Updated NCERT Solutions for Class 11 Statistics Chapter 1: Introduction

(i) Statistics can only deal with quantitative data.

Answer: True. Statistics primarily deals with data that can be expressed in numbers. Qualitative phenomena like honesty or friendship are not directly studied in statistics unless they are converted into a numerical form through ranking or scaling.

(ii) Statistics solves economic problems.

Answer: False. Statistics is a crucial tool that helps in understanding economic problems and in formulating policies to solve them. However, it does not solve the problems by itself. It provides the data and analysis, but the final decision-making and implementation are done by economists and policymakers.

(iii) Statistics is of no use to Economics without data.

Answer: True. The entire foundation of statistical methods and economic analysis rests on the availability of data. Without data, statistical tools cannot be applied, and economic theories cannot be tested or validated. Data is the raw material for statistics.

The "ordinary business of life" refers to the activities people undertake to earn a living and spend their income. Here is a list of such activities:

• A farmer tilling his land to grow crops.
• A factory worker operating machinery to produce goods.
• A doctor attending to patients in a clinic.
• A teacher teaching students in a school.
• A shopkeeper selling groceries to customers.
• A software engineer writing code for a company.
• A family buying a new television for their home.

Yes, these are all economic activities.

An activity is considered an economic activity if it involves the use of scarce resources (like money, time, and labour) to satisfy human wants. All the activities listed above involve production, consumption, or distribution of goods and services, which are the core of economics. They are concerned with "making a living."

This statement is the cornerstone of modern economics. It can be explained with the following points:

1. Unlimited Human Wants: Human wants for goods and services are endless. If we satisfy one want, another emerges. For example, after buying a bicycle, a person may desire a motorcycle, and then a car.
2. Limited/Scarce Resources: The resources available to produce goods and services to satisfy these wants are limited. These resources (also called factors of production) are land, labour, capital, and entrepreneurship.
3. Alternative Uses of Resources: To make matters more complex, these scarce resources have alternative uses. For example, a piece of land can be used to grow wheat, build a factory, or construct a hospital.

The mismatch between unlimited wants and scarce resources that have alternative uses creates the problem of choice. We have to choose which wants to satisfy and which to leave unsatisfied. This problem of choice, arising from scarcity, is the root of all economic problems. Every economy—rich or poor—faces this issue and must decide:

• What to produce? (e.g., More guns or more butter?)
• How to produce? (e.g., Using more labour or more machines?)
• For whom to produce? (How should the output be distributed among the population?)

Thus, scarcity forces us to make choices, and the study of these choices is what economics is all about.

This situation is faced by everyone daily. Here are two common examples:

Example 1: Managing Pocket Money

• Unlimited Wants: With my monthly pocket money of ₹1000, I want to buy a new video game (₹800), go out for a movie with friends (₹400), buy a new book (₹300), and also save some money. My total wants amount to more than ₹1500.
• Limited Resource: My resource is my fixed pocket money, which is only ₹1000.
• Choice/Economic Problem: Due to scarcity of money, I cannot satisfy all my wants. I must make a choice. I might decide to buy the book and go for the movie, but postpone buying the video game for next month. This is an economic decision driven by scarcity.

Example 2: Time Management During Exams

• Unlimited Wants: The night before my exam, I want to revise all 10 chapters, solve two sample papers, watch a quick summary video, and also get 8 hours of sleep.
• Limited Resource: The resource is time, which is limited to 24 hours a day. I only have about 8-10 hours to study.
• Choice/Economic Problem: I cannot do everything. I have to prioritize. I might choose to revise the most important 5 chapters thoroughly and get 6 hours of sleep, sacrificing the sample papers and the remaining chapters. This allocation of my scarce time is an economic problem.

When faced with limited resources and multiple wants, a rational person will choose the wants to be satisfied based on priority and intensity. The guiding principle is to maximize satisfaction.

