1————— is a true statement for expressing Loss of information.
A. When the classification of data does not present the details which are available in organised data.
B. When the classification of data does not present the details which are available in raw data.
C. When the classification of data does not present the details which are available in secondary data.
D. When the classification of data does not present the details which are available in time series data.
Answer:
B. When the classification of data does not present the details which are available in raw data.
2.Under exclusive method,
A. The upper class limit of a class is excluded in the class interval.
B. The upper class limit of a class is included in the class interval.
C. The lower class limit of a class is excluded in the class interval.
D. The lower & the upper class limits of a class are included in the class interval.
Answer:
A. The upper class limit of a class is excluded in the class interval.
In the exclusive method, the upper class limit is excluded from the interval, meaning the class includes values strictly less than the upper limit.
3.Identify the statement which is not false:
A. Statistics deals with individuals.
B. Statistics are true only on an average.
C. Statistics deals with qualitative statements only.
D. Statistics does not help in condensing mass data.
Answer:
B. Statistics are true only on an average.
This statement is not false because statistics often involve summarizing data in terms of averages (mean, median, mode) to provide insights about a large set of data
4.————— is a positional average. (1)
A. Arithmetic mean
B. Arithmetic mean & mode
C. Arithmetic mean & median
D. Median
Answer:
D. Median
The median is a positional average because it is determined based on the position of values in a sorted data set, rather than being influenced by the actual values themselves like the arithmetic mean..
5.Read the following statements carefully: (1)
Statement 1 – Simple arithmetic mean is not affected by change of origin.
Statement 2 – Simple arithmetic mean gives equal importance to all items of the series.
Choose the correct alternative:
A. Statement 1 is true and statement 2 is false.
B. Statement 1 is false and statement 2 is true.
C. Both the statements 1 & 2 are true.
D. Both the statements 1 & 2 are false.
Answer:
C. Both the statements 1 & 2 are true.
- Statement 1 is true because the arithmetic mean is not affected by a shift in the origin (i.e., adding or subtracting a constant to all values does not change the mean).
- Statement 2 is also true because the arithmetic mean assigns equal weight to all data points in the series
6.Identify the correct statement/s: (1)
(i) If the difference of consecutive values is equal, r & rk would give identical results.
(ii) In case of presence of extreme values, rk should be preferred over Pearson’s coefficient.
(iii) r < rk or r = rk
Alternatives:
A. (i)
B. (ii)
C. (i) & (ii)
D. (i) & (iii)
Answer:
C. (i) & (ii)
- Statement (i) is correct because when the difference between consecutive values is equal, both Pearson’s correlation coefficient (r) and the rank correlation coefficient (rk) will yield the same result.
- Statement (ii) is also correct because the rank correlation coefficient (rk) is less sensitive to extreme values compared to Pearson’s correlation coefficient (r), so it is preferred in the presence of outliers.
- Statement (iii) is incorrect because r (Pearson’s coefficient) can be greater than rk (rank correlation) in some cases, depending on the distribution of the data.
Identify the incorrect set of statements: (1)
7.Column I | Column II
(i) Interpretation of data | (a) Drawing conclusions
(ii) Presentation of data | (b) Tables, graphs & diagrams
(iii) Statistics | (c) Not numerically expressed
(iv) Scarcity of resources | (d) A cause of economic problem
Alternatives:
A. (i), (a)
B. (ii), (b)
C. (iii), (c)
D. (iv), (d)
Answer:
C. (iii), (c)
- (iii) Statistics refers to data that is usually numerically expressed, not “not numerically expressed,” so this pair is incorrect.
- (i), (a) is correct because interpretation of data involves drawing conclusions.
- (ii), (b) is correct because presentation of data often uses tables, graphs, and diagrams.
- (iv), (d) is correct because scarcity of resources is a fundamental cause of economic problems.
8.Read the following statements: Assertion (A) and Reason (R). (1)
Assertion (A): Economic problem is essentially a problem arising from the necessity of choice.
Reason (R): Since given resources are limited & wants are unlimited, an individual has to make a choice as to which want to be satisfied.
