StudyOSStudyOS CBSE Study Material, Class 5–12

Use of Statistical Tools

NCERT Class 11 · Economics Based on NCERT Class 11 Economics textbook · Free CBSE study kit

Everything you need to ace this chapter, in one place.
Notes · Mind Map · Quiz · Assertion-Reason · Case Studies · Question Bank · Past Papers

Get Full Study Kit →
Studying with friends? Send them this chapter.

Chapter Notes

Overview
This chapter bridges the gap between learning statistical tools and applying them to real-world economic problems. It exists in the syllabus to teach students how to design and execute a statistical investigation project, from identifying a problem to drawing conclusions. The one big idea a student must walk away with is that statistics is not just theory—it is a practical, step-by-step process for collecting, organising, analysing, and interpreting data to make informed decisions. A student who missed every class should understand that this chapter is about the 'how' of doing a survey and writing a project report.
Key Concepts (14)
Statistical Tools
Methods used for the analysis of data pertaining to economic activities such as production, consumption, distribution, banking and insurance, trade, transport, etc.
e.g. Using mean and standard deviation to analyse the monthly expenditure on toothpaste in a survey of 100 households.
Project
A systematic study conducted by conducting a survey and preparing a report to analyse relevant information and suggest improvements in a product or system.
e.g. A project to study consumer awareness about rights of consumers in a particular area.
Identifying a problem or an area of study
The first step in making a project where you must be clear about what you want to study; on the basis of your objective, you proceed with the collection and processing of data.
e.g. Studying the production or sale of a product like car, mobile phone, shoe polish, bathing soap or a detergent.
Choice of Target Group
The identification of the persons on whom you focus your attention; it is important for framing appropriate questions for your questionnaire.
e.g. For a project relating to cars, the target group will mainly be the middle income and the higher income groups.
Collection of Data
The process of gathering information using primary method, secondary method, or both, determined by the objective of the survey.
e.g. Collecting primary data by going to each family to study primary and secondary level female literacy.
Primary Data
First hand collection of data by using a questionnaire or an interview schedule, which may be obtained by personal interviews, mailing/postal surveys, phone, email, etc.
e.g. Visiting households to collect information about the brand of toothpaste they use.
Secondary Data
Data that is already collected by someone else and is used when there is paucity of time, money and manpower resources and the information is easily available.
e.g. Using data from magazines, newspapers, or research reports for a project.
Questionnaire
A list of questions prepared by an investigator on the subject of enquiry; the respondent is required to answer the questions.
e.g. A questionnaire asking about monthly family income, brand of toothpaste used, and media influences.
Organisation and Presentation of Data
Processing the collected information by organising and presenting them with the help of tabulation and suitable diagrams, e.g. bar diagrams, pie diagrams.
e.g. Creating a bar diagram to show the number of families using different brands of toothpaste.
Analysis and Interpretation
Using Measures of Central Tendency (e.g. mean), Measures of Dispersion (e.g. Standard deviation), and Correlation to calculate the average, variability and relationship among variables.
e.g. Calculating the mean monthly expenditure on toothpaste as Rs. 104 and standard deviation as Rs. 35.60.
Conclusion
The last step in a project where meaningful conclusions are drawn after analysing and interpreting the results, including predictions about future prospects and suggestions relating to growth and government policies.
e.g. Concluding that Pepsodent, Colgate and Close-up were the most preferred brands and that television is the most popular medium for advertisements.
Bibliography
A section in the project report where details of all the secondary sources, i.e., magazines, newspapers, research reports used for developing the project, are mentioned.
e.g. Listing the names of newspapers and magazines from which secondary data was taken.
Covering Letter
A letter that must accompany a postal questionnaire, giving details about the purpose of inquiry.
