CBSE Class 11 Mathematics Statistics Assignment Set 01

Multiple Choice Questions

Question. The scores of a batsman in 10 innings are 48, 80, 58, 44, 52, 65, 73, 56, 64, 54, then the mean deviation from the median is
(a) 7.6
(b) 8.6
(c) 9.6
(d) 10.1
Answer : B

Question. Mean deviation about the median for the data
3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21 is
(a) 4.27
(b) 5.24
(c) 5.27
(d) 4.24
Answer : C

Question. If mean and standard deviation of 100 items are 50 and 4 respectively, then the sum of all the item and the sum of the squares of item is
(a) 5000, 251600
(b) 5000, 256100
(c) 4000, 215600
(d) 4000, 255600
Answer : A

Question. Consider the following data 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
If 2 is added to each number, then variance of the numbers so obtained is
(a) 6.5
(b) 2.87
(c) 3.87
(d) 8.25
Answer : D

Question. 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.
The mean deviation about the mean for the given data is
(a) 8.4
(b) 7.4
(c) 6.3
(d) 4
Answer : A

Question. The mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12 respectively are
(a) 9, 9.50
(b) 8, 8.50
(c) 9, 9.25
(d) 8, 8.25
Answer : C

Question. 6, 7, 10, 12, 13, 4, 8, 12
The variance for the given data is
(a) 8.25
(b) 9.25
(c) 10.5
(d) 8.9
Answer : B

Question. Variance of the data 2, 4, 5, 6, 8, 17 is 23.33. Then, variance of 4, 8, 10, 12, 16, 34 will be
(a) 23.33
(b) 25.33
(c) 46.66
(d) 48.66
Answer : C

Question. 6, 5, 5.25, 5.5, 4.75, 4.5, 6.25, 7.75, 9.
The mean deviation from the mean for the given data is
(a) 1.1
(b) 2.1
(c) 4.1
(d) 5.1
Answer : A

Question. When tested, the lives (in hours) of 5 bulbs were noted as follows 1357, 1090, 1666, 1494, 1623
The mean deviations (in hours) from their mean is
(a) 178
(b) 179
(c) 220
(d) 356
Answer : A

Question. Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. If 1 is added to each number the variance of the numbers, so obtained is
(a) 6.5
(b) 2.87
(c) 3.87
(d) 8.25
Answer : D

Question. The standard deviation for the data 6, 7, 10, 12, 13, 4, 8, 12 is
(a) √8.25
(b) √7.25
(c) √9.25
(d) √10.25
Answer : C

Question. 45, 60, 62, 60, 50, 65, 58, 68, 44, 48
The variance for the given data is
(a) 56.2
(b) 66.2
(c) 65.2
(d) 55
Answer : B

Assertion-Reasoning MCQs

Directions Each of these questions contains two statements Assertion (A) and Reason (R). Each of the questions has four alternative choices, any one of the which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) A is true, R is true; R is a correct explanation of A.
(b) A is true, R is true; R is not a correct explanation of A.
(c) A is true; R is false
(d) A is false; R is true.

Question. Assertion (A) The weights (in kg) of 15 students are as follows
31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30
If the weight 44 kg is replaced by 46 kg and 27 kg is by 25 kg, then new median is 35.
Reason (R) The mean deviation from the median of the weights (in kg) 54,
50, 40, 42, 51, 45, 47, 57 is 4.78.
Answer : B

Question. Assertion (A) The proper measure of dispersion about the mean of a set of observations i.e. standard deviation is expressed as positive square root of the variance.
Reason (R) The units of individual observations xi and the unit of their mean are different that of variance. Since, variance involves sum of squares of (x − x ).
Answer : A

Question. Assertion (A) If each of the observations x1, x2 , …, xn is increased by a, where a is a negative or positive number, then the variance remains unchanged.
Reason (R) Adding or subtracting a positive or negative number to (or from) each observation of a group does not affect the variance.
Answer : A

Question. If for a distribution ∑(x − 5) = 3, ∑(x − 5)² = 43 and the total number of items is 18.
Assertion (A) Mean of the distribution is 4.1666.
Reason (R) Standard deviation of the distribution is 1.54.
Answer : D

Case Based MCQs

You are given some observations as 34, 66, 30, 38, 44, 50, 40, 60, 42, 51.

Based on these observations, answer the following questions.'