Choose the correct option:
A. Both Assertion (A) and Reason (R) are True and Reason (R) is the correct explanation of Assertion (A).
B. Both Assertion (A) and Reason (R) are True and Reason (R) is not the correct explanation of Assertion (A).
C. Assertion (A) is True but Reason (R) is False.
D. Assertion (A) is False but Reason (R) is True.
Answer:
A. Both Assertion (A) and Reason (R) are True and Reason (R) is the correct explanation of Assertion (A).
The economic problem arises due to the scarcity of resources and the unlimited nature of human wants. This requires individuals and societies to make choices regarding which wants to satisfy, which is explained by Reason (R).
9.Choose the correct sequence of the given functions of statistics related to the formulation of economic plans: (1)
(i) Use of a measure of analysis
(ii) Organisation & presentation of data
(iii) Collection of data
(iv) Interpretation of data & forecasting.
Alternatives:
A. ii, iii, iv, i
B. iii, i, ii, iv
C. iii, ii, i, iv
D. i, iii, ii, iv
Answer:
C. iii, ii, i, iv
The correct sequence is:
- Collection of data (iii) – Gathering the necessary data for analysis.
- Organisation & presentation of data (ii) – Structuring the data for better understanding.
- Use of a measure of analysis (i) – Applying statistical tools to analyze the data.
- Interpretation of data & forecasting (iv) – Drawing conclusions and making future predictions.
10.Index number for base year is: (1)
A. 0
B. 1
C. 10
D. 100
Answer:
D. 100
In the context of index numbers, the base year is typically assigned an index value of 100.
11.Illustrate the meaning of structured questions. List an advantage & disadvantage each of the same in comparison to unstructured questions.
Answer:
Structured questions are those questions that are pre-determined and have fixed response options. They provide a specific set of answers, making it easier to analyze and compare responses.
- Advantage of structured questions:
They provide quantifiable data, are easier to analyze, and are less time-consuming for respondents since the options are predefined. - Disadvantage of structured questions:
They limit the depth of response as respondents are constrained to select from given options, which may not fully capture their opinions or experiences.
Comparison with unstructured questions:
- Unstructured questions allow for more open-ended responses, enabling respondents to provide more detailed, nuanced answers. However, they are more difficult to analyze because they may vary significantly in format and content.
12. Corrected Mean Calculation (4)
In a class of 50 students, the mean marks in English were 58. Later, it was found that two students with marks 40 and 42 joined the class, while it was realized that the marks of a student were wrongly recorded as 25 instead of 20, and the same student left the section. Calculate the corrected mean.
Given:
- Number of students = 50
- Mean marks = 58
- Total marks of 50 students = 50 × 58 = 2900
- Marks of students joining: 40 and 42
- Incorrect mark recorded for a student = 25 (instead of 20), and this student leaves.
Steps:
- Initial total marks = 2900
- Adjust for the two students joining:
The total marks after the two students joined:
New Total Marks=2900+40+42=2982\text{New Total Marks} = 2900 + 40 + 42 = 2982 - Adjust for the student who left:
The student who left had marks recorded as 25 but should have been 20, so the correction is: Corrected Total Marks=2982−25+20=2977\text{Corrected Total Marks} = 2982 – 25 + 20 = 2977 - Total number of students after changes = 50 + 2 – 1 = 51 students
- Corrected mean = 297751\frac{2977}{51} = 58.37 (rounded to two decimal places)
So, the corrected mean marks are 58.37.
13. Median Using Less Than Ogive (4)
Given data:
| X (Class Interval) | Frequency (F) |
|---|---|
| 0-10 | 6 |
| 10-20 | 7 |
| 20-30 | 8 |
| 30-40 | 10 |
| 40-50 | 16 |
| 50-60 | 3 |
Steps:
- Cumulative Frequency (CF):
| X (Class Interval) | Frequency (F) | Cumulative Frequency (CF) |
|---|---|---|
| 0-10 | 6 | 6 |
| 10-20 | 7 | 13 |
| 20-30 | 8 | 21 |
| 30-40 | 10 | 31 |
| 40-50 | 16 | 47 |
| 50-60 | 3 | 50 |
- Median Class:
The total number of students (N) = 50.
The median class corresponds to the cumulative frequency just greater than or equal to N2=502=25\frac{N}{2} = \frac{50}{2} = 25.
So, the median class is 30-40, where CF = 31.
