Multiple Correct Answers MCQs for Sub-Topics of Topic 14: Index Numbers & Time-Based Data

Question 1. Which of the following are key characteristics of index numbers?

(A) They measure relative changes.

(B) They are always expressed in monetary units.

(C) They serve as statistical barometers of economic activity.

(D) They compare values over time or across different locations.

Question 2. The purpose of constructing index numbers includes which of the following?

(A) To simplify complex data into a single representative figure.

(B) To measure the average change in prices of a group of commodities.

(C) To determine the absolute total value of all goods produced.

(D) To facilitate comparisons of economic conditions between different periods or places.

Question 3. When choosing a base period for constructing an index number, it is important that the period is:

(A) Recent, to ensure relevance.

(B) Normal, meaning free from abnormal events like war or natural disaster.

(C) Representative of the typical conditions being studied.

(D) A period with the lowest values in the series.

Question 4. If the price relative for commodity 'A' in $2024$ with $2020$ as base is $150\%$, what does this indicate?

(A) The price of commodity 'A' in $2024$ is $150\%$ of its price in $2020$.

(B) The price of commodity 'A' has increased by $50\%$ between $2020$ and $2024$.

(C) The price of commodity 'A' in $2024$ is $\textsf{₹}150$.

(D) For every $\textsf{₹}100$ spent on 'A' in $2020$, $\textsf{₹}150$ would be needed to buy the same quantity in $2024$.

Question 5. Index numbers are dimensionless figures, usually expressed as percentages. This means:

(A) They are ratios and do not have units of measurement.

(B) They can be easily compared with other index numbers.

(C) The base period index value is typically set to $1$.

(D) The value $100$ represents the base level.

Question 6. Which of the following are examples of variables for which index numbers are commonly constructed?

(A) Prices of a basket of consumer goods.

(B) Quantity of industrial production.

(C) Stock market prices (e.g., Sensex, Nifty).

(D) Single individual's height over time.

Question 7. The base period is also sometimes referred to as the:

(A) Comparison period

(B) Reference period

(C) Benchmark period

(D) Current period

Question 8. A quantity relative helps in understanding the change in the volume of a commodity. If the production of wheat in Punjab was $100$ lakh tonnes in $2015$ (base) and $130$ lakh tonnes in $2020$ (current), the quantity relative for $2020$ is:

(A) $130/100 = 1.3$

(B) $(130-100)/100 \times 100 = 30$

(C) $\frac{130}{100} \times 100 = 130$

(D) $\frac{100}{130} \times 100 \approx 76.92$

Question 9. The process of updating the base period of an index number series is called:

(A) Shifting the base

(B) Linking of index numbers

(C) Revision of index numbers

(D) Weighting the index

Question 10. Which of the following are considered limitations in the construction and use of index numbers?

(A) Difficulty in selecting representative commodities for the basket.

(B) Challenges in obtaining accurate price or quantity data.

(C) Changes in the quality of goods over time.

(D) The base period always remaining constant.

Question 11. Index numbers are valuable tools for policymakers and economists because they:

(A) Help in understanding the overall trend in prices or production.

(B) Provide a quantitative measure of economic changes.

(C) Are used to adjust other economic data for inflation.

(D) Are perfect measures without any limitations.

Question 12. A price index of $110$ in the current year, with the base year index of $100$, signifies:

(A) Prices have increased by $10\%$ on average since the base year.

(B) Prices in the current year are $110\%$ of the prices in the base year.

(C) There has been a decrease in purchasing power.

(D) The price level is lower than the base year.

Question 1. The Simple Aggregate Method for constructing a price index has which of the following characteristics?

(A) It sums up the prices of commodities in the current and base periods.

(B) It gives equal weight to the percentage change of each commodity.

(C) It is affected by the units in which the prices are quoted.

(D) Its formula is $P_{01} = \frac{\sum p_1}{\sum p_0} \times 100$.

Question 2. The Simple Average of Price Relatives Method involves:

(A) Calculating the price relative for each commodity.

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

(C) Using the arithmetic mean or geometric mean of the price relatives.

(D) Giving more importance to commodities with higher prices.

Question 3. Consider the following prices for two commodities in Base Year (BY) and Current Year (CY):
Commodity A: BY = $\textsf{₹}10$, CY = $\textsf{₹}15$
Commodity B: BY = $\textsf{₹}100$, CY = $\textsf{₹}110$
Which of the following are true regarding simple index methods?

(A) The Simple Aggregate Price Index is $\frac{15+110}{10+100} \times 100 = \frac{125}{110} \times 100 \approx 113.64$.

(B) The price relative for Commodity A is $\frac{15}{10} \times 100 = 150$.

(C) The price relative for Commodity B is $\frac{110}{100} \times 100 = 110$.

(D) The Simple Average of Price Relatives (AM) is $\frac{150+110}{2} = 130$.

Question 4. Which of the following statements are limitations of Simple Aggregate Method?

(A) It is influenced by the absolute prices of commodities, giving more weight to expensive items.

(B) It does not consider the relative importance of different commodities.