Question. The mean of the given data is
(a) 40.5
(b) 45.0
(c) 45.5
(d) 50.5
Answer : C

Question. The mean deviation about the mean is
(a) 10.0
(b) 9.5
(c) 9.1
(d) 9.0
Answer : D

Question. The median of the given data is
(a) 41
(b) 42
(c) 43
(d) 44
Answer : C

Question. The mean deviation about the median is
(a) 8.0
(b) 8.3
(c) 8.5
(d) 8.7
Answer : D

Question. The difference between mean deviation about the mean and mean deviation about the median is
(a) 0.1
(b) 0.2
(c) 0.3
(d) 0.4
Answer : C

Consider the data

x_i  4  8 11  17  20  24  32
f_i  3  5   9    5   4    3     1

Based on above information answer the following questions

Question. Mean of the given data is
(a) 10
(b) 12
(c) 14
(d) 15
Answer : C

Question. Variance of the given data is
(a) 40
(b) 45.8
(c) 41.5
(d) 39.8
Answer : B

Question. Standard deviation of the given data is
(a) 6.77
(b) 5
(c) 4.8
(d) 3.19
Answer : A

Q1. Define statistics. What are the limitations of it?
Answer: Statistics can be defined in two senses - plural sense and singular sense. In the plural sense, statistics refers to numerical facts and figures collected in a systematic manner for a predetermined purpose in any field of study. In the singular sense, statistics refers to the science of collecting, presenting, analyzing, and interpreting numerical data.
The main limitations of statistics are:
1. Statistics does not study qualitative phenomena: Phenomena like honesty, poverty, beauty, and intelligence cannot be expressed directly in numbers unless assigned arbitrary quantitative ranks.
2. Statistics deals with aggregates, not individuals: A single observation or isolated figure does not constitute statistics, as it cannot be analyzed comparatively.
3. Statistics results are true only on an average: Statistical laws are not universal truths; they hold true only under certain conditions or on an average.
4. Possibility of misuse: Statistical data can be manipulated or misinterpreted by unskilled persons to support preconceived notions.
In simple words: Statistics deals with numerical data in aggregates, but it ignores qualitative facts and its results are only true on an average.

Exam Tip: Clearly distinguish between the singular and plural definitions of statistics before listing at least three standard limitations.

Q2. Write down the importance of statistics from the point of view of business planning and in business?
Answer: Statistics plays a vital role in business planning and decision-making by removing uncertainty through scientific analysis of past data and current market trends. Its key importance includes:
1. Business Forecasting: Statistical tools like time series analysis and regression help business firms forecast future demand, sales, and prices, enabling effective production planning.
2. Quality Control: Statistical Quality Control (SQC) charts and sampling techniques help in monitoring manufacturing processes to ensure products meet required quality standards with minimum wastage.
3. Market Research: Businesses use statistical surveys to understand consumer preferences, purchasing power, competitor strategies, and market segmentation.
4. Financial Analysis: Budgeting, profit planning, investment appraisal, and risk assessment rely heavily on statistical and probability techniques.
In simple words: Statistics helps businesses forecast demand, control product quality, study market trends, and make profitable financial decisions.

Exam Tip: Structure your answer around core business functions such as forecasting, quality control, and market research.

Q3. What are types of data? Explain the different method of collecting primary data?
Answer: Data is broadly classified into two types:
1. Primary Data: Data originally collected by the investigator for the first time for a specific research purpose. It is first-hand and original.
2. Secondary Data: Data that has already been collected, processed, and published by someone else for some other purpose.
The principal methods of collecting primary data are:
1. Direct Personal Investigation: The investigator collects data personally by coming into direct contact with the respondents.
2. Indirect Oral Investigation: Data is collected through third parties or witnesses who are closely connected with the subject matter when direct contact is not feasible.
3. Information through Correspondents: Local agents or correspondents are appointed in different areas to collect and report information regularly.
4. Mailed Questionnaire Method: Questionnaires are mailed to respondents who fill them out and return them.
5. Schedules through Enumerators: Enumerators go to respondents with the questionnaire, ask questions, and record the answers themselves.
In simple words: Primary data is freshly collected by the investigator, whereas secondary data is borrowed from existing sources.

Exam Tip: Mention both the definition of data types and clearly enumerate the five standard methods of primary data collection.

