Single Best Answer MCQs for Sub-Topics of Topic 14: Index Numbers & Time-Based Data

Question 1. What is an index number?

(A) A ratio of two different quantities at the same time

(B) A statistical device for measuring relative change in a group of related variables over time or space

(C) A measure of absolute change in a single variable

(D) A graphical representation of data trends

Question 2. The primary purpose of constructing index numbers is to:

(A) Calculate the average value of a series

(B) Measure absolute changes in economic variables

(C) Facilitate comparison of the change in magnitude of a group of related variables

(D) Forecast future values of a single variable

Question 3. Which of the following is NOT a characteristic of index numbers?

(A) They are expressed in percentages

(B) They measure relative changes

(C) They compare values at different times or places

(D) They always use quantities as the basis for comparison

Question 4. The base period in index number construction is:

(A) The period for which the index is being calculated

(B) The period against which comparisons are made

(C) Always the most recent period

(D) The period with the highest values

Question 5. The value of an index number for the base period is conventionally taken as:

(A) 0

(B) 10

(C) 100

(D) 1000

Question 6. The current period in index number construction is:

(A) The period used for comparison

(B) The period chosen as the base

(C) The period for which the index is being calculated

(D) Always a period in the past

Question 7. A price relative for a single commodity is calculated as:

(A) $\frac{\text{Price in current period}}{\text{Price in base period}} \times 100$

(B) $\frac{\text{Price in base period}}{\text{Price in current period}} \times 100$

(C) Price in current period - Price in base period

(D) Price in current period + Price in base period

Question 8. A quantity relative for a single commodity is calculated as:

(A) $\frac{\text{Quantity in base period}}{\text{Quantity in current period}} \times 100$

(B) $\frac{\text{Quantity in current period}}{\text{Quantity in base period}} \times 100$

(C) Quantity in current period - Quantity in base period

(D) Quantity in current period + Quantity in base period

Question 9. If the price relative for a commodity is 125 in the current period, it means the price has:

(A) Decreased by 25% compared to the base period

(B) Increased by 25% compared to the base period

(C) Increased by 125% compared to the base period

(D) Decreased by 125% compared to the base period

Question 10. If the quantity relative for a commodity is 80 in the current period, it means the quantity has:

(A) Increased by 20% compared to the base period

(B) Decreased by 80% compared to the base period

(C) Decreased by 20% compared to the base period

(D) Increased by 80% compared to the base period

Question 11. Index numbers are often called:

(A) Economic indicators

(B) Statistical barometers

(C) Price aggregators

(D) Time series analysts

Question 12. When selecting a base period, it is desirable that it is:

(A) A period of economic stability

(B) A period of economic boom

(C) A period of economic recession

(D) The most recent period available

Question 13. Shifting the base of an index number series means:

(A) Changing the current period to the base period

(B) Expressing the index numbers relative to a new base period

(C) Multiplying the index numbers by a constant

(D) Dividing the index numbers by 100

Question 14. Linking of index number series is done when:

(A) The base period changes frequently

(B) Different index series need to be combined into a continuous series

(C) The index numbers are very large

(D) The commodities included in the index change over time

Question 15. Index numbers are used to measure changes in:

(A) Prices only

(B) Quantities only

(C) Values only

(D) Prices, quantities, or values

Question 16. Which of the following is a major use of index numbers in economics?

(A) Measuring national income

(B) Analyzing the cost of living

(C) Calculating population growth

(D) Determining interest rates

Question 17. A simple price relative is:

(A) The price of a single commodity in the current period

(B) The ratio of the price of a single commodity in the current period to its price in the base period, multiplied by 100

(C) The average of prices of several commodities

(D) The total price of a basket of goods

Question 18. If the price of commodity A in 2020 was $\textsf{₹}50$ and in 2023 was $\textsf{₹}60$, taking 2020 as the base year, the price relative for 2023 is:

(A) $\frac{50}{60} \times 100 = 83.33$

(B) $\frac{60}{50} \times 100 = 120$

(C) $60 - 50 = 10$

(D) $\frac{60}{50} = 1.2$

Question 19. If the quantity of commodity B produced in 2021 was 1000 units and in 2024 was 1200 units, taking 2021 as the base year, the quantity relative for 2024 is:

(A) $\frac{1000}{1200} \times 100 = 83.33$

(B) $\frac{1200}{1000} \times 100 = 120$

(C) $1200 - 1000 = 200$

(D) $\frac{1200}{1000} = 1.2$

Question 20. Index numbers are valuable tools for:

(A) Only government agencies

(B) Only businesses

(C) Only researchers

(D) Government, businesses, researchers, and general public

Question 21. A change in an index number from 150 to 165 represents a percentage increase of:

(A) 10%

(B) 15%

(C) 25%

(D) 115%

Question 22. If the price index is 180 in the current year with 2015 as base year (Index = 100), it indicates that prices have:

(A) Increased by 80% since 2015

(B) Increased by 180% since 2015

(C) Decreased by 20% since 2015

(D) Are 180% of the base year prices

Question 23. Which of the following is generally used as a base period?

(A) A year of war

(B) A year with abnormal price fluctuations

(C) A normal year with relative stability

(D) Any random year

Question 24. Price relatives help us to understand the relative change in price of:

(A) A group of commodities

(B) A single commodity

(C) Total expenditure

(D) Average price level

Question 25. A quantity index number measures the change in:

(A) Total value of commodities

(B) Average price level

(C) Volume of production or consumption

(D) Cost of living

Question 1. In the Simple Aggregate Method for constructing a price index, the index number is calculated as:

(A) The average of price relatives

(B) The ratio of the sum of current year prices to the sum of base year prices, multiplied by 100

(C) The product of price relatives

(D) The average of weighted price relatives

Question 2. The formula for Simple Aggregate Price Index ($P_{01}$) is:

(A) $P_{01} = \frac{\sum p_1}{\sum p_0} \times 100$

(B) $P_{01} = \frac{\sum p_0}{\sum p_1} \times 100$

(C) $P_{01} = \frac{1}{n} \sum \left(\frac{p_1}{p_0} \times 100\right)$

(D) $P_{01} = \frac{\sum p_1 q_1}{\sum p_0 q_0} \times 100$

Question 3. The Simple Aggregate Quantity Index ($Q_{01}$) is calculated using the formula:

(A) $Q_{01} = \frac{\sum q_1}{\sum q_0} \times 100$

(B) $Q_{01} = \frac{\sum p_1}{\sum p_0} \times 100$

(C) $Q_{01} = \frac{1}{n} \sum \left(\frac{q_1}{q_0} \times 100\right)$

(D) $Q_{01} = \frac{\sum p_0 q_1}{\sum p_0 q_0} \times 100$

Question 4. A major limitation of the Simple Aggregate Method for constructing a price index is that it is affected by:

(A) The number of commodities included

(B) The units in which prices are quoted

(C) The choice of base period

(D) Changes in quantities consumed

Question 5. In the Simple Average of Price Relatives method, the index is calculated by:

(A) Summing the price relatives and dividing by the number of commodities

(B) Summing the current prices and dividing by the number of commodities

(C) Taking the arithmetic mean of the ratios of sum of prices

(D) Taking the geometric mean of price relatives

Question 6. The formula for Simple Average of Price Relatives Index ($P_{01}$) using Arithmetic Mean is:

(A) $P_{01} = \frac{\sum p_1}{\sum p_0} \times 100$

(B) $P_{01} = \frac{1}{n} \sum \left(\frac{p_1}{p_0}\right) \times 100$

(C) $P_{01} = \left(\prod \frac{p_1}{p_0}\right)^{1/n} \times 100$

(D) $P_{01} = \frac{\sum (p_1/p_0) w}{\sum w} \times 100$

Question 7. If using Geometric Mean in the Simple Average of Price Relatives method, the formula for $P_{01}$ is:

(A) $P_{01} = \frac{1}{n} \sum \left(\frac{p_1}{p_0} \times 100\right)$

(B) $P_{01} = \left(\prod_{i=1}^n \frac{p_{1i}}{p_{0i}}\right)^{1/n} \times 100$

(C) $P_{01} = \frac{\sum p_1}{\sum p_0} \times 100$

(D) $P_{01} = \frac{\text{GM of } p_1}{\text{GM of } p_0} \times 100$

Question 8. Which simple method is not affected by the units in which prices are quoted?