e.g. A letter explaining that the survey is for a project on toothpaste consumption and requesting participation.
Sample Size
The total number of units (e.g., households) from which data is collected in a survey.
e.g. In the sample project, the total sample size was 100 households.
Formulas & Equations (3)
Mean = A + (Σfd' / Σf) × h
Reads as: Mean equals assumed mean plus (sum of f d' divided by sum of f) times class interval
Variables: A = Assumed Mean; f = frequency; d' = (X - A)/h; h = class interval
Use when: Calculating the mean from a grouped frequency distribution using the step-deviation method
⚠ Forgetting to multiply by h at the end, or using the wrong assumed mean
Standard Deviation = h × √[(Σfd'² / Σf) - (Σfd' / Σf)²]
Reads as: Standard deviation equals class interval times square root of (sum of f d' squared divided by sum of f minus square of (sum of f d' divided by sum of f))
Variables: h = class interval; f = frequency; d' = (X - A)/h
Use when: Calculating the standard deviation from a grouped frequency distribution using the step-deviation method
⚠ Forgetting to subtract (Σfd'/Σf)² before taking the square root, or not multiplying by h
d' = (X - A) / h
Reads as: d' equals (midpoint minus assumed mean) divided by class interval
Variables: X = midpoint of class; A = assumed mean; h = class interval
Use when: Converting class midpoints to step-deviation values for simplified calculation of mean and standard deviation
⚠ Using the wrong assumed mean or class interval, leading to incorrect d' values
How It Works
Steps Towards Making a Project
  1. Step 1 — Identifying a problem or an area of study: Be clear about what you want to study.
  2. Step 2 — Choice of Target Group: Identify the persons on whom you will focus your attention.
  3. Step 3 — Collection of Data: Determine whether to use primary method, secondary method, or both.
  4. Step 4 — Organisation and Presentation of Data: Process the information using tabulation and diagrams (bar diagrams, pie diagrams).
  5. Step 5 — Analysis and Interpretation: Use measures of central tendency, dispersion, and correlation to calculate average, variability, and relationship.
  6. Step 6 — Conclusion: Draw meaningful conclusions, predict future prospects, and give suggestions.
  7. Step 7 — Bibliography: Mention details of all secondary sources used.
💡 Students often skip the 'Choice of Target Group' step or confuse it with data collection. The target group determines the questions you ask, not just who you ask.
Designing and Using a Questionnaire
  1. Step 1 — Identify the information needed for the study (e.g., average monthly expenditure, brands in demand, customer attitudes).
  2. Step 2 — Either use a pre-tested questionnaire (after modification) or prepare a new one.
  3. Step 3 — Ensure the questionnaire asks for all required information (e.g., name, sex, age, income, brand preferences, media influence).
  4. Step 4 — Include a covering letter for postal questionnaires explaining the purpose of inquiry.
  5. Step 5 — Administer the questionnaire via personal interviews, mail, phone, email, etc.
💡 A common mistake is to ask irrelevant questions or miss key questions. Every question must directly serve the objective of the study.
Data Analysis and Interpretation using Mean and Standard Deviation
  1. Step 1 — Organise the raw data into a frequency distribution table with class intervals and frequencies.
  2. Step 2 — Calculate the midpoint (X) for each class.
  3. Step 3 — Choose an assumed mean (A) and calculate d' = (X - A)/h for each class.
  4. Step 4 — Compute fd' and fd'² for each class.
  5. Step 5 — Sum the fd' and fd'² columns.
  6. Step 6 — Calculate Mean = A + (Σfd'/Σf) × h.
  7. Step 7 — Calculate Standard Deviation = h × √[(Σfd'²/Σf) - (Σfd'/Σf)²].
💡 Students often forget to multiply by h at the end of both mean and standard deviation calculations. Also, ensure the class interval (h) is consistent across all classes.
Exam Traps — Don't Make These Mistakes
⚠ Confusing Primary and Secondary Data
✗ Secondary data is collected by the investigator themselves.
→ Secondary data is already collected by someone else; primary data is collected first-hand by the investigator.
✓ Primary data is first-hand data collected by the investigator using methods like questionnaires or interviews. Secondary data is data that has already been collected by someone else and is used when there is paucity of time, money, and manpower.
⚠ Skipping the 'Choice of Target Group' Step
✗ The first step in a project is to collect data.
→ The first step is identifying the problem, and the choice of target group is a separate crucial step that determines the questionnaire design.