Here is the process:

1. Prioritize Wants: I will rank my wants in order of their urgency and importance. The most urgent and important wants will be placed at the top of the list, and the least important ones at the bottom.
2. Evaluate Intensity: I will consider how much satisfaction (or utility) I will get from fulfilling each want. A want that gives me higher satisfaction will be given a higher priority.
3. Allocate Resources: I will start allocating my limited resources (like money or time) to satisfy the wants at the top of my priority list. I will continue down the list until my resources are exhausted.
4. Sacrifice/Postpone: The wants that are lower on the priority list and cannot be fulfilled with the current resources will be postponed or sacrificed.

For example, if I have ₹100 and I want to buy a textbook (very important for exams) and a comic book (for leisure), I will prioritize buying the textbook first because the satisfaction and necessity associated with it are much higher.

As a student, I have several reasons for studying Economics:

1. Understanding the World: Economics helps me understand how the world works. It explains issues like inflation (why prices rise), unemployment, poverty, and international trade, which I read about in the news every day.
2. Improved Decision-Making: The principles of Economics, like scarcity, opportunity cost, and marginal analysis, help me make better decisions in my own life, such as managing my pocket money or allocating my study time.
3. Understanding Government Policies: It helps me understand why the government imposes taxes, how the budget is made, and the purpose of schemes like 'Make in India' or subsidies on LPG cylinders. It makes me a more informed citizen.
4. Excellent Career Prospects: A degree in Economics opens up a wide range of career opportunities in banking, finance, consulting, data analysis, civil services, and research.
5. Foundation for Higher Studies: It is a foundational subject for further studies in Commerce, Management (MBA), Public Policy, and Finance.

This statement means that while statistics is a powerful tool for analysis, it must be interpreted with logic, domain knowledge, and common sense. Data can be misleading if not viewed in the right context. Blindly trusting statistical results without applying common sense can lead to absurd conclusions.

Comment: The statement is absolutely correct. Statistics provides the 'what', but common sense helps us understand the 'why' and 'how'.

Examples from Daily Life:

1. Example: The Average Depth of a River
   • Statistical Fact: The average depth of a river is only 4 feet.
   • Flawed Conclusion: Based on this statistic, a person who cannot swim and is 6 feet tall might think it's safe to cross the river.
   • Common Sense: Common sense tells us that the "average" depth hides the variation. The river could be only 1 foot deep at the edges but 15 feet deep in the middle. Relying only on the average would be dangerous and potentially fatal. Common sense dictates that one should check the actual depth at all points before crossing.
2. Example: Increased Ice Cream Sales and Crime
   • Statistical Fact: A study shows that in a city, when ice cream sales increase, the crime rate also increases. Statistically, there is a strong positive correlation.
   • Flawed Conclusion: A person without common sense might conclude that eating ice cream causes people to commit crimes or that criminals love ice cream. They might even suggest banning ice cream to reduce crime!
   • Common Sense: Common sense helps us look for a third, underlying factor. In this case, the factor is hot weather (summer). In summer, more people are outdoors, which increases opportunities for crime, and more people also buy ice cream to cool down. The two are correlated but one does not cause the other. Statistical methods showed the correlation, but common sense provided the correct interpretation.

These examples show that statistics are just tools. Their effective use depends on the intelligence and common sense of the person using them.

Quantitative data is information that can be measured and expressed numerically. It answers questions like "how much" or "how many". Example: The heights of students in a class (e.g., 155 cm, 160 cm).

Qualitative data is descriptive information that cannot be measured numerically. It describes qualities or characteristics. Example: The honesty of employees in a company (e.g., honest, dishonest).

Two key functions of statistics are:

1. Simplifies Complex Data: Statistics presents large volumes of complex data in a simplified and understandable form like averages, percentages, graphs, and tables.
2. Facilitates Comparison: It helps in comparing data from different sources or time periods. For example, we can compare the literacy rates of two different states.

Data without context is just a number and has no meaning. For a number to become a useful statistic, it must be placed in the context of time, place, and other related facts.

