suppose you are asked to prepare a project on “The impact of rise in price of pulses on household consumption.” Outline how you will conduct it.
Answer: (i) Problem: to study how a rise in the price of pulses has affected the quantity consumed by households in my locality. (ii) Target group: thirty randomly selected households of varying income levels. (iii) Data collection: a short questionnaire asking the quantity of pulses consumed per month last year and this year, the price paid each year, and any change in substitutes (soyabean, eggs, etc.). (iv) Organisation: tabulate quantity and price for each household, then for the whole sample; classify households into low, middle and high income. (v) Analysis: compute the price relative, the percentage fall in quantity consumed, the price elasticity of demand, and present the figures through bar diagrams. (vi) Inference: conclude whether demand is elastic or inelastic, whether low-income families have cut down more sharply, and discuss policy suggestions such as targeted subsidy. State limitations like recall bias and small sample.
Q5. Explain the precautions that must be observed at each stage of a statistical project.
Answer: (i) While selecting the topic — keep it specific, manageable and ethically acceptable. (ii) While choosing the target group — make sure it represents the population; avoid bias by using random selection where possible. (iii) While collecting data — questions must be simple, the investigator should be polite and unbiased, and respondents’ confidentiality must be respected. (iv) While organising and presenting data — use proper class intervals, clear headings, accurate scales in diagrams, and avoid distortion. (v) While analysing data — choose appropriate tools (mean, median, correlation, index) according to the nature of data, and interpret results in context. (vi) While reporting — write in a logical sequence, acknowledge sources, point out limitations and avoid exaggeration. These precautions ensure that the project produces honest, useful knowledge.
Q6. Construct a Consumer Price Index from the following data and interpret the result.
Items: Rice (weight 40, base price 30, current price 36); Wheat (weight 20, base price 25, current price 30); Milk (weight 25, base price 40, current price 50); Sugar (weight 15, base price 40, current price 44).
Answer: Step 1 — compute price relative R = (p₁ / p₀) × 100 for each item.
Rice: (36/30) × 100 = 120; Wheat: (30/25) × 100 = 120; Milk: (50/40) × 100 = 125; Sugar: (44/40) × 100 = 110.
Step 2 — compute WR for each item: 40 × 120 = 4800; 20 × 120 = 2400; 25 × 125 = 3125; 15 × 110 = 1650.
Step 3 — ΣW = 100 and ΣWR = 4800 + 2400 + 3125 + 1650 = 11975.
Step 4 — CPI = ΣWR / ΣW = 11975 / 100 = 119.75.
Interpretation: the cost of the same basket has risen by about 19.75 per cent over the base year. If a worker’s money wage has not risen by at least this percentage, his real wage and standard of living have fallen. Hence the index gives a clear basis for revising wages and dearness allowance.
Additional Multiple Choice Questions
Q1. The first stage of a statistical project is —
(a) data collection (b) data analysis (c) identifying the problem (d) writing the report
Q2. Data collected by the investigator personally for the first time are —
(a) primary data (b) secondary data (c) classified data (d) tabulated data
Q3. Census of India is an example of —
(a) primary source (b) secondary source (c) sample survey (d) field study
Q4. The CPI for the current year is 120 with base 100. It indicates —
(a) prices have fallen by 20% (b) prices have risen by 20% (c) prices are unchanged (d) real income has risen
Q5. Which of the following is NOT a stage of a statistical project?
(a) Identifying the problem (b) Data collection (c) Advertising the report (d) Drawing inferences
Q6. A pie chart is most suitable to show —
(a) time series data (b) parts of a whole (c) two-variable correlation (d) frequency distribution
Q7. The average of a series is best computed by —
(a) bar diagram (b) histogram (c) arithmetic mean (d) ogive
Q8. The Dearness Allowance of employees is generally linked to —
(a) GDP (b) Consumer Price Index (c) Wholesale Price Index for capital goods (d) export price index
Q9. A statistical project should preferably be —
(a) very wide and abstract (b) specific and manageable (c) about foreign data only (d) without analysis
Q10. Real wage is calculated by —
(a) money wage × CPI (b) (money wage / CPI) × 100 (c) money wage − CPI (d) money wage + CPI
Additional practice tip: while writing answers in the examination, mention the relevant formula, substitute given values, and round off the final figure to two decimal places. Always state the units (rupees, kilograms, percentage) so that the answer is meaningful and complete.