✓ After identifying the problem, the next step is the choice of target group. For example, for a project on cars, the target group is middle and higher income groups.
⚠ Forgetting the Covering Letter in Postal Surveys
✗ A postal questionnaire does not need any additional document.
→ The chapter explicitly states that a postal questionnaire must have a covering letter giving details about the purpose of inquiry.
✓ When using a postal questionnaire, it must be accompanied by a covering letter that explains the purpose of the inquiry to the respondent.
⚠ Misinterpreting the Mean and Standard Deviation Calculation
✗ Mean = Σfd'/Σf, without multiplying by h.
→ The formula for mean using step-deviation is Mean = A + (Σfd'/Σf) × h. Forgetting to multiply by h gives a wrong answer.
✓ Mean = A + (Σfd'/Σf) × h, where A is the assumed mean, h is the class interval, and d' = (X - A)/h.
⚠ Confusing 'Analysis' with 'Conclusion'
✗ The conclusion is the same as analysis and interpretation.
→ Analysis involves using statistical tools like mean and standard deviation. Conclusion is the final step where meaningful conclusions are drawn from the analysis, including predictions and suggestions.
✓ Analysis and interpretation involve calculating measures like mean and standard deviation. The conclusion is the last step where we draw meaningful conclusions, predict future prospects, and give suggestions based on the analysed data.
⚠ Omitting the Bibliography Section
✗ A project report only needs the data and analysis.
→ The chapter clearly states that a bibliography section is required to mention details of all secondary sources used.
✓ The project report must include a bibliography section listing all secondary sources such as magazines, newspapers, and research reports used.
Compare & Contrast
Source of data collection
Primary Data
Secondary Data
Primary data is collected first-hand by the investigator using methods like questionnaires or interviews, while secondary data is already collected by someone else and is used when there is paucity of time, money, and manpower.
Method of administration
Questionnaire
Interview Schedule
A questionnaire is a list of questions that the respondent answers on their own (e.g., via mail), while an interview schedule is used by an enumerator who asks the questions and records the answers in a personal interview.
Exam Focus
Marks pattern: 1-2 MCQs (1 mark each) on definitions and steps, 1 SA (3 marks) on steps of project or difference between primary/secondary data, 1 LA (5 marks) on calculation of mean and standard deviation from a frequency distribution or on designing a questionnaire and interpreting results.
Most asked: Steps in designing a project · Difference between primary and secondary data · Calculation of mean and standard deviation from grouped data · Interpretation of data using bar diagrams and pie diagrams · Purpose and components of a questionnaire
Don't skip: Long answer question on calculating mean and standard deviation from a grouped frequency distribution using the step-deviation method; Question on listing and explaining the steps in making a project with examples
One-Line Revision (read aloud before the exam)
  1. The first step in making a project is identifying a problem or an area of study.
  2. The choice of target group is important for framing appropriate questions for your questionnaire.
  3. Primary data is first-hand data collected by the investigator using methods like questionnaires or interviews.
  4. Secondary data is already collected by someone else and is used when there is paucity of time, money, and manpower.
  5. A postal questionnaire must have a covering letter giving details about the purpose of inquiry.
  6. After collecting data, organise and present it using tabulation, bar diagrams, and pie diagrams.
  7. Analysis involves using measures of central tendency (mean), dispersion (standard deviation), and correlation.
  8. The mean of grouped data can be calculated using the formula Mean = A + (Σfd'/Σf) × h.
  9. Standard deviation of grouped data is calculated as h × √[(Σfd'²/Σf) - (Σfd'/Σf)²].
  10. The conclusion is the last step where meaningful conclusions are drawn and future prospects are predicted.
  11. The bibliography section must list all secondary sources like magazines, newspapers, and research reports.
  12. In the sample project, the mean monthly expenditure on toothpaste was Rs. 104 and standard deviation was Rs. 35.60.
  13. Majority of people in the sample project came to know about toothpaste through television advertisements.
  14. A questionnaire must be capable of generating the information needed for the study.