(A) Simple Aggregate Method

(B) Simple Average of Price Relatives Method

(C) Both methods are affected

(D) Neither method is affected

Question 9. Let's say prices of three commodities in 2022 (base) were $\textsf{₹}10, \textsf{₹}20, \textsf{₹}30$, and in 2023 (current) were $\textsf{₹}12, \textsf{₹}25, \textsf{₹}36$. The Simple Aggregate Price Index for 2023 (base 2022) is:

(A) $\frac{(10+20+30)}{(12+25+36)} \times 100 = \frac{60}{73} \times 100 \approx 82.19$

(B) $\frac{(12+25+36)}{(10+20+30)} \times 100 = \frac{73}{60} \times 100 \approx 121.67$

(C) $\frac{1}{3} \left(\frac{12}{10} + \frac{25}{20} + \frac{36}{30}\right) \times 100$

(D) $\left(\frac{12}{10} \times \frac{25}{20} \times \frac{36}{30}\right)^{1/3} \times 100$

Question 10. Using the same data as Question 9, the price relatives for 2023 (base 2022) are:

(A) 1.2, 1.25, 1.2

(B) 120, 125, 120

(C) 0.833, 0.8, 0.833

(D) 83.3, 80, 83.3

Question 11. Using the data from Question 9, the Simple Average of Price Relatives Index (Arithmetic Mean) for 2023 (base 2022) is:

(A) $\frac{1}{3} (1.2 + 1.25 + 1.2) \times 100 = \frac{3.65}{3} \times 100 \approx 121.67$

(B) $\frac{1}{3} (120 + 125 + 120) = \frac{365}{3} \approx 121.67$

(C) $\frac{1}{3} (83.3 + 80 + 83.3) = \frac{246.6}{3} \approx 82.2$

(D) $\frac{(12+25+36)}{(10+20+30)} \times 100 \approx 121.67$

Question 12. The Simple Aggregate Method gives equal importance to the absolute price change of each commodity, regardless of its significance. This is a:

(A) Strength of the method

(B) Limitation of the method

(C) Feature that makes it ideal

(D) Benefit for all types of index numbers

Question 13. The Simple Average of Price Relatives Method is affected by:

(A) The units in which quantities are measured

(B) The units in which prices are measured

(C) The presence of extreme price relatives

(D) The total sum of prices

Question 14. If one commodity's price drops from $\textsf{₹}100$ to $\textsf{₹}10$ and another's increases from $\textsf{₹}10$ to $\textsf{₹}20$, which simple method is likely to be more distorted?

(A) Simple Aggregate Method

(B) Simple Average of Price Relatives Method (using AM)

(C) Both methods equally

(D) Neither method is significantly distorted

Question 15. Simple index number methods do not account for the relative importance or weights of different commodities. This is their primary:

(A) Advantage

(B) Limitation

(C) Feature

(D) Purpose

Question 16. The Simple Average of Price Relatives Method is sometimes preferred over the Simple Aggregate Method because:

(A) It is easier to calculate

(B) It is not affected by the units of measurement for prices

(C) It implicitly gives weight to expensive commodities

(D) It accounts for quantity changes

Question 17. For calculating a simple quantity index, the Simple Aggregate Method uses the ratio of the sum of:

(A) Current year quantities to base year quantities

(B) Current year prices to base year prices

(C) Base year quantities to current year quantities

(D) Current year values to base year values

Question 18. Let's say quantities of three commodities in 2022 (base) were 100, 200, 50 and in 2023 (current) were 120, 220, 60. The Simple Aggregate Quantity Index for 2023 (base 2022) is:

(A) $\frac{(100+200+50)}{(120+220+60)} \times 100 = \frac{350}{400} \times 100 = 87.5$

(B) $\frac{(120+220+60)}{(100+200+50)} \times 100 = \frac{400}{350} \times 100 \approx 114.28$

(C) $\frac{1}{3} \left(\frac{120}{100} + \frac{220}{200} + \frac{60}{50}\right) \times 100$

(D) $\frac{\sum q_1 p_0}{\sum q_0 p_0} \times 100$

Question 19. The Simple Average of Quantity Relatives method can be used to construct a quantity index. What is the formula using Arithmetic Mean?

(A) $\frac{\sum q_1}{\sum q_0} \times 100$

(B) $\frac{1}{n} \sum \left(\frac{q_1}{q_0}\right) \times 100$

(C) $\frac{1}{n} \sum \left(\frac{p_1}{p_0}\right) \times 100$

(D) $\frac{\sum p_1 q_1}{\sum p_0 q_0} \times 100$

Question 20. Simple index number methods are most suitable when:

(A) The commodities have significantly different importance

(B) There are major price fluctuations

(C) There is no basis for assigning weights to commodities

(D) High accuracy is required

Question 21. If commodities A and B have prices $\textsf{₹}10, \textsf{₹}100$ in the base year and $\textsf{₹}20, \textsf{₹}110$ in the current year. In the Simple Aggregate Price Index, the absolute increase of $\textsf{₹}10$ for A and $\textsf{₹}10$ for B have equal impact. This illustrates the limitation regarding:

(A) Choice of base year

(B) Units of measurement

(C) Absence of weights

(D) Formula complexity

Question 22. If using Simple Average of Price Relatives (AM), commodities A and B have base prices $\textsf{₹}10, \textsf{₹}100$ and current prices $\textsf{₹}20, \textsf{₹}110$. The price relative for A is 200 and for B is 110. The average index is $\frac{200+110}{2} = 155$. This illustrates that the method is affected by:

(A) Units of measurement

(B) Base year quantities

(C) Extreme price changes leading to extreme relatives

(D) Total sum of current prices

Question 23. Both Simple Aggregate and Simple Average of Price Relatives methods share the common limitation of not considering:

(A) Time reversal test

(B) The relative importance of commodities

(C) The current year values

(D) The number of items in the basket

Question 24. Which simple method gives equal importance to the percentage change in price of each commodity?