(C) It is not suitable when prices are quoted in different units (e.g., per kg and per litre).

(D) It always overstates the price increase.

Question 5. The Simple Average of Price Relatives Method addresses which limitation of the Simple Aggregate Method?

(A) It is not affected by the units of measurement of prices.

(B) It gives equal importance to the percentage change in price of each commodity.

(C) It uses explicit weights based on consumption patterns.

(D) It is easier to calculate.

Question 6. Simple index number methods are appropriate for situations where:

(A) All commodities in the group are equally important.

(B) The number of commodities is small.

(C) A quick and simple measure of overall change is needed without detailed weighting information.

(D) High accuracy and theoretical properties are critical.

Question 7. If the prices of three commodities change from $(\textsf{₹}5, \textsf{₹}10, \textsf{₹}20)$ in the base year to $(\textsf{₹}10, \textsf{₹}20, \textsf{₹}30)$ in the current year, which statements are true?

(A) The Simple Aggregate Price Index is $\frac{10+20+30}{5+10+20} \times 100 = \frac{60}{35} \times 100 \approx 171.43$.

(B) The price relatives are $200$, $200$, $150$.

(C) The Simple Average of Price Relatives (AM) is $\frac{200+200+150}{3} = \frac{550}{3} \approx 183.33$.

(D) The Simple Aggregate method gives more weight to the percentage change of the first commodity (price doubled).

Question 8. Simple Quantity Index using the Simple Aggregate Method is calculated by:

(A) Summing the quantities in the current year and dividing by the sum of quantities in the base year, multiplied by $100$.

(B) Using the formula $Q_{01} = \frac{\sum q_1}{\sum q_0} \times 100$.

(C) Averaging the quantity relatives for each commodity.

(D) Considering the total value of quantities in both periods.

Question 9. Which of the following are major limitations of simple index number methods (both aggregate and average of relatives)?

(A) They do not account for the varying importance of different commodities.

(B) They can be distorted by extreme values or changes.

(C) They are always easier to calculate than weighted methods.

(D) They do not satisfy basic tests of adequacy like the Time Reversal Test (generally).

Question 10. If using the Geometric Mean for the Simple Average of Price Relatives, which statements are true?

(A) It gives less weight to extreme values compared to the Arithmetic Mean.

(B) It satisfies the Time Reversal Test (under specific conditions, e.g., for two commodities). For multiple, generally not the standard geometric mean.

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

(D) It is always easier to calculate than using the Arithmetic Mean.

Question 11. Simple index numbers are often used for:

(A) Casual comparisons of price changes.

(B) Calculating official inflation rates for policy making.

(C) Introductory examples in statistics.

(D) Situations where weighting information is unavailable or impractical to obtain.

Question 1. Weighted index numbers are developed to overcome the limitations of simple index numbers. They primarily do this by:

(A) Assigning weights to commodities based on their relative importance.

(B) Using only price relatives and not aggregate prices.

(C) Eliminating the need for a base period.

(D) Providing a more realistic measure of average change in a group of items.

Question 2. In Weighted Aggregate Methods, weights are typically based on quantities. Laspeyres Price Index ($P_{01}^L$) uses which quantities as weights?

(A) Quantities consumed in the base period ($q_0$).

(B) Quantities consumed in the current period ($q_1$).

(C) Average of base and current period quantities.

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

Question 3. Paasche Price Index ($P_{01}^P$) uses which quantities as weights?

(A) Quantities consumed in the base period ($q_0$).

(B) Quantities consumed in the current period ($q_1$).

(C) Average of base and current period quantities.

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

Question 4. Consider the formulas for Laspeyres and Paasche Price Indices:

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

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

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

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

Question 5. Fisher's Ideal Index is defined as the geometric mean of Laspeyres and Paasche indices. Which of the following correctly represents Fisher's Ideal Price Index ($P_{01}^F$)?

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

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

(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) $P_{01}^F = \sqrt{\left(\frac{\sum p_1 q_0}{\sum p_0 q_0}\right) \times \left(\frac{\sum p_1 q_1}{\sum p_0 q_1}\right)} \times 100$ (assuming $P^L, P^P$ are ratios, not percentages)

Question 6. Which statements are true about Laspeyres and Paasche Price Indices?

(A) Laspeyres index tends to overstate price increases due to the use of base period quantities.

(B) Paasche index tends to understate price increases due to the use of current period quantities.

(C) Laspeyres requires current period quantity data for each period being calculated.

(D) Paasche reflects changes in current consumption patterns.

Question 7. Marshall-Edgeworth Index ($P_{01}^{ME}$) uses weights based on the average of base and current period quantities ($\frac{q_0+q_1}{2}$). The formula is:

(A) $P_{01}^{ME} = \frac{\sum p_1 (\frac{q_0+q_1}{2})}{\sum p_0 (\frac{q_0+q_1}{2})} \times 100$

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

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

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

Question 8. In the Weighted Average of Price Relatives method, if weights ($W$) are used, the formula is $P_{01}^{WAR} = \frac{\sum (\frac{p_1}{p_0} \times 100) W}{\sum W}$. Which of the following choices for $W$ would make this method equivalent to the Laspeyres Price Index?