MCQs — 10 Questions with Answers

Q1. Which of the following is the FIRST step in developing an economic project?

  • A. Identifying the problem or area of study ✓
  • B. Collecting data from respondents
  • C. Preparing tables and diagrams
  • D. Drawing conclusions and predictions

Answer: A — Identifying the problem clearly defines the research objective, which then guides all decisions about target group, data collection method, and analysis tools.

Q2. A District Education Officer wants to study literacy levels and school dropout reasons. Which target group is most appropriate?

  • A. Only urban school children
  • B. Only rural school children
  • C. Both urban and rural school children and their families ✓
  • D. Only government school teachers

Answer: C — To understand literacy levels and dropout reasons comprehensively, both urban and rural populations must be included as dropout patterns differ between regions.

Q3. When should secondary data be preferred over primary data in project development?

  • A. Always, as it is more accurate
  • B. When there is limited time, money, and manpower, and required information is readily available ✓
  • C. Only when studying consumer preferences
  • D. Never, as secondary data is unreliable

Answer: B — Secondary data from existing sources is cost-effective and time-saving when resources are limited and the available information suits the project objective.

Q4. A toothpaste entrepreneur collects data showing: Brand A: 45%, Brand B: 35%, Brand C: 20%. Which presentation method is MOST suitable?

  • A. Line graph
  • B. Frequency distribution table
  • C. Pie diagram ✓
  • D. Scatter plot

Answer: C — Pie diagrams are ideal for showing proportions and market share percentages, making brand preferences immediately visible and comparable.

Q5. In a project studying monthly toothpaste expenditure across 500 households, the mean is ₹150 and standard deviation is ₹40. What does the standard deviation reveal?

  • A. Average expenditure is ₹150
  • B. Expenditure varies by ₹40 around the mean, showing variability in consumer spending patterns ✓
  • C. Most households spend exactly ₹150
  • D. Total expenditure of all households is ₹40

Answer: B — Standard deviation measures dispersion; SD of ₹40 means household expenditure typically varies by ₹40 above or below the mean of ₹150.

Q6. A postal questionnaire regarding safe drinking water must include:

  • A. Only the list of questions
  • B. A covering letter stating purpose of inquiry, objectives, and instructions ✓
  • C. Only the respondent's personal details
  • D. Only the conclusion section

Answer: B — Covering letters for postal surveys must clearly state the inquiry's purpose, research objectives, and detailed instructions so respondents understand what is being studied.

Q7. Which statement is INCORRECT regarding project development? (A) Primary data is always more accurate than secondary data (B) Target group selection depends on project objective (C) Questionnaires should be designed based on target group characteristics (D) Analysis uses correlation to study relationships between variables

  • A. (A) Primary data is always more accurate than secondary data ✓
  • B. (B) Target group selection depends on project objective
  • C. (C) Questionnaires should be designed based on target group characteristics
  • D. (D) Analysis uses correlation to study relationships between variables

Answer: A — Statement (A) is false: primary data is customised but can have biases; secondary data may be highly accurate if from reliable sources like government reports.

Q8. A Bank Officer studies saving habits by analyzing income and expenditure of 300 people. She calculates correlation coefficient = +0.85. This indicates: (A) Strong positive relationship between income and savings (B) People with higher income save more (C) Both (A) and (B) are correct (D) No relationship exists between variables

  • A. Strong positive relationship between income and savings only
  • B. People with higher income save more only
  • C. Both (A) and (B) are correct interpretations ✓
  • D. No relationship exists between variables

Answer: C — Correlation of +0.85 (close to +1) shows strong positive relationship, meaning as income increases, savings increase proportionally—both statements are correct interpretations.