(A) Simple Aggregate Method

(B) Simple Average of Price Relatives Method

(C) Neither method

(D) Both methods equally

Question 25. Consider a basket of goods with base year prices $\textsf{₹}10, \textsf{₹}50$ and current year prices $\textsf{₹}15, \textsf{₹}60$. Simple Aggregate Price Index is:

(A) $\frac{10+50}{15+60} \times 100 = \frac{60}{75} \times 100 = 80$

(B) $\frac{15+60}{10+50} \times 100 = \frac{75}{60} \times 100 = 125$

(C) $\frac{1}{2}(\frac{15}{10} \times 100 + \frac{60}{50} \times 100) = \frac{1}{2}(150 + 120) = 135$

(D) $\left(\frac{15}{10} \times \frac{60}{50}\right)^{1/2} \times 100 = (1.5 \times 1.2)^{1/2} \times 100 = (1.8)^{1/2} \times 100 \approx 134.16$

Question 26. Using the data from Question 25, the Simple Average of Price Relatives Index (Arithmetic Mean) is:

(A) 80

(B) 125

(C) 135

(D) 134.16

Question 1. Weighted index numbers are preferred over simple index numbers because they:

(A) Are easier to calculate

(B) Account for the relative importance of different commodities

(C) Are not affected by the base period choice

(D) Only consider price changes, not quantity changes

Question 2. In weighted aggregate methods, weights are usually based on:

(A) The number of units sold

(B) The price of the commodity

(C) The quantity of the commodity consumed or produced

(D) The arbitrary choice of the statistician

Question 3. Laspeyres Price Index ($P_{01}^L$) uses weights based on:

(A) Base period quantities

(B) Current period quantities

(C) Average of base and current period quantities

(D) Base period values ($p_0 q_0$)

Question 4. The formula for Laspeyres Price Index is:

(A) $P_{01}^L = \frac{\sum p_1 q_1}{\sum p_0 q_0} \times 100$

(B) $P_{01}^L = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$

(C) $P_{01}^L = \frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100$

(D) $P_{01}^L = \sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_0 q_1}} \times 100$

Question 5. Paasche Price Index ($P_{01}^P$) uses weights based on:

(A) Base period quantities

(B) Current period quantities

(C) Average of base and current period quantities

(D) Current period values ($p_1 q_1$)

Question 6. The formula for Paasche Price Index is:

(A) $P_{01}^P = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$

(B) $P_{01}^P = \frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100$

(C) $P_{01}^P = \frac{\sum p_1 q_1}{\sum p_0 q_0} \times 100$

(D) $P_{01}^P = \sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_0 q_1}} \times 100$

Question 7. Laspeyres index tends to overstate the price rise because it uses base period quantities. This does not account for the likely consumer behavior of:

(A) Increasing consumption of all goods

(B) Shifting consumption towards relatively cheaper goods

(C) Decreasing consumption of all goods

(D) Keeping consumption levels constant

Question 8. Paasche index tends to understate the price rise because it uses current period quantities. This implicitly reflects the consumer behavior of:

(A) Increasing consumption of relatively more expensive goods

(B) Decreasing consumption of all goods

(C) Increasing consumption of goods whose relative price has increased

(D) Shifting consumption towards relatively cheaper goods in the current period

Question 9. Fisher's Ideal Index is considered 'ideal' because it is the geometric mean of:

(A) Simple Aggregate and Simple Average of Relatives indices

(B) Laspeyres and Paasche indices

(C) Base year and current year quantities

(D) Base year and current year prices

Question 10. The formula for Fisher's Ideal Price Index ($P_{01}^F$) is:

(A) $P_{01}^F = \frac{P_{01}^L + P_{01}^P}{2} \times 100$

(B) $P_{01}^F = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$

(C) $P_{01}^F = \sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_0 q_1}} \times 100$

(D) $P_{01}^F = \sqrt{P_{01}^L \times P_{01}^P}$

Question 11. Marshall-Edgeworth Index ($P_{01}^{ME}$) uses weights based on:

(A) Base period quantities

(B) Current period quantities

(C) Arithmetic mean of base and current period quantities

(D) Geometric mean of base and current period quantities

Question 12. The formula for Marshall-Edgeworth Price Index is:

(A) $P_{01}^{ME} = \frac{\sum p_1 (q_0 + q_1)}{\sum p_0 (q_0 + q_1)} \times 100$

(B) $P_{01}^{ME} = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$

(C) $P_{01}^{ME} = \frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100$

(D) $P_{01}^{ME} = \frac{\sum p_1 \sqrt{q_0 q_1}}{\sum p_0 \sqrt{q_0 q_1}} \times 100$

Question 13. Which weighted index number formula is a geometric mean of Laspeyres and Paasche?

(A) Marshall-Edgeworth Index

(B) Fisher's Ideal Index

(C) Weighted Average of Price Relatives

(D) Simple Aggregate Method

Question 14. In the Weighted Average of Price Relatives method, the weights used are typically based on:

(A) Current period quantities

(B) Base period quantities

(C) Base period values ($\textsf{₹} = p_0 q_0$)

(D) Current period values ($p_1 q_1$)

Question 15. The formula for Weighted Average of Price Relatives ($P_{01}^{WAR}$) using base period value weights ($W = p_0 q_0$) is:

(A) $P_{01}^{WAR} = \frac{\sum (\frac{p_1}{p_0}) W}{\sum W} \times 100$

(B) $P_{01}^{WAR} = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$

(C) $P_{01}^{WAR} = \frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100$

(D) $P_{01}^{WAR} = \frac{\sum p_1 q_0}{\sum p_0 q_1} \times 100$

Question 16. The Weighted Average of Price Relatives method with base year value weights is equivalent to:

(A) Simple Aggregate Method

(B) Laspeyres Price Index

(C) Paasche Price Index

(D) Fisher's Ideal Index

Question 17. Let's consider two commodities: Rice and Gold. Base year prices: Rice $\textsf{₹}40$/kg, Gold $\textsf{₹}40000$/10g. Base year quantities: Rice 1000 kg, Gold 10g. If we use Simple Aggregate Price Index, the price change in Gold will dominate heavily over Rice due to its high price. Which method addresses this issue?

(A) Simple Average of Price Relatives

(B) Weighted Aggregate Methods

(C) Neither Simple nor Weighted methods

(D) Simple methods are better in this case

Question 18. A major advantage of Laspeyres method is that it:

(A) Reflects current consumption patterns accurately

(B) Only requires base period quantity data for calculation over multiple periods

(C) Tends to understate price increases

(D) Satisfies the Factor Reversal Test

Question 19. A major disadvantage of Paasche method is that it:

(A) Tends to overstate price increases

(B) Requires current period quantity data for each period's calculation, which can be costly or difficult to obtain

(C) Does not satisfy the Time Reversal Test

(D) Uses outdated consumption patterns

Question 20. Fisher's Ideal Index is considered the "ideal" index because it:

(A) Is the easiest to calculate

(B) Satisfies both Time Reversal and Factor Reversal tests

(C) Only requires price data

(D) Uses current period quantities as weights

Question 21. Marshall-Edgeworth Index is often considered a good compromise between Laspeyres and Paasche because its weights are based on the average of base and current period quantities, making it:

(A) Easier to calculate than Laspeyres

(B) More theoretical than practical

(C) Less prone to the substitution bias inherent in Laspeyres and Paasche

(D) Satisfies the Circular Test

Question 22. If base year prices are $\textsf{₹}10, \textsf{₹}12$ and quantities are $100, 50$. Current year prices are $\textsf{₹}15, \textsf{₹}18$ and quantities are $80, 60$. Calculate $\sum p_0 q_0$:

(A) $10 \times 100 + 12 \times 50 = 1000 + 600 = 1600$

(B) $15 \times 80 + 18 \times 60 = 1200 + 1080 = 2280$

(C) $10 \times 80 + 12 \times 60 = 800 + 720 = 1520$

(D) $15 \times 100 + 18 \times 50 = 1500 + 900 = 2400$

Question 23. Using the data from Question 22, calculate $\sum p_1 q_0$:

(A) 1600

(B) 2280

(C) 1520

(D) $15 \times 100 + 18 \times 50 = 1500 + 900 = 2400$

Question 24. Using the data from Question 22, calculate $\sum p_0 q_1$:

(A) 1600

(B) 2280

(C) $10 \times 80 + 12 \times 60 = 800 + 720 = 1520$

(D) 2400

Question 25. Using the data from Question 22, calculate $\sum p_1 q_1$:

(A) 1600

(B) $15 \times 80 + 18 \times 60 = 1200 + 1080 = 2280$

(C) 1520

(D) 2400

Question 26. Using the data from Question 22, the Laspeyres Price Index ($P_{01}^L$) is:

(A) $\frac{1520}{1600} \times 100 = 95$

(B) $\frac{2400}{1600} \times 100 = 150$

(C) $\frac{2280}{1520} \times 100 = 150$

(D) $\frac{2400}{1520} \times 100 \approx 157.89$

Question 27. Using the data from Question 22, the Paasche Price Index ($P_{01}^P$) is:

(A) $\frac{2400}{1600} \times 100 = 150$

(B) $\frac{2280}{1520} \times 100 = 150$

(C) $\frac{1520}{1600} \times 100 = 95$

(D) $\frac{2280}{1600} \times 100 \approx 142.5$

Question 28. Using the data from Question 22, Fisher's Ideal Price Index ($P_{01}^F$) is approximately:

(A) $\sqrt{150 \times 150} = 150$

(B) $\sqrt{150 \times 142.5} \approx \sqrt{21375} \approx 146.19$

(C) $\sqrt{95 \times 150} \approx \sqrt{14250} \approx 119.37$

(D) $\sqrt{150 \times 95} \approx 119.37$

Question 29. The Weighted Average of Price Relatives method gives weight to each price relative based on the commodity's importance, usually measured by its share in total expenditure in the base period. This makes it similar to which index?

(A) Simple Aggregate Index

(B) Laspeyres Index

(C) Paasche Index

(D) Marshall-Edgeworth Index

Question 30. If weights in the Weighted Average of Price Relatives method are taken as $p_0 q_0$, which index is obtained?

(A) Simple Aggregate Index

(B) Laspeyres Index

(C) Paasche Index

(D) Fisher's Ideal Index

Question 31. If weights in the Weighted Average of Price Relatives method are taken as $p_0 q_1$, this does not correspond directly to a standard weighted aggregate index like Laspeyres or Paasche. This type of weighting might be used for specific purposes but is not common for general price index construction like CPI or WPI. It uses current quantities with base prices. This might relate to a theoretical calculation but isn't a standard named index. Which standard index uses $p_0 q_1$ in its calculation?

(A) Laspeyres Price Index denominator

(B) Paasche Price Index numerator

(C) Paasche Quantity Index numerator

(D) Laspeyres Quantity Index denominator

Question 32. Weighted quantity indices are also constructed using Laspeyres, Paasche, Fisher, and Marshall-Edgeworth formulas, where the roles of price and quantity are interchanged in the weights. For example, the Laspeyres Quantity Index ($Q_{01}^L$) uses weights based on:

(A) Base period quantities

(B) Current period quantities

(C) Base period prices

(D) Current period prices

Question 33. The formula for Laspeyres Quantity Index ($Q_{01}^L$) is:

(A) $Q_{01}^L = \frac{\sum q_1 p_0}{\sum q_0 p_0} \times 100$

(B) $Q_{01}^L = \frac{\sum q_1 p_1}{\sum q_0 p_1} \times 100$

(C) $Q_{01}^L = \sqrt{\frac{\sum q_1 p_0}{\sum q_0 p_0} \times \frac{\sum q_1 p_1}{\sum q_0 p_1}} \times 100$

(D) $Q_{01}^L = \frac{\sum q_1 (p_0+p_1)}{\sum q_0 (p_0+p_1)} \times 100$

Question 1. Tests of adequacy are applied to index number formulae to check for their:

(A) Ease of calculation

(B) Compliance with statistical principles

(C) Sensitivity to outliers

(D) Approval by government agencies

Question 2. The Time Reversal Test ($TRT$) requires that the index number calculated from period 0 to period 1 should be the reciprocal of the index number calculated from period 1 to period 0. Mathematically, this is expressed as:

(A) $P_{01} \times P_{10} = 0$

(B) $P_{01} \times P_{10} = 1$

(C) $P_{01} + P_{10} = 1$

(D) $P_{01} = P_{10}$

Question 3. Which of the following index number formulas satisfies the Time Reversal Test?

(A) Laspeyres Price Index

(B) Paasche Price Index

(C) Fisher's Ideal Price Index

(D) Simple Aggregate Price Index

Question 4. The Factor Reversal Test ($FRT$) requires that the product of a price index and a quantity index should be equal to the corresponding value index. Mathematically, for index from period 0 to 1, this is expressed as:

(A) $P_{01} \times Q_{01} = V_{01}$

(B) $P_{01} + Q_{01} = V_{01}$

(C) $P_{01} / Q_{01} = V_{01}$

(D) $P_{01} \times P_{10} = V_{01}$

Question 5. Which of the following index number formulas satisfies the Factor Reversal Test?

(A) Laspeyres Index

(B) Paasche Index

(C) Marshall-Edgeworth Index

(D) Fisher's Ideal Index

Question 6. The Circular Test is an extension of the Time Reversal Test and requires that for three periods 0, 1, and 2, the index number from period 0 to 1 multiplied by the index number from period 1 to 2 should be equal to the index number from period 0 to 2. Mathematically, this is expressed as:

(A) $P_{01} + P_{12} = P_{02}$

(B) $P_{01} \times P_{12} = P_{02}$

(C) $P_{01} / P_{12} = P_{02}$

(D) $P_{01} \times P_{21} = P_{02}$

Question 7. Which of the following standard weighted index number formulas satisfies the Circular Test?

(A) Laspeyres Price Index

(B) Paasche Price Index

(C) Fisher's Ideal Price Index

(D) None of the commonly used weighted index numbers (Laspeyres, Paasche, Fisher) satisfy the Circular Test

Question 8. The value index ($V_{01}$) represents the change in the total value of the basket of goods from period 0 to period 1. Its formula is:

(A) $V_{01} = \frac{\sum p_0 q_0}{\sum p_1 q_1} \times 100$

(B) $V_{01} = \frac{\sum p_1 q_1}{\sum p_0 q_0} \times 100$

(C) $V_{01} = P_{01} \times Q_{01}$

(D) $V_{01} = \frac{P_{01}}{Q_{01}} \times 100$

Question 9. Does the Laspeyres Price Index satisfy the Factor Reversal Test? $P_{01}^L \times Q_{01}^L = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum q_1 p_0}{\sum q_0 p_0}$. Does this equal $V_{01} = \frac{\sum p_1 q_1}{\sum p_0 q_0}$?

(A) Yes, it satisfies the test

(B) No, it does not satisfy the test

(C) Only under specific conditions

(D) The test is not applicable to Laspeyres index

Question 10. Does the Paasche Price Index satisfy the Factor Reversal Test? $P_{01}^P \times Q_{01}^P = \frac{\sum p_1 q_1}{\sum p_0 q_1} \times \frac{\sum q_1 p_1}{\sum q_0 p_1}$. Does this equal $V_{01} = \frac{\sum p_1 q_1}{\sum p_0 q_0}$?