- Median Formula:
Median=L+(N2−CFf)×h\text{Median} = L + \left( \frac{\frac{N}{2} – CF}{f} \right) \times h
Where:
- LL = Lower class boundary of median class = 30
- NN = Total frequency = 50
- CFCF = Cumulative frequency before the median class = 21
- ff = Frequency of median class = 10
- hh = Class width = 10
Median=30+(25−2110)×10=30+(410)×10=30+4=34\text{Median} = 30 + \left( \frac{25 – 21}{10} \right) \times 10 = 30 + \left( \frac{4}{10} \right) \times 10 = 30 + 4 = 34
So, the median is 34.
14. Mode Calculation (4)
Given data:
| Marks More Than | No. of Students |
|---|---|
| 0 | 15 |
| 20 | 13 |
| 40 | 9 |
| 60 | 3 |
| 80 | 1 |
Steps:
- Calculate the frequencies for each class interval by subtracting the “more than” values:
| Marks (Class Interval) | Frequency (f) |
|---|---|
| 0-20 | 15 |
| 20-40 | 13 – 9 = 4 |
| 40-60 | 9 – 3 = 6 |
| 60-80 | 3 – 1 = 2 |
| 80-100 | 1 |
- Identify the modal class:
The modal class is the class with the highest frequency. Here, the frequency is highest in the 40-60 range, with a frequency of 6. - Mode Formula:
Mode=L+(f1−f02f1−f0−f2)×h\text{Mode} = L + \left( \frac{f_1 – f_0}{2f_1 – f_0 – f_2} \right) \times h
Where:
- LL = Lower boundary of the modal class = 40
- f1f_1 = Frequency of the modal class = 6
- f0f_0 = Frequency of the class before the modal class = 4
- f2f_2 = Frequency of the class after the modal class = 2
- hh = Class width = 20
Mode=40+(6−42(6)−4−2)×20\text{Mode} = 40 + \left( \frac{6 – 4}{2(6) – 4 – 2} \right) \times 20 Mode=40+(212−4)×20=40+(28)×20=40+5=45\text{Mode} = 40 + \left( \frac{2}{12 – 4} \right) \times 20 = 40 + \left( \frac{2}{8} \right) \times 20 = 40 + 5 = 45
So, the mode is 45.
15. Uses of Index Numbers in Economics (4)
Uses of Index Numbers:
- Measurement of Inflation: Index numbers are used to measure inflation by comparing the price levels of a basket of goods over time.
- Economic Planning: They help in assessing economic performance and guiding policy decisions by comparing data over time or between different regions.
- Comparing Economic Performance: Index numbers allow for comparing the performance of various sectors of the economy, such as agriculture or industry.
- Price Comparison: They help compare prices across different locations or over different periods, aiding businesses and governments in making informed decisions.
OR
(i) Wholesale Price Index (WPI):
If the WPI for week 1 = 800 and for week 2 = 880, the weekly rate of inflation is calculated as: Rate of Inflation=(WPI in Week 2−WPI in Week 1WPI in Week 1)×100\text{Rate of Inflation} = \left( \frac{\text{WPI in Week 2} – \text{WPI in Week 1}}{\text{WPI in Week 1}} \right) \times 100 Rate of Inflation=(880−800800)×100=(80800)×100=10%\text{Rate of Inflation} = \left( \frac{880 – 800}{800} \right) \times 100 = \left( \frac{80}{800} \right) \times 100 = 10\%
So, the weekly rate of inflation is 10%.
(ii) Price Index Number & Simple Aggregative Method:
- Price Index Number: An index number is a statistical measure designed to show changes in a variable or a group of related variables over time.
- Simple Aggregative Method: This method calculates the price index by taking the sum of prices in the current period, dividing it by the sum of prices in the base period, and multiplying by 100:
Price Index=(∑Current Prices∑Base Prices)×100\text{Price Index} = \left( \frac{\sum \text{Current Prices}}{\sum \text{Base Prices}} \right) \times 100
16. Tabulation of Data (6)
(i) Tabulate the given information for the educational exchange trip:
| Year | Number of Girls | Number of Boys | Total Students | Number of Teachers | Female Teachers |
|---|---|---|---|---|---|
| 2023 | 40 | 20 | 60 | 5 | 3 |
| 2024 | 1/4 of 80 = 20 | 60 – 20 = 60 | 80 | 6 | 3 |
(ii) Pie Diagram for Expenditure Data:
| Item | A | B | C | D |
|---|---|---|---|---|
| Expenditure (%) | 50 | 15 | 10 | 25 |
17. Coefficient of Correlation using Spearman’s Rank (6)
Given:
| X | 90 | 88 | 78 | 78 | 74 | 70 | 65 | 62 |
|---|---|---|---|---|---|---|---|---|
| Y | 18 | 25 | 30 | 30 | 30 |
42 | 38 | 47 |
Spearman’s Rank Method:
- Assign ranks to each value for X and Y.