Q9. A Gram Panchayat head surveys 250 households about safe drinking water availability. Data shows: 60% have access, 25% have partial access, 15% have no access. To determine if this situation warrants government intervention, which statistical measure would be MOST useful?

  • A. Only the percentages shown
  • B. Mean and standard deviation of water availability
  • C. Correlation between income and water access ✓
  • D. Mode of the access category

Answer: C — Correlation between household income and water access reveals whether poor families lack access (socio-economic issue), helping target government intervention effectively.

Q10. In a project examining the effect of advertisements on product sales, if the researcher collects primary data through personal interviews with 200 shopkeepers instead of using 5-year historical sales records, what is the PRIMARY advantage?

  • A. Historical records are always unreliable
  • B. Interviews provide customised information about current advertising effectiveness and recent market changes ✓
  • C. Personal interviews cost less than accessing records
  • D. Historical data cannot be used for any economic project

Answer: B — Primary data through interviews captures current perceptions, recent advertising impact, and market dynamics that 5-year-old records may not reflect accurately.

Flashcards

What is the first step in project development?

Identifying the problem or area of study that you want to investigate and understanding the clear objective of your research.

What is a target group in project design?

The specific population or group of people whose characteristics, behaviour, or opinions are the focus of your survey study.

When should you use primary data collection?

When you need first-hand, customised information directly from the source through questionnaires or interviews for your specific objective.

What is the purpose of data organisation and presentation?

To process raw data into tables, diagrams, and graphs so that patterns, trends, and comparisons become visually clear and understandable.

Name two measures used in analysis and interpretation phase.

Measures of Central Tendency (mean, median, mode) and Measures of Dispersion (standard deviation, range) help calculate averages and variability.

What information must be included in a covering letter for postal questionnaires?

Details about the purpose of inquiry, objectives of the study, and instructions for completing the questionnaire must be clearly stated.

When is secondary data preferred over primary data?

When there is limited time, money, and manpower resources available and the required information is already easily accessible from existing sources.

What is the final step in project development before submission?

Drawing meaningful conclusions, predicting future prospects, suggesting improvements in products or systems, and listing all secondary sources in bibliography.

How does correlation help in project analysis?

Correlation measures the relationship between two variables, such as whether increased advertising leads to increased sales of a product.

What is the role of measures of central tendency in project analysis?

They calculate the average value of data collected, such as mean monthly expenditure on toothpaste or average literacy levels in a district.

Important Board Questions

Define target group in the context of project development and give one example suitable for studying consumer awareness about toothpaste brands. [2 marks]

Target group is the specific population chosen for study. For toothpaste, select families with regular consumption; state age, income level, or urban/rural location if relevant.

A Bank Officer wants to survey saving habits of 500 people in a district. Explain with justification whether primary or secondary data should be collected. Also state two methods of primary data collection suitable for this study. [5 marks]

Primary data is justified because saving habits are individual-specific and may vary by current income levels; secondary data may be outdated. Methods: questionnaires via personal interview or postal survey, or structured interviews using interview schedule.

A researcher studying female literacy in a district collects primary data using a questionnaire from 1000 households. After tabulation, mean literacy rate is 65% with standard deviation 12%. Organise this data into a frequency distribution table and interpret what the standard deviation reveals about literacy variation across households. Also suggest which measure of central tendency would be most appropriate if the literacy data is skewed, and explain why conclusions about government educational policy should be based on complete statistical analysis rather than just averages. [6 marks]

Create frequency classes (e.g., 40-50%, 50-60%, 60-70%, etc.) with frequencies. SD of 12% means literacy varies ±12 around 65% mean—show high variability across households. For skewed data, median is better than mean. Explain that SD reveals dispersion; correlation with income/caste may show targeted policy needs; conclusions require full analysis using central tendency, dispersion, and correlation together.

Assertion-Reason Questions for Use of Statistical Tools

Q1. Assertion (A):

Identifying a target group is essential before framing questionnaire questions in a project study.