(A) Yes, it satisfies the test

(B) No, it does not satisfy the test

(C) Only under specific conditions

(D) The test is not applicable to Paasche index

Question 11. Why is Fisher's Ideal Index preferred for its theoretical properties based on the tests of adequacy?

(A) It is simpler to calculate than Laspeyres or Paasche.

(B) It uses current period weights, reflecting current consumption.

(C) It satisfies both the Time Reversal Test and the Factor Reversal Test.

(D) It requires less data than other weighted indices.

Question 12. The Circular Test is important when:

(A) Comparing price changes between only two periods

(B) Calculating index numbers for a single commodity

(C) Shifting the base period and maintaining consistency over multiple periods

(D) Calculating a quantity index

Question 13. While theoretically desirable, the Circular Test is often not satisfied by practical index number formulas. What is a consequence of not satisfying the Circular Test?

(A) The index becomes difficult to calculate

(B) Base shifting leads to different results than direct calculation

(C) The index only works for price changes

(D) The index fails the Time Reversal Test

Question 14. Marshall-Edgeworth Index satisfies which of the following tests?

(A) Only Time Reversal Test

(B) Only Factor Reversal Test

(C) Both Time Reversal and Factor Reversal Tests

(D) Neither Time Reversal nor Factor Reversal Tests

Question 15. The Simple Aggregate Index fails the Time Reversal Test. If prices in period 0 are $\textsf{₹}10, \textsf{₹}20$ and in period 1 are $\textsf{₹}20, \textsf{₹}10$, $P_{01} = \frac{20+10}{10+20} \times 100 = 100$. $P_{10} = \frac{10+20}{20+10} \times 100 = 100$. In this specific case, it appears to satisfy TRT. Let's try different values. Period 0: $\textsf{₹}10, \textsf{₹}20$. Period 1: $\textsf{₹}30, \textsf{₹}15$. $P_{01} = \frac{30+15}{10+20} \times 100 = \frac{45}{30} \times 100 = 150$. $P_{10} = \frac{10+20}{30+15} \times 100 = \frac{30}{45} \times 100 = 66.67$. $150 \times 66.67 \neq 10000$. Thus it fails TRT generally. Which test does the Simple Aggregate Index generally fail?

(A) Time Reversal Test

(B) Factor Reversal Test

(C) Both Time Reversal and Factor Reversal Tests

(D) Circular Test

Question 16. Consider index $I$. If $I_{01} \times I_{10} = 10000$ (for percentage indices), it satisfies:

(A) Factor Reversal Test

(B) Circular Test

(C) Time Reversal Test

(D) Both Time and Factor Reversal Tests

Question 17. The Factor Reversal Test ensures that the formula is symmetric with respect to the interchanging of prices and quantities. This is important for theoretical consistency between price and quantity indices. Which index formula satisfies this property?

(A) Laspeyres Index

(B) Paasche Index

(C) Simple Average of Price Relatives

(D) Fisher's Ideal Index

Question 18. The Circular Test is useful for long-term comparisons or when chaining index numbers. An index that satisfies the Circular Test allows for consistent comparisons across multiple periods without needing to refer back to the original base period for every comparison. Which index is NOT suitable for chaining over long periods due to its failure of the Circular Test?

(A) Fisher's Ideal Index

(B) Simple Geometric Mean of Price Relatives

(C) Simple Aggregate Index

(D) Marshall-Edgeworth Index

Question 19. The tests of adequacy are theoretical criteria. In practice, sometimes an index that fails one or more tests might still be used because:

(A) It is easier to compute

(B) The required data is more readily available

(C) It serves the specific purpose of its construction better

(D) All of the above

Question 20. The Time Reversal Test ensures that the comparison between two periods is consistent, regardless of which period is taken as the base. If $P_{01} = 120$, for the Time Reversal Test to hold, $P_{10}$ should be:

(A) $120$

(B) $100/120 \times 100 = 83.33$

(C) $1/120 \times 100$

(D) $1/1.2 = 0.8333$. The index is $100/120 * 100$. $P_{10}$ implies current is 0, base is 1. So $\frac{\sum p_0 q?}{\sum p_1 q?} \times 100$. For TRT $P_{01} \times P_{10} = 1$. If $P_{01}$ is in percentage form (e.g., 120), then $P_{01}/100 \times P_{10}/100 = 1$, or $P_{01} \times P_{10} = 10000$. Or if $P_{01}$ is ratio form (e.g., 1.2), $P_{01} \times P_{10} = 1$. Assuming standard percentage index: $120 \times P_{10} = 10000$, so $P_{10} = 10000/120 = 1000/12 = 250/3 = 83.33$. If ratio form: $1.2 \times P_{10} = 1$, $P_{10} = 1/1.2 \approx 0.833$. Let's assume percentage form is standard for options.

(A) 120

(B) $100/120 = 0.8333$

(C) $1/1.2 = 0.8333$

(D) $10000 / 120 = 83.33$

Question 21. If a price index ($P_{01}$) is 150 and the corresponding quantity index ($Q_{01}$) for the same basket of goods is 120, what is the value index ($V_{01}$) assuming the Factor Reversal Test holds for some formula?

(A) $150 \times 120 = 18000$. Value index is typically ratio * 100. $1.5 \times 1.2 = 1.8$. $1.8 \times 100 = 180$.

(A) $150 \times 120 = 18000$

(B) $(150/100) \times (120/100) \times 100 = 1.5 \times 1.2 \times 100 = 180$

(C) $150 + 120 = 270$

(D) $\sqrt{150 \times 120} \approx 134.16$

Question 22. Consider index $I$. If $I_{01} \times I_{10} = 10000$ (for percentage indices), it satisfies:

(A) Factor Reversal Test

(B) Circular Test

(C) Time Reversal Test

(D) Both Time and Factor Reversal Tests

Question 23. The Factor Reversal Test ensures that the formula is symmetric with respect to the interchanging of prices and quantities. This is important for theoretical consistency between price and quantity indices. Which index formula satisfies this property?

(A) Laspeyres Index

(B) Paasche Index

(C) Simple Average of Price Relatives

(D) Fisher's Ideal Index

Question 24. The Circular Test is useful for long-term comparisons or when chaining index numbers. An index that satisfies the Circular Test allows for consistent comparisons across multiple periods without needing to refer back to the original base period for every comparison. Which index is NOT suitable for chaining over long periods due to its failure of the Circular Test?

(A) Fisher's Ideal Index

(B) Simple Geometric Mean of Price Relatives

(C) Simple Aggregate Index

(D) Marshall-Edgeworth Index

Question 25. The tests of adequacy are theoretical criteria. In practice, sometimes an index that fails one or more tests might still be used because:

(A) It is easier to compute

(B) The required data is more readily available

(C) It serves the specific purpose of its construction better

(D) All of the above

Question 1. What is a time series?

(A) Data collected at random points in time

(B) A set of observations collected, recorded, or observed at successive points in time or over successive periods of time

(C) Data collected for different variables at a single point in time

(D) Data arranged in alphabetical order

Question 2. Which of the following is NOT an example of time series data?