- Calculate the difference in ranks (d).
- Square the differences (d²).
- Apply the formula:
ρ=1−6∑d2n(n2−1)\rho = 1 – \frac{6 \sum d^2}{n(n^2 – 1)}
Where n = number of pairs.
OR
Properties of Correlation Coefficient:
- Range: The correlation coefficient lies between -1 and 1.
- Symmetry: The correlation between X and Y is the same as between Y and X.
- Magnitude: The closer the correlation coefficient is to ±1, the stronger the correlation.
- Linearity: The coefficient measures the linear relationship between variables, not necessarily causal relationships.
Here are the answers to the provided questions:
18. The factor causing extension in supply of a good is (1)
(D) Increase in price of the good.
Explanation: An increase in the price of a good typically leads to an extension in supply, as producers are willing to supply more of the good at higher prices.
19. Coefficient of Inelastic supply is (1)
(C) Zero.
Explanation: Inelastic supply means that the quantity supplied does not respond significantly to changes in price, which is represented by a coefficient of elasticity that is less than one, approaching zero.
20. Match the statements in Column A and B (1)
| COLUMN A | COLUMN B |
|---|---|
| (i) Buffer Stock | (d) A consequence of price support program |
| (ii) Price floor | (c) Price fixed above equilibrium |
| (iii) Rationing | (a) Price fixed below equilibrium |
| (iv) Price ceiling and support price | (b) Direct intervention by government |
Answer: (A) (i) d (ii) c (iii) a (iv) b
21. In the following questions, Statement 1 is followed by Statement 2. (1)
Statement 1: Positive statements do not pass any value judgment.
Statement 2: Normative statements are verifiable.
Answer: (C) Statement 1 is true and Statement 2 is false.
Explanation: Positive statements are objective and fact-based, without value judgment, while normative statements are subjective and concerned with what ought to be. Normative statements are not verifiable since they express opinions or beliefs.
22. Read the following statements: Assertion (A) and Reason (R). (1)
Assertion (A): A rational producer always seeks to operate in Phase II of the Law of Variable Proportions.
Reason (R): In Phase II of the Law of Variable Proportions, Marginal Product is negative.
Answer: (C) Assertion (A) is True but Reason (R) is False.
Explanation: Phase II of the Law of Variable Proportions is the stage where the marginal product is positive but diminishing. A rational producer seeks to operate in this phase, not the one where marginal product becomes negative (which occurs in Phase III).
23. Price of a good ‘X’ rises from 20 per unit to 40 per unit. The consumer buys the same quantity, he bought at 20 per unit. What would be price elasticity of demand? (1)
Answer: (B) Zero.
Explanation: If the consumer buys the same quantity despite the price doubling, the price elasticity of demand is zero, meaning demand is perfectly inelastic.
24. All the curves except________ are U-shaped curves: (1)
(A) Average Fixed Cost Curve.
Explanation: The Average Fixed Cost curve is always downward sloping and does not have a U-shape, unlike the Average Cost, Average Variable Cost, and Marginal Cost curves.
25. Budget set includes: (1)
(D) All those combinations of two goods which a consumer can afford.
Explanation: A budget set shows all the possible combinations of goods that a consumer can purchase given their income and the prices of the goods.
26. Which Law states that: “When a consumer consumes more and more units of a product, the utility derived from each additional unit decreases”? (1)
(D) Law of Diminishing Marginal Utility.
Explanation: The Law of Diminishing Marginal Utility states that as a person consumes more units of a good, the additional satisfaction (utility) gained from consuming each additional unit decreases.
Here are brief answers for the given questions:
Q27. Based on the given schedule, state the effect on the demand curve: (3)
PRICE (Rs) | QUANTITY (Kg)
4 | 50
4 | 30
Answer: (A) Leftward shift of demand curve.
Explanation: As the price remains constant but the quantity demanded decreases from 50 to 30, it suggests a leftward shift in the demand curve, indicating a decrease in demand at that price.