Example: If I say "100," it means nothing. But if I say, "The price of petrol in Delhi is ₹100 per litre," the number now has context and becomes meaningful information.

This statement is true. Statistics can be considered both a science and an art.

Statistics as a Science:
Science is a systematic body of knowledge. Statistics is called a science because its methods are systematic and have universal application.

• Systematic Approach: It involves a clear sequence of steps: collection, organization, presentation, analysis, and interpretation of data (COPAl).
• Universal Methods: The statistical methods for calculating mean, median, correlation, etc., are universal and follow specific formulas and principles.

Statistics as an Art:
Art refers to the skill of applying knowledge to achieve a desired result. Statistics is an art because its successful application requires skill, experience, and common sense.

• Skill in Data Collection: Choosing the right method (census or sample) and framing a good questionnaire requires skill.
• Skill in Analysis: Two analysts using the same data can arrive at different conclusions depending on the tools they choose and how they interpret the results.
• Real-world Problem Solving: Applying statistical knowledge to solve real-world problems (like poverty, unemployment) is an art that requires adapting methods to the specific context of the problem.

Therefore, statistics is a science as it provides the methods, and it is an art as it teaches how to apply these methods effectively.

A statistical study involves five distinct stages, which are crucial for any meaningful analysis.

1. Stage 1: Collection of Data: This is the first and most important step. The data can be collected through a census or sampling method. It can be primary data (collected for the first time) or secondary data (already collected by someone else).
   Example: To study the spending habits of Class 11 students, a researcher creates a questionnaire and gives it to 100 students.
2. Stage 2: Organisation of Data: The raw data collected in the first stage is often huge and unorganized. It needs to be organized and structured. This involves editing, classifying, and tabulating the data.
   Example: The researcher organizes the filled questionnaires and creates a table, classifying students based on their monthly pocket money (e.g., <₹500, ₹500-₹1000, >₹1000).
3. Stage 3: Presentation of Data: The organized data is presented in a simple and attractive manner to make it easily understandable. This is done using tables, graphs (bar diagrams, pie charts), and diagrams.
   Example: The researcher presents the data using a pie chart showing the percentage of income students spend on food, entertainment, and stationery.
4. Stage 4: Analysis of Data: The presented data is now analyzed to draw meaningful conclusions. This is done by using statistical measures like averages (mean, median, mode), measures of dispersion, and correlation.
   Example: The researcher calculates the average pocket money of a student and the average amount spent on entertainment.
5. Stage 5: Interpretation of Data: This is the final stage where the analyzed results are interpreted and conclusions are drawn. The interpretation must be done carefully and with common sense.
   Example: Based on the analysis, the researcher concludes that, on average, students spend 40% of their pocket money on food, which is the highest expenditure category.

Questions:

(i) In the above case, identify the consumer and producer of statistical services.

• Producer of Statistics: Ms. Priya and her team are the producers. They are collecting, organizing, and analyzing the data to generate statistical information.
• Consumer of Statistics: The government agency is the consumer. It will use the statistical report (unemployment rate of 15%) provided by Ms. Priya to formulate policies (like the skill development program).

(ii) Is the study using the singular or plural sense of statistics? Justify.

The study is using both the singular and plural sense of statistics.

• Plural Sense: The raw data collected from 50,000 households (e.g., number of graduates, employment status) represents statistics in the plural sense (numerical data).
• Singular Sense: The entire process undertaken by Ms. Priya—preparing a questionnaire (collection), creating tables (organization), calculating the unemployment rate (analysis), and recommending a program (interpretation)—represents statistics in the singular sense (the method/science).

(iii) Which stage of statistical study is represented by "the unemployment rate among graduates was 15%?"

The statement "the unemployment rate among graduates was 15%" represents the Analysis of Data stage. It is a result obtained after processing and condensing the raw data into a meaningful measure (a percentage) that summarizes the situation.