(A) Annual GDP of India from 1990 to 2023

(B) Monthly rainfall data for Delhi over 10 years

(C) Cross-sectional data on income of individuals in different cities at one point in time

(D) Daily closing prices of a stock on NSE over a year

Question 3. The main objective of time series analysis is to:

(A) Find relationships between different variables

(B) Understand the underlying patterns and behavior of data over time for forecasting and planning

(C) Determine cause-and-effect relationships

(D) Describe the data using summary statistics

Question 4. Time series analysis is primarily concerned with data that is ordered by:

(A) Magnitude

(B) Category

(C) Time

(D) Location

Question 5. Univariate time series analysis deals with:

(A) Data collected from multiple sources

(B) Data involving only one variable over time

(C) Data involving multiple variables over time

(D) Data collected at irregular intervals

Question 6. The significance of time series analysis lies in its ability to:

(A) Provide insights into past behavior

(B) Facilitate forecasting of future values

(C) Help in policy formulation and decision making

(D) All of the above

Question 7. Which field heavily relies on time series analysis for forecasting and planning?

(A) Genetics

(B) Marketing and Sales

(C) Geology

(D) Archaeology

Question 8. The points in time where observations are recorded in a time series are typically:

(A) Equally spaced

(B) Unequally spaced

(C) Can be either equally or unequally spaced, but analysis is easier with equal spacing

(D) Only relevant for short time series

Question 9. Time series analysis is also used for quality control, where variations in a production process are monitored over time. This helps in identifying:

(A) The cost of production

(B) Abnormal variations and process shifts

(C) The market demand for the product

(D) The efficiency of the workforce

Question 10. The price movement of agricultural commodities over successive harvest seasons in India would constitute which type of data?

(A) Cross-sectional data

(B) Panel data

(C) Time series data

(D) Spatial data

Question 11. One key assumption often made for simplifying time series analysis is that the observations are:

(A) Independent of each other

(B) Dependent on time

(C) Randomly distributed

(D) Constant over time

Question 12. Time series analysis helps in isolating and understanding the different factors that influence the variations in the data over time. These factors are known as the:

(A) Parameters of the model

(B) Errors in measurement

(C) Components of time series

(D) Exogenous variables

Question 13. Understanding the past behaviour of a time series helps in:

(A) Identifying the patterns and trends

(B) Designing appropriate forecasting models

(C) Evaluating the effectiveness of past policies

(D) All of the above

Question 14. Time series data is crucial for analyzing economic phenomena such as:

(A) Inflation and unemployment rates

(B) Stock market fluctuations

(C) Industrial production

(D) All of the above

Question 15. When analyzing the sales of air conditioners in India over the years, one would expect to see which type of pattern prominently?

(A) Secular Trend

(B) Seasonal Variation

(C) Cyclical Variation

(D) Irregular Variation

Question 16. What is the primary characteristic that distinguishes time series data from cross-sectional data?

(A) The number of variables

(B) The order of observations

(C) The source of data

(D) The scale of measurement

Question 17. Time series analysis can be broadly classified into descriptive analysis and inferential analysis. Descriptive analysis focuses on:

(A) Building forecasting models

(B) Identifying and quantifying the components of the time series

(C) Hypothesis testing

(D) Determining correlation with other series

Question 18. The data on quarterly unemployment rates in India would be considered:

(A) Cross-sectional data

(B) A time series

(C) Panel data

(D) Spatial data

Question 19. Which of the following is a key assumption for many time series models?

(A) Stationarity (statistical properties do not change over time)

(B) Non-linearity

(C) Absence of trend

(D) Presence of strong seasonality

Question 20. Time series analysis is useful in identifying patterns that may not be obvious from a simple visual inspection of the data. This is especially true for:

(A) Secular trend

(B) Strong seasonal variations

(C) Cyclical and irregular variations

(D) All components equally

Question 1. The long-term gradual movement of a time series, either upwards or downwards, is known as the:

(A) Seasonal Variation

(B) Cyclical Variation

(C) Secular Trend

(D) Irregular Variation

Question 2. Which component of a time series represents fluctuations that repeat over a fixed period, such as a year or a quarter?

(A) Secular Trend

(B) Seasonal Variation

(C) Cyclical Variation

(D) Irregular Variation

Question 3. Fluctuations in a time series that occur over periods longer than a year and are typically associated with economic cycles (prosperity, recession, depression, recovery) are called:

(A) Secular Trend

(B) Seasonal Variation

(C) Cyclical Variation

(D) Irregular Variation

Question 4. Random or unpredictable fluctuations in a time series that are not attributable to trend, seasonality, or cyclical patterns are known as:

(A) Secular Trend

(B) Seasonal Variation

(C) Cyclical Variation

(D) Irregular Variation

Question 5. The additive model of time series decomposition is given by:

(A) $Y = T \times S \times C \times I$

(B) $Y = T + S + C + I$

(C) $Y = T + S \times C \times I$

(D) $Y = T \times S + C + I$

Question 6. The multiplicative model of time series decomposition is given by:

(A) $Y = T + S + C + I$

(B) $Y = T \times S \times C \times I$

(C) $Y = T + S \times C + I$

(D) $Y = T + S + C \times I$

Question 7. The choice between additive and multiplicative models often depends on whether the magnitude of fluctuations (seasonal, cyclical) is independent of the level of the series (additive) or proportional to it (multiplicative). When is the multiplicative model generally more appropriate?

(A) When the seasonal variations have constant absolute amplitude over time

(B) When the seasonal variations increase in proportion to the trend

(C) When there is no clear trend

(D) When the data is highly volatile

Question 8. An increase in population over several decades is an example of which time series component?

(A) Seasonal Variation

(B) Cyclical Variation

(C) Secular Trend

(D) Irregular Variation

Question 9. The increase in sales of ice cream during summer months in India is an example of which time series component?

(A) Secular Trend

(B) Seasonal Variation

(C) Cyclical Variation

(D) Irregular Variation

Question 10. A recession affecting the entire economy for a period of 2-3 years is an example of which time series component?

(A) Seasonal Variation

(B) Cyclical Variation

(C) Secular Trend

(D) Irregular Variation

Question 11. A sudden strike by factory workers causing a drop in production for a month is an example of which time series component?

(A) Seasonal Variation

(B) Cyclical Variation

(C) Secular Trend

(D) Irregular Variation

Question 12. The component of time series that is usually considered unpredictable is:

(A) Secular Trend

(B) Seasonal Variation

(C) Cyclical Variation

(D) Irregular Variation

Question 13. Seasonal variations can occur within a year (e.g., monthly, quarterly). Their period is:

(A) Fixed and less than a year

(B) Fixed and greater than a year

(C) Not fixed

(D) Always exactly one year

Question 14. Cyclical variations typically have a period of:

(A) Less than a year

(B) Exactly one year

(C) More than a year, but not necessarily fixed

(D) Exactly ten years

Question 15. Decomposition of time series refers to the process of:

(A) Collecting the time series data

(B) Separating the time series into its various components

(C) Forecasting future values based on the trend

(D) Plotting the time series data on a graph

Question 16. If a time series shows a consistent increase over a long period, despite short-term ups and downs, this represents a dominant:

(A) Seasonal pattern

(B) Cyclical pattern

(C) Secular trend

(D) Irregular movement

Question 17. Which component is also known as residual variation?

(A) Secular Trend

(B) Seasonal Variation

(C) Cyclical Variation

(D) Irregular Variation

Question 18. Which component is most likely caused by events like earthquakes, floods, or unexpected political changes?