Q4. What do you understand by “Questionnaire”? What are the essential characteristics of a good questionnaire?
Answer: A questionnaire is a structured instrument consisting of a list of carefully framed questions related to a specific investigation or research topic, designed to be answered by respondents.
The essential characteristics of a good questionnaire are:
1. Limited number of questions: The questionnaire should not be too long to avoid fatiguing the respondent.
2. Simple and clear language: Questions should be easy to understand, unambiguous, and free from technical jargon.
3. Proper sequence of questions: Questions should follow a logical progression from general to specific.
4. Avoidance of personal or sensitive questions: Questions that hurt personal feelings or probe confidential matters should be avoided.
5. Cross-check questions: It should include reliability checks through related questions to verify the consistency of answers.
6. Instructions and layout: Clear instructions and neat formatting are necessary to encourage high response rates.
In simple words: A questionnaire is a list of survey questions, and a good one must be short, clear, logically ordered, and free of sensitive topics.

Exam Tip: Highlight clarity, proper sequence, and brevity as the core pillars of a successful questionnaire design.

Q5. What do you mean by secondary data? Explain various methods of collecting secondary data.
Answer: Secondary data refers to data that is already in existence and has been collected and published by an agency, institution, or researcher for some other purpose. It is economical in terms of time, money, and effort.
The main sources and methods of collecting secondary data are:
1. Published Sources:
- Government publications (e.g., Census of India, Reserve Bank of India reports).
- Reports of international bodies (e.g., IMF, World Bank, UN).
- Publications of research institutions, universities, and trade associations.
- Newspapers, journals, and periodicals.
2. Unpublished Sources:
- Unpublished research reports, records maintained by business houses, or studies conducted by private agencies.
In simple words: Secondary data comes from pre-existing records and published reports created by other organizations.

Exam Tip: Always categorize secondary sources into published and unpublished sources for a comprehensive answer.

Q6. What do you understand by discrete and continuous variables?
Answer: 1. Discrete Variable: A discrete variable is a variable that can take only exact, definite integer values and cannot take fractional values in between. The values are distinct and separate. For example, the number of students in a class (25, 30, 42) or the number of children in a family.
2. Continuous Variable: A continuous variable is a variable that can take any numerical value, including fractions and decimals, within a given range. It is measured on a continuous scale rather than counted. For example, height, weight, temperature, and time.
In simple words: Discrete variables take exact whole-number counts, whereas continuous variables can take any decimal or fractional value within a range.

Exam Tip: Use clear examples like 'number of rooms' for discrete and 'height in cm' for continuous to secure full marks.

Q7. Find out Arithmetic mean from the following series: - (step deviation method)
Less than 10 | 20 | 30 | 40 | 50 | 60
No. of students 7 | 15 | 20 | 24 | 16 | 8
Answer: First, convert the 'less than' cumulative frequency series into a continuous frequency distribution with class intervals and simple frequencies:

Let Assumed Mean \(A = 35\) and class interval width \(c = 10\).
Formula for step deviation method:
\(\bar{X} = A + \left( \frac{\sum fu}{N} \right) \times c\)
Substitute the values:
\(\bar{X} = 35 + \left( \frac{-10}{48} \right) \times 10\)
\(\bar{X} = 35 - \frac{100}{48}\)
\(\bar{X} = 35 - 2.083 = 32.92\)
In simple words: Convert cumulative frequencies to simple frequencies, choose an assumed mean, apply the step deviation formula, and calculate the mean as 32.92.
Exam Tip: Always double-check your subtraction when converting less-than cumulative frequencies into simple frequencies.

Q8. Draw 'Less than ogive curve and More than ogive curve' on the basis of this data:
Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
No. of students: 4, 10, 14, 20, 6, 3 (Total = 57)
Answer: To draw the Less than and More than ogives, we first prepare the cumulative frequency table:

Construction Steps:
1. Plot upper class limits against less than cumulative frequencies to draw the Less than ogive.
2. Plot lower class limits against more than cumulative frequencies to draw the More than ogive.
3. The intersection point of both ogives gives the median value on the X-axis.
In simple words: Plot the less-than cumulative frequencies against upper limits and more-than cumulative frequencies against lower limits to draw the two curves.
Exam Tip: Remember that less-than ogive slopes upward from left to right, whereas more-than ogive slopes downward.

Q9. Calculate mode by using grouping method.
Marks: 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60
No. of students: 4 | 10 | 25 | 15 | 10 | 6
Answer: Step 1: Prepare the Grouping Table:

Step 2: Analysis Table shows maximum frequency concentration in class interval \(20 - 30\).
Model class is \(20 - 30\).
Formula for mode:
\(Z = L + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h\)
Where \(L = 20\), \(f_1 = 25\), \(f_0 = 10\), \(f_2 = 15\), \(h = 10\).
Substitute values:
\(Z = 20 + \left( \frac{25 - 10}{2(25) - 10 - 15} \right) \times 10\)
\(Z = 20 + \left( \frac{15}{50 - 25} \right) \times 10\)
\(Z = 20 + \left( \frac{15}{25} \right) \times 10 = 20 + 6 = 26\)
In simple words: Create grouping and analysis tables to identify the modal class 20-30, then apply the mode interpolation formula to get 26.
Exam Tip: Always construct both the 6-column grouping table and the analysis table when asked to find mode by grouping method.