Reason (R):

The target group determines the characteristics and preferences of the population from which data will be collected, enabling researchers to create appropriate and relevant questions.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both the assertion and reason are true, and the reason correctly explains why target group identification is important. Understanding the target group's characteristics helps design relevant questionnaires. For example, a car project targets middle and high-income groups, which influences question design.

Q2. Assertion (A):

Secondary data should always be preferred over primary data in project studies.

Reason (R):

Secondary data collection is more expensive and time-consuming than primary data collection.

Answer: D — A is false but R is true — Both the assertion and reason are false. The chapter states that secondary data is preferred when resources are LIMITED, not always. Additionally, the reason is reversed—secondary data is actually LESS expensive and time-consuming than primary data collection. Primary data is preferred when accuracy and specificity are critical.

Q3. Assertion (A):

Standard deviation is used in project analysis to understand variability in data.

Reason (R):

Standard deviation measures how far individual data points typically deviate from the mean, providing insights into the consistency or spread of values.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both statements are true, and the reason correctly explains the assertion. The chapter mentions that measures of dispersion like standard deviation enable calculation of variability among variables, which is exactly what the reason describes. This is a key analytical step in project development.

Unlock more Assertion-Reason questions in Premium — unlock →

Case-Based Questions (CBQ) for Use of Statistical Tools

Case Study:

A District Education Officer (DEO) is conducting a project to understand school dropout rates across 100 schools in her district. She identifies dropout patterns, reasons for leaving school, and socioeconomic factors. She collects primary data through questionnaires from 100 schools, organizing responses into tables showing dropout percentages by grade level and gender. She calculates mean dropout rate as 8.5% with standard deviation of 2.3%. She also finds a strong positive correlation (0.78) between poverty level and dropout rates.

Q1. What is the primary advantage of calculating standard deviation (2.3%) in addition to the mean (8.5%) dropout rate?

  • A. It shows that exactly 2.3% of students drop out in some schools
  • B. It reveals variability in dropout rates across schools, indicating which schools perform better or worse than average ✓
  • C. It proves that poverty directly causes students to drop out
  • D. It calculates the total number of students who dropped out across all schools

Answer: B

Q2. The DEO finds correlation coefficient of 0.78 between poverty level and dropout rates. Which interpretation is MOST appropriate?

  • A. Poverty is the only cause of school dropouts
  • B. There is a strong positive relationship between poverty and dropout rates, but other factors may also contribute ✓
  • C. Poverty level has no relationship with dropout decisions
  • D. The correlation proves that reducing poverty will eliminate all dropouts

Answer: B

Q3. If the DEO wants to compare dropout patterns across rural and urban schools, which additional analysis would be most useful?

  • A. Calculating separate means and standard deviations for rural and urban schools and comparing them ✓
  • B. Using only the overall mean dropout rate for all schools
  • C. Ignoring the data and making decisions based on personal experience
  • D. Calculating only the mode (most common) dropout rate value

Answer: A

Q4. Based on her findings, the DEO should include which recommendations in her final project report?

  • A. Target socioeconomic support programs in areas with high dropout rates, especially where poverty correlation is strong ✓
  • B. Increase poverty in the district to see if dropout rates change
  • C. Stop all educational programs since dropout rates are above zero
  • D. Use only correlation coefficient without any reference to mean or standard deviation

Answer: A

Unlock more case studies in Premium — unlock →

Class 11 Economics Formula Sheet

Every formula from the Statistics and Microeconomics chapters on one page, checked against the NCERT textbook and the CBSE 2026-27 syllabus. Free PDF download.

View the formula sheet →

Next chapterIntroduction to Micro Economics →
Found this useful? Share it with your class group.

You've seen the free preview. Open the full interactive study kit — mind map, instant-graded quiz, progress tracking — free, no sign-in required.

Open Full Study Kit — Free →

Premium unlocks the full Question Bank, Daily Practice Papers, Chapter Quiz and Full Mock Papers for every chapter.