(A) Secular Trend

(B) Seasonal Variation

(C) Cyclical Variation

(D) Irregular Variation

Question 19. Understanding the Secular Trend helps in forecasting because it represents the:

(A) Short-term fluctuations

(B) Regular periodic movements

(C) Underlying long-term direction of the series

(D) Random changes

Question 20. The cyclical component is characterized by:

(A) Fixed period and amplitude

(B) Fixed period but varying amplitude

(C) Varying period and amplitude

(D) Amplitude proportional to the trend

Question 1. Which method of measuring trend involves plotting the time series data on a graph and drawing a smooth curve by hand?

(A) Method of Semi-Averages

(B) Moving Average Method

(C) Method of Least Squares

(D) Freehand Curve Method

Question 2. A major limitation of the Freehand Curve Method is that it is:

(A) Difficult to plot

(B) Subjective and depends on the judgment of the statistician

(C) Only suitable for linear trends

(D) Computationally intensive

Question 3. The Method of Semi-Averages involves dividing the time series data into two equal parts and calculating the arithmetic mean of each part. These averages are plotted at the mid-point of their respective periods, and a straight line is drawn through them. This method is best suited for fitting which type of trend?

(A) Linear Trend

(B) Parabolic Trend

(C) Exponential Trend

(D) Seasonal Trend

Question 4. If a time series has an odd number of observations, say 7 years, in the Method of Semi-Averages, how is the data divided?

(A) Into three and four years

(B) The middle observation is excluded, and the remaining are divided equally

(C) Into two equal halves of 3.5 years each

(D) The first observation is excluded

Question 5. The Moving Average Method is used to smooth out short-term fluctuations and reveal the underlying trend. A 3-year moving average is calculated by:

(A) Averaging the data for a block of 3 years and centering the average at the middle year

(B) Averaging the data for a block of 3 years and placing the average at the end of the block

(C) Taking the average of all data points and dividing by 3

(D) Calculating the geometric mean of 3 years' data

Question 6. When calculating a moving average with an even period (e.g., 4-year moving average), the calculated averages fall between years. To center these averages on a specific year, we use:

(A) A simple moving average

(B) A weighted moving average

(C) A centered moving average (average of two consecutive moving averages)

(D) Exponential smoothing

Question 7. A limitation of the Moving Average Method is that:

(A) It cannot be used for forecasting

(B) It is affected by extreme values

(C) It results in loss of data points at the beginning and end of the series

(D) It requires fitting a specific mathematical equation

Question 8. The Method of Least Squares is a mathematical method for fitting a trend line or curve. For a linear trend $Y_t = a + bT$, where $Y_t$ is the time series value and $T$ is time, the values of $a$ and $b$ are determined by minimizing the sum of the squared differences between the observed values and the fitted trend values. This method provides:

(A) A subjective trend line

(B) An objective fit to the data

(C) A trend line that passes through the mean of the data

(D) Only the slope of the trend

Question 9. For fitting a linear trend $Y = a + bT$ using the Method of Least Squares, the normal equations are $\sum Y = na + b \sum T$ and $\sum YT = a \sum T + b \sum T^2$. If we shift the origin of time such that $\sum T = 0$, the equations simplify to:

(A) $\sum Y = na$ and $\sum YT = b \sum T^2$

(B) $\sum Y = nb$ and $\sum YT = a \sum T^2$

(C) $\sum Y = na$ and $\sum YT = a \sum T^2$

(D) $\sum Y = nb$ and $\sum YT = b \sum T^2$

Question 10. If the time series data consists of an even number of years (e.g., 2010, 2011, 2012, 2013) and we shift the origin for the Method of Least Squares, how are the values of $T$ assigned to make $\sum T = 0$?

(A) -1.5, -0.5, 0.5, 1.5

(B) -2, -1, 0, 1

(C) 1, 2, 3, 4

(D) -3, -1, 1, 3 (by taking the origin between the two central years and unit as half year)

Question 11. If the time series data consists of an odd number of years (e.g., 2010, 2011, 2012, 2013, 2014) and we shift the origin for the Method of Least Squares, how are the values of $T$ assigned to make $\sum T = 0$?

(A) -2.5, -1.5, -0.5, 0.5, 1.5

(B) -2, -1, 0, 1, 2

(C) 1, 2, 3, 4, 5

(D) -4, -2, 0, 2, 4 (by taking the origin at the middle year and unit as half year)

Question 12. For fitting a parabolic trend $Y_t = a + bT + cT^2$ using the Method of Least Squares, additional normal equations are required. This method is used when the trend is:

(A) Linear

(B) Non-linear and follows a U or inverted U shape

(C) Strictly increasing

(D) Seasonal

Question 13. The Method of Least Squares provides the 'best fit' trend line in the sense that it minimizes:

(A) The sum of errors

(B) The sum of absolute errors

(C) The sum of squared errors

(D) The product of errors

Question 14. Which method is generally considered the most objective method for measuring trend among the listed options?

(A) Freehand Curve Method

(B) Method of Semi-Averages

(C) Moving Average Method

(D) Method of Least Squares

Question 15. If a time series shows a trend that is increasing at an increasing rate, which type of trend might be most appropriate to fit?

(A) Linear

(B) Parabolic ($c > 0$)

(C) Parabolic ($c < 0$)

(D) Constant

Question 16. The Method of Moving Averages is effective in removing:

(A) Long-term trend

(B) Cyclical variations

(C) Seasonal and irregular variations, especially if the period of moving average matches the period of seasonal variation

(D) Only irregular variations

Question 17. Data for a time series is given below for 5 years: Year: 2019, 2020, 2021, 2022, 2023 Value: 100, 110, 120, 130, 140 Using the Method of Semi-Averages, the two halves are (2019, 2020) and (2022, 2023) if the middle year is excluded. The averages are $\frac{100+110}{2} = 105$ (mid-point 2019.5) and $\frac{130+140}{2} = 135$ (mid-point 2022.5). The line passes through (2019.5, 105) and (2022.5, 135). If the method is applied with 2.5 year halves and the middle point of each half period (2019-2021 -> mid 2020, 2021-2023 -> mid 2022), the averages are $\frac{100+110+120}{3} = 110$ and $\frac{120+130+140}{3} = 130$. The midpoints are 2020 and 2022. The line passes through (2020, 110) and (2022, 130). What are the semi-averages for the data: 100, 110, 120, 130, 140 for years 1 to 5?

(A) 105, 135

(B) 110, 130

(C) 120 (single average)

(D) 100, 140

Question 18. If we use a 3-year moving average for the data: 10, 12, 15, 13, 16, 18, 20. What are the moving averages?

(A) 12, 13.33, 14.67, 15.67, 18

(B) 11, 12.33, 14, 15.33, 17

(C) 12, 13, 15, 16, 18, 20

(D) 10, 12, 15, 13, 16, 18, 20

Question 19. When fitting a linear trend $Y = a + bT$ using least squares to yearly data where the origin is taken at the middle year, the intercept 'a' represents:

(A) The value of Y at the base year

(B) The average value of Y over the entire period

(C) The trend value of Y at the origin (middle year)

(D) The average rate of change of Y per year

Question 20. In the least squares method for a linear trend $Y = a + bT$, the coefficient 'b' represents:

(A) The trend value of Y at the origin

(B) The average rate of change in Y per unit of time (slope of the trend line)

(C) The average value of Y

(D) The seasonal variation

Question 21. Which method is suitable for estimating trend if the trend is not linear?