Q10. Calculate median.
Marks: 10-20 | 20-30 | 30-40 | 40-50 | 50-60
No. of students: 14 | 12 | 15 | 10 | 6
Answer: Prepare the cumulative frequency table:

Find median item position:
\(\frac{N}{2} = \frac{57}{2} = 28.5\)
The cumulative frequency just greater than 28.5 is 41, corresponding to the median class \(30 - 40\).
Formula for median:
\(M = L + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h\)
Where \(L = 30\), \(cf = 26\), \(f = 15\), \(h = 10\).
Substitute values:
\(M = 30 + \left( \frac{28.5 - 26}{15} \right) \times 10\)
\(M = 30 + \left( \frac{2.5}{15} \right) \times 10\)
\(M = 30 + \frac{25}{15} = 30 + 1.67 = 31.67\)
In simple words: Find N/2 to locate the median class 30-40, then use the interpolation formula to get the median as 31.67.
Exam Tip: Ensure you take the cumulative frequency of the preceding class interval as \(cf\) in the formula.

INDIAN ECONOMY

Q1. What do you understand by structural changes?
Answer: Structural changes refer to large-scale, fundamental shifts in the basic composition and relative importance of different sectors of an economy over a period of time. In the context of the Indian economy, it refers to the transition from an agrarian economy dominated by primary activities to a diversified economy with substantial contributions from the secondary (industrial) and tertiary (services) sectors, along with changes in technology, employment patterns, and institutional frameworks.
In simple words: Structural changes mean a fundamental shift in the economy from agriculture toward industry and services.

Exam Tip: Emphasize the shift in sectoral contribution to GDP and workforce distribution.

Q2. Explain semi-feudal economy.
Answer: A semi-feudal economy is an economic system that exhibits a combination of traditional feudal social relations and capitalist market elements. On the eve of independence, the Indian economy was termed semi-feudal because agriculture was characterized by landlordism (zamindari system), high rents, forced labor, and exploitation of tenants by intermediaries, alongside primitive technology and stagnation, while commercial and monetary transactions existed in urban pockets.
In simple words: A semi-feudal economy combines oppressive traditional landlord systems with primitive agricultural practices and limited modern markets.

Exam Tip: Mention landlordism and agricultural backwardness as key features of pre-independence semi-feudalism.

Q3. What are the three sectors of occupational structure?
Answer: Occupational structure refers to the distribution of working population across different sectors of economic activity. The three main sectors are:
1. Primary Sector: Activities directly dependent on nature, such as agriculture, forestry, animal husbandry, fishing, and mining.
2. Secondary Sector: Activities involving manufacturing, processing, construction, and generation of electricity and gas.
3. Tertiary Sector: Service-related activities, including trade, transport, banking, communication, insurance, and public administration.
In simple words: The three sectors are primary (agriculture and extraction), secondary (manufacturing), and tertiary (services).

Exam Tip: Clearly define each sector with relevant examples to ensure complete credit.

Q4. What do you mean by depleted and stagnant economy?
Answer: A depleted and stagnant economy refers to an economy where production capacity is continuously reduced, per capita income remains extremely low, and there is little to no growth in overall economic output over long periods. On the eve of independence, India was characterized as stagnant because growth was nearly zero, and depleted due to the systematic drain of wealth and neglect of productive infrastructure by the British colonial administration.
In simple words: A stagnant economy shows no growth, while a depleted economy suffers from destroyed or exhausted wealth and resources.

Exam Tip: Link stagnation and depletion directly to the colonial impact on Indian agriculture and industry.

Q5. When was planning commission constituted?
Answer: The Planning Commission of India was constituted by a resolution of the Government of India on March 15, 1950, with Prime Minister Jawaharlal Nehru as its first Chairperson. Its mandate was to formulate five-year plans for the effective and balanced utilization of the country's resources.
In simple words: The Planning Commission was established on March 15, 1950, to formulate India's Five-Year Plans.

Q6. What do mean by mixed economy?
Answer: A mixed economy is an economic system that combines elements of both capitalist (market) economies and socialist (command) economies. In a mixed economy, both the private sector and the public (government) sector coexist and operate side by side. While private enterprises function for profit under market mechanisms, the government controls strategic sectors, ensures social welfare, and regulates economic activities to prevent market failures.
In simple words: A mixed economy features both private businesses and government enterprises working together.