Q28. The government establishes a large number of institutes of Science and technology. How will it affect the PPC? Explain. (3)
Answer:
The establishment of more science and technology institutes will lead to better education, skill development, and technological advancements. This increases human capital, which enhances the production capacity of the economy, shifting the Production Possibility Curve (PPC) outward, indicating growth in the economy’s potential output.
OR
Explanation:
If production is below potential due to unemployment and the government starts employment generation schemes, more people will be employed. This will increase the economy’s total output, leading to a rightward shift in the PPC, as resources are being fully utilized.
Q29. “In a perfectly competitive market, buyers treat products by all the firms homogeneous.” Explain the significance of homogeneity of goods in a perfectly competitive market. (4)
Answer:
In a perfectly competitive market, all firms produce identical or homogeneous products. This means that consumers do not differentiate between products from different firms and are willing to buy from the firm offering the lowest price. This ensures perfect competition where firms are price takers, not price makers. Homogeneity leads to uniform pricing and efficient allocation of resources.
Q30. With the help of a diagram, explain the effect of the increase in the level of air pollution on the market demand curve for Air Purifiers in Delhi. (4)
Answer:
As air pollution increases in Delhi, people become more aware of health risks and demand more air purifiers. This causes a rightward shift in the demand curve, as consumers are now willing to purchase more at every price level. The demand curve for air purifiers shifts to the right due to increased awareness of pollution.
OR
(i) If the price of good X increases, the demand for X will decrease, causing the demand curve to shift leftward.
(ii) If the income of the consumer increases, the demand for good X will increase, causing the demand curve to shift rightward.
Q31. Delhites witnessed a sharp rise in temperature in summer this year. This has rapidly increased the demand for cotton shirts in the market. On the other hand, India witnessed bumper cotton produce due to favourable climate conditions. (4)
(I) The bumper cotton produce will increase the supply of cotton shirts as more raw materials are available. This will lead to a rightward shift in the supply curve.
(II) If the increase in demand is equal to the increase in supply, the equilibrium price will remain the same, but the equilibrium quantity will increase. This will result in a higher quantity of cotton shirts being sold, but the price might stay stable.
Q32. PRICE (Rs) | OUTPUT (Units) | TOTAL REVENUE (Rs) | MARGINAL REVENUE (Rs)
7 | – | 7 | –
- | 2 | 10 | –
- | 3 | – | -1
1 | – | – | -5
Answer:
To fill the missing values:
- Marginal revenue = Change in total revenue / Change in output.
For output 2, MR = (10-0) / (2-0) = 5.
For output 3, MR = (unknown value) – 10. We need to calculate further.
Q33. A consumer consumes only two goods X and Y whose prices are Rs 2 and Rs 1 per unit respectively. If the consumer chooses a combination of the two goods with marginal utility of X being 4 and that of Y also being 4, Is the consumer in equilibrium? Give reasons. Explain what will a rational consumer do in this situation? Use Marginal Utility Analysis. (6)
Answer:
The consumer is not in equilibrium. In equilibrium, the ratio of marginal utility to price (MU/P) should be equal for both goods.
For X: MU/P = 4/2 = 2
For Y: MU/P = 4/1 = 4
Since the ratio for Y is higher, the rational consumer will buy more of good Y and less of good X until the marginal utility per unit of money spent is equal for both goods, achieving equilibrium.
Q34. The equality of marginal cost and marginal revenue is a condition necessary for equilibrium, but it is not by itself sufficient to assure the attainment of producer’s equilibrium. Comment. (6)
Answer:
The condition that marginal cost (MC) equals marginal revenue (MR) is necessary for producer equilibrium, as it ensures the firm is producing at an optimal level. However, this condition alone does not guarantee equilibrium because:
- The firm must also check if MC is rising (ensuring profit maximization).
- If MC is falling after the point where MR = MC, the firm may still not be in equilibrium. Thus, a rising MC beyond the point of MR = MC is also necessary for equilibrium.
OR
Explanation:
When agricultural land is limited and demand for food grains is increasing, it is not possible to increase food grain supply indefinitely by increasing just one input, such as seeds. This is due to the Law of Diminishing Returns, which states that as more of a variable input (seeds) is added to a fixed input (land), the marginal product of the variable input will eventually decrease. This law is illustrated with a curve that shows the diminishing returns to increasing one input in the presence of limited resources.