(A) Freehand Curve Method

(B) Moving Average Method

(C) Method of Least Squares (using appropriate curve like parabola)

(D) All of the above (depending on the nature of non-linearity and required precision)

Question 22. The Method of Semi-Averages is relatively easy to calculate but is sensitive to:

(A) The number of observations

(B) Extreme values in the first or second half of the data

(C) The period of seasonal variation

(D) The slope of the trend

Question 23. A key limitation of the Moving Average Method is that it cannot provide trend values for:

(A) The middle of the series

(B) The entire length of the series, especially at the ends

(C) Only for short time series

(D) Only for seasonal data

Question 24. If the Method of Least Squares is used to fit a trend line $Y_t = a + bT$, and $b$ is found to be negative, it indicates that the trend is:

(A) Increasing

(B) Decreasing

(C) Stable

(D) Cyclical

Question 25. For fitting a parabolic trend $Y_t = a + bT + cT^2$, if $c$ is found to be positive, it suggests that the trend is:

(A) Increasing at an increasing rate or decreasing at a decreasing rate (U-shape)

(B) Increasing at a decreasing rate or decreasing at an increasing rate (inverted U-shape)

(C) Linear

(D) Constant

Question 1. The Consumer Price Index (CPI) measures the change in the retail prices of a fixed basket of goods and services purchased by a representative household. It is used to measure:

(A) Changes in wholesale prices

(B) Inflation and its impact on the purchasing power of money

(C) Changes in industrial production

(D) Fluctuations in stock market prices

Question 2. In India, CPI is primarily calculated and published by which organization?

(A) Reserve Bank of India (RBI)

(B) Ministry of Finance

(C) National Statistical Office (NSO)

(D) NITI Aayog

Question 3. The CPI is generally constructed using which method?

(A) Simple Aggregate Method

(B) Simple Average of Price Relatives Method

(C) Weighted Average of Price Relatives Method (using base period consumption expenditure weights)

(D) Paasche Price Index Method

Question 4. The Wholesale Price Index (WPI) measures the change in the average price of goods at the wholesale level. It is often used as a broad indicator of:

(A) Cost of living

(B) Inflation at the producer/wholesale level

(C) Wage rates

(D) Retail prices

Question 5. In India, WPI is primarily calculated and published by which organization?

(A) National Statistical Office (NSO)

(B) Ministry of Commerce & Industry (Office of Economic Adviser)

(C) Reserve Bank of India (RBI)

(D) Securities and Exchange Board of India (SEBI)

Question 6. Which index is often used for policy decisions by the government and for dearness allowance calculations for employees in India?

(A) Wholesale Price Index (WPI)

(B) Consumer Price Index (CPI)

(C) Index of Industrial Production (IIP)

(D) Producer Price Index (PPI)

Question 7. The Index of Industrial Production (IIP) measures the short-term changes in the volume of production of a basket of industrial products. It is a key indicator of:

(A) Price changes in the industrial sector

(B) Growth or decline in industrial sector output

(C) Employment levels in industries

(D) Profitability of industries

Question 8. A major limitation of index numbers is that they are subject to:

(A) Sampling errors

(B) Errors in data collection

(C) Errors due to choice of base period and formula

(D) All of the above

Question 9. The CPI might overstate the actual increase in the cost of living because it often does not fully account for:

(A) Quality improvements in goods over time

(B) Changes in consumer spending patterns (substitution effect)

(C) Introduction of new products

(D) All of the above are potential sources of overstatement

Question 10. Which index is more relevant for understanding the impact of inflation on the average consumer's household budget?

(A) WPI

(B) CPI

(C) IIP

(D) Stock Market Index

Question 11. Which index is more relevant for understanding inflationary pressures in the economy from the supply side, before they reach the final consumer?

(A) WPI

(B) CPI

(C) IIP

(D) Cost of Production Index

Question 12. A limitation of WPI in India is that it traditionally does not include services. Which index includes both goods and services?

(A) IIP

(B) CPI

(C) WPI

(D) Agricultural Price Index

Question 13. The base year for the current series of CPI (Combined) in India is:

(A) 2005

(B) 2011-12

(C) 2014

(D) 2016

Question 14. The base year for the current series of WPI in India is:

(A) 2004-05

(B) 2011-12

(C) 2014

(D) 2016

Question 15. Which index is a crucial indicator for assessing the manufacturing activity and overall economic growth momentum in India?

(A) CPI

(B) WPI

(C) IIP

(D) Sensex/Nifty

Question 16. A limitation of index numbers is the problem of changing relative importance of goods and services over time due to changes in consumer preferences, technology, etc. This is addressed by:

(A) Keeping the base year fixed permanently

(B) Periodically revising the basket of goods and weights and updating the base year

(C) Using simple index number methods

(D) Only using Laspeyres index

Question 17. The problem of comparability arises when using index numbers constructed with different base periods or using different methodologies. This can often be addressed by:

(A) Ignoring the base period

(B) Using only one type of index number

(C) Shifting the base period or linking different index series

(D) Only comparing index numbers for consecutive periods

Question 18. Real wages are nominal wages adjusted for changes in the price level. If the nominal wage increases by 10% and the CPI increases by 5%, the real wage has approximately increased by:

(A) 5%

(B) 15%

(C) 2%

(D) -5%

Question 19. Deflating a value series (converting nominal values to real values) is done using a relevant price index. The formula for converting a nominal value to a real value is:

(A) $\text{Real Value} = \text{Nominal Value} \times \text{Price Index}$

(B) $\text{Real Value} = \frac{\text{Nominal Value}}{\text{Price Index}} \times 100$ (assuming index base is 100)

(C) $\text{Real Value} = \text{Nominal Value} + \text{Price Index}$

(D) $\text{Real Value} = \frac{\text{Price Index}}{\text{Nominal Value}} \times 100$

Question 20. If a person's salary in 2020 was $\textsf{₹}5,00,000$ and the CPI for 2020 (base 2015=100) was 120, what was their real salary in 2020 with 2015 as base?

(A) $\textsf{₹}5,00,000 \times 120 / 100 = \textsf{₹}6,00,000$

(B) $\textsf{₹}5,00,000 / 120 \times 100 = \textsf{₹}4,16,666.67$

(C) $\textsf{₹}5,00,000 - 120 = \textsf{₹}4,99,880$

(D) $\textsf{₹}5,00,000 \times 1.2 = \textsf{₹}6,00,000$

Question 21. What is the main difference between CPI and WPI?

(A) CPI measures price changes at the wholesale level, while WPI measures them at the retail level.

(B) CPI basket includes only goods, while WPI includes goods and services.

(C) CPI measures price changes for consumers, while WPI measures them for producers/wholesalers.

(D) CPI uses current period weights, while WPI uses base period weights.

Question 22. The weights in CPI are derived from:

(A) Industrial production data

(B) Household consumption expenditure surveys

(C) Wholesale trade volumes

(D) Government budget allocations

Question 23. A rise in WPI might indicate future inflation in CPI because:

(A) Price increases at the wholesale level are often passed on to consumers at the retail level.

(B) WPI directly measures the cost of living.

(C) CPI and WPI are always the same.

(D) WPI only includes services.

Question 24. Index numbers are approximate indicators and should be interpreted with caution because:

(A) They only represent average changes and may not reflect the situation for specific individuals or groups.

(B) Their construction involves choices of base period, formula, and basket of goods, which can influence the result.

(C) Data collection errors and quality changes can affect accuracy.

(D) All of the above.

Question 25. The CPI is used for 'indexing' payments, meaning adjusting them for inflation. Which of the following is commonly indexed using CPI in India?

(A) Salaries (Dearness Allowance)

(B) Pensions

(C) Rent agreements

(D) All of the above in various contexts