Exam Tip: Highlight the coexistence of private property and public welfare regulation in a mixed economy.

Q7. What dare the objectives of planning?
Answer: The general and specific objectives of economic planning in India across various Five-Year Plans include:
1. Economic Growth: Increasing the country's capacity to produce more goods and services by raising the Gross Domestic Product (GDP).
2. Modernization: Adopting new technology in production and bringing about social changes such as gender empowerment.
3. Self-Reliance: Reducing dependence on foreign countries for food, capital goods, and technology.
4. Equity and Social Justice: Ensuring a fair and equitable distribution of wealth and income to reduce poverty and inequality.
In simple words: The main objectives of planning are economic growth, technological modernization, self-reliance, and social equity.

Q8. Give achievement and failure of planning.
Answer: Achievements of Planning:
1. Increase in national income and per capita income.
2. Development of heavy and basic industries and diversified industrial base.
3. Substantial progress in agricultural output (Green Revolution).
4. Development of economic infrastructure like transport, communication, and power.
Failures of Planning:
1. Persistent poverty and high unemployment rates.
2. Widening economic inequalities between the rich and the poor.
3. High rate of inflation, eroding purchasing power.
4. Inadequate social infrastructure in rural education and healthcare.
In simple words: Planning boosted industrial and agricultural output, but failed to fully eradicate poverty and income inequality.

Exam Tip: Balance your answer equally between economic achievements (Green Revolution, GDP growth) and failures (poverty, inequality).

Q9. What are the objectives of WTO?
Answer: The World Trade Organization (WTO), established in 1995 as the successor to GATT, has the following primary objectives:
1. To implement and administer multilateral trade agreements.
2. To provide a forum for negotiating further reduction of trade barriers and tariffs.
3. To resolve trade disputes among member countries through a transparent mechanism.
4. To ensure optimal use of world resources and promote sustainable development.
5. To remove discriminatory practices in international trade and protect intellectual property rights.
In simple words: The WTO aims to promote free and fair international trade, reduce tariffs, and resolve trade disputes between nations.

Exam Tip: Mention trade liberalization, dispute settlement, and elimination of trade barriers as core WTO functions.

Q10. Mention three causes that forced India to follow economic reforms.
Answer: The three main causes that forced India to adopt the New Economic Policy (LPG reforms) in 1991 were:
1. Balance of Payments (BOP) Crisis: India faced severe foreign exchange reserves depletion, falling to levels barely sufficient to import goods for a couple of weeks.
2. High Inflation: Escalating prices of essential commodities due to excessive money supply and fiscal deficits.
3. Poor Performance of Public Sector Enterprises (PSEs): Most public sector undertakings were running into heavy financial losses due to bureaucratic inefficiency and corruption.
In simple words: India adopted 1991 economic reforms due to a severe foreign exchange crisis, high inflation, and losses in public sector enterprises.

Q11. Give the features of Liberalisation and Globalisation.
Answer: Features of Liberalisation:
1. Abolition of industrial licensing except for a few sensitive industries.
2. Freedom in deciding the scale of business activities and fixing prices.
3. Reduction in tax rates and simplification of tariff structures.
4. Making it easier to import capital goods and technology.
Features of Globalisation:
1. Free flow of capital, technology, and labor across international borders.
2. Integration of the domestic economy with the world economy.
3. Reduction of import tariffs and removal of quantitative trade restrictions.
4. Establishment of global sourcing and multinational market expansion.
In simple words: Liberalisation removes government controls on business, while globalisation integrates national economies into a single global market.
Exam Tip: Clearly separate the domestic deregulation features of liberalization from the international integration features of globalization.

Q12. Define Privatisation. What measures were taken to privatise Indian Economy?
Answer: Privatisation refers to the transfer of ownership, management, and control of public sector enterprises (PSEs) from the government to private entrepreneurs, either partially or entirely.
Measures taken to privatize the Indian economy include:
1. Disinvestment: Selling a part of equity shares of Public Sector Undertakings (PSUs) to the private sector and general public.
2. Denationalization / Outsourcing: Handing over the management and operation of state-owned enterprises or public services to private operators.
3. Withdrawal of government support from loss-making public enterprises and encouraging private entry into previously reserved sectors.
In simple words: Privatization transfers state-owned businesses to private hands, primarily through disinvestment and selling government equity.

Exam Tip: Highlight 'disinvestment' as the principal instrument used by the Indian government to implement privatization.