Fill in the Blanks
Q1. A statistical project has ______ main stages. Answer: six
Q2. Data already collected by some other agency are called ______ data. Answer: secondary
Q3. CPI stands for ______. Answer: Consumer Price Index
Q4. The base year index is always taken as ______. Answer: 100
Q5. A pie chart shows the ______ of a whole. Answer: parts (or components)
True or False
Q1. Statistics can study every qualitative aspect of human behaviour. Answer: False
Q2. The questionnaire method is a way of collecting primary data. Answer: True
Q3. A rise in CPI from 100 to 115 means inflation of 15 per cent over the base year. Answer: True
Q4. A statistical project does not require mentioning its limitations. Answer: False
Q5. Diagrams make data easier to understand and compare. Answer: True
Glossary
| Term | Meaning |
|---|---|
| Statistical Project | A planned study that applies statistical tools to investigate an economic or social problem. |
| Target Group | The specific population or sample about which information is collected. |
| Primary Data | Original data collected first-hand by the investigator for the study at hand. |
| Secondary Data | Data already collected and published by another agency or person. |
| Questionnaire | A printed list of questions used to gather information from respondents. |
| Tabulation | Arranging classified data in rows and columns of a table. |
| Bar Diagram | A diagram in which lengths of bars represent the magnitude of variables. |
| Pie Chart | A circular diagram showing components of a whole through sectors. |
| Arithmetic Mean | The sum of all observations divided by their number; a measure of central tendency. |
| Index Number | A statistical measure of relative change in a variable or group of variables over time. |
| Consumer Price Index (CPI) | An index measuring change in the cost of a fixed basket of consumer goods and services. |
| Base Year | The reference year whose value is set as 100 for comparison. |
| Inflation | A sustained rise in the general price level of goods and services. |
| Real Wage | Money wage adjusted for changes in the price level; shows actual purchasing power. |
| Inference | A conclusion drawn from analysed data based on logical reasoning. |
| Project Report | The final written document presenting the methodology, findings and conclusions of a study. |
Sample Project Outline (For Reference)
Title: A Study of Monthly Food Expenditure of Twenty Households in Ward Number 4 of My Town.
Objectives: (i) to find the average monthly food expenditure; (ii) to find its share in total household income; (iii) to study how the share changes with income; (iv) to test whether the data support Engel’s law.
Methodology: The investigator selects twenty households at random, prepares a short questionnaire of ten questions covering family size, monthly income, expenditure on cereals, vegetables, milk, edible oil, meat or fish, and miscellaneous food items. Each household is visited personally, and the answers are noted in a schedule. After collection, the data are tabulated by income groups (below ₹15,000; ₹15,000–₹30,000; above ₹30,000).
Tools used: arithmetic mean for average expenditure, ratio (food expenditure / income) × 100 for the share, bar diagram to compare groups, and a simple correlation coefficient between income and proportion spent on food.
Expected Findings: the average monthly food expenditure is, say, ₹6,200; the share of food in total income falls from about 55 per cent in low-income households to 25 per cent in high-income households; the correlation between income and food share turns out to be negative, supporting Engel’s law.
Limitations: the sample is small and confined to one ward; respondents reported figures from memory; only one month was studied so seasonal effects are not captured.
This outline shows in miniature how every stage of the chapter works together to produce a coherent piece of applied economics.
Quick Revision Notes
1. Statistics is the language of economics; it converts observations into numbers, numbers into patterns and patterns into policy.
2. Every statistical project follows a fixed sequence — problem, target group, data, organisation, analysis, inference. Skipping any stage weakens the conclusion.
3. Primary data are fresh and tailor-made; secondary data are ready-made and economical. The investigator chooses according to time, money and accuracy needed.
4. Tables are the skeleton, diagrams are the face and analysis is the brain of the report. Each is needed for a complete study.
5. The CPI is the most directly felt index by ordinary citizens because it relates to the cost of daily living, while indices like the Wholesale Price Index serve businesses and policy makers.
6. A good project always states its limitations. Honesty about gaps in data and method strengthens, not weakens, the credibility of the work.
Important Formulas at a Glance
Price Relative: R = (p₁ / p₀) × 100
Weighted CPI (Family Budget Method): CPI = ΣWR / ΣW
Weighted Aggregative CPI: CPI = (Σ p₁q₀ / Σ p₀q₀) × 100
Real Wage: Real Wage = (Money Wage / CPI) × 100
Inflation Rate: ((CPI₁ − CPI₀) / CPI₀) × 100
Arithmetic Mean (Direct): x̄ = Σx / n
Median (Continuous Series): Median = L + ((N/2 − cf) / f) × h
Standard Deviation: σ = √(Σ(x − x̄)² / N)
Karl Pearson’s Correlation: r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)² × Σ(y − ȳ)²)
Common Exam Mistakes to Avoid
1. Confusing CPI with WPI — CPI relates to consumer goods, WPI relates to wholesale or producer prices.
2. Forgetting that the base year index is 100 — students sometimes write 1 or 0.
3. Mixing up primary and secondary data — primary is collected first-hand, secondary is reused from another source.
4. Skipping the “interpretation” step — calculating an index without saying what it means is incomplete.
5. Using a single average without commenting on dispersion — the average alone can hide huge variation.
6. Forgetting to mention the unit of measurement in the final answer.
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