(A) $W = p_0 q_0$ (Base period value)

(B) $W = q_0$ (Base period quantity)

(C) $W = p_0$ (Base period price)

(D) $W = \frac{p_1}{p_0} \times 100$ (Price relative)

Question 9. Weighted index numbers are crucial for measuring inflation and changes in production in India because:

(A) Different commodities have vastly different levels of consumption and importance in the economy.

(B) They provide a more realistic measure of average change in an aggregate change compared to simple methods.

(C) They are the only methods that can incorporate data from different sources.

(D) Simple methods are not permitted by regulatory bodies.

Question 10. A major practical difficulty in using the Paasche Price Index is:

(A) The need to collect current period quantity data for every period of calculation.

(B) Its tendency to overstate price changes.

(C) Its formula is more complex than Laspeyres.

(D) It does not account for changes in consumption patterns.

Question 11. Fisher's Ideal Index is considered theoretically superior because:

(A) It is a compromise between Laspeyres and Paasche.

(B) It satisfies the Time Reversal Test.

(C) It satisfies the Factor Reversal Test.

(D) It is always equal to the simple average of price relatives.

Question 12. Which weighted index formula uses the arithmetic mean of base and current period quantities as weights?

(A) Laspeyres Index

(B) Paasche Index

(C) Fisher's Ideal Index

(D) Marshall-Edgeworth Index

Question 13. Weighted Quantity Indices are constructed similarly to price indices, but the roles of prices and quantities in the weights are swapped. The Laspeyres Quantity Index ($Q_{01}^L$) formula uses which weights?

(A) Base period prices ($p_0$).

(B) Current period prices ($p_1$).

(C) Base period quantities ($q_0$).

(D) Current period quantities ($q_1$).

Question 14. The formula for the 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) $Q_{01}^L = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$

Question 1. The Time Reversal Test ($TRT$) checks if an index number formula works symmetrically with respect to time. Which of the following correctly states the condition for the Time Reversal Test for a price index ($P$) from period 0 to 1?

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

(B) $P_{01} \times P_{10} = 1$ (when indices are ratios)

(C) $P_{01} \times P_{10} = 10000$ (when indices are percentages with base 100)

(D) $P_{01} / P_{10} = 1$

Question 2. The Factor Reversal Test ($FRT$) examines if the product of a price index and a quantity index equals the corresponding value index. For an index from period 0 to 1, this means:

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

(B) $P_{01} \times Q_{01} = \frac{\sum p_1 q_1}{\sum p_0 q_0} \times 100$ (when P and Q are ratios)

(C) $\left(\frac{P_{01}}{100}\right) \times \left(\frac{Q_{01}}{100}\right) \times 100 = \frac{\sum p_1 q_1}{\sum p_0 q_0} \times 100$ (when P and Q are percentages)

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

Question 3. Which of the following index number formulae satisfy the Time Reversal Test?

(A) Laspeyres Price Index

(B) Paasche Price Index

(C) Fisher's Ideal Price Index

(D) Marshall-Edgeworth Index

Question 4. Which of the following index number formulae satisfy the Factor Reversal Test?

(A) Laspeyres Index

(B) Paasche Index

(C) Fisher's Ideal Index

(D) Simple Aggregate Index

Question 5. The Circular Test is important for maintaining consistency when shifting the base period or chaining indices across multiple periods ($0$, $1$, $2$). It requires that:

(A) $P_{01} \times P_{12} = P_{02}$ (when indices are ratios)

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

(C) $\left(\frac{P_{01}}{100}\right) \times \left(\frac{P_{12}}{100}\right) \times 100 = P_{02}$ (when indices are percentages)

(D) $P_{01} \times P_{12} \times P_{20} = 1$ (when indices are ratios)

Question 6. Which of the commonly used weighted index number formulae (Laspeyres, Paasche, Fisher) fail the Circular Test?

(A) Laspeyres Index

(B) Paasche Index

(C) Fisher's Ideal Index

(D) Marshall-Edgeworth Index satisfies the Circular Test.

Question 7. Fisher's Ideal Index satisfies which of the following tests?

(A) Time Reversal Test

(B) Factor Reversal Test

(C) Circular Test

(D) Neither Time Reversal nor Factor Reversal Test

Question 8. The tests of adequacy (TRT, FRT, Circular) are theoretical properties. Why are they important?

(A) They help in selecting an appropriate formula based on desired theoretical consistency.

(B) They ensure that the formula behaves symmetrically under certain operations (like time reversal or factor reversal).

(C) They guarantee that the index number is perfectly accurate in practice.

(D) They provide criteria for evaluating the mathematical soundness of index number formulae.

Question 9. If a price index formula satisfies the Time Reversal Test, it implies that:

(A) The price change from period $0$ to $1$ is the same as from $1$ to $0$.

(B) The index number calculation from period $0$ to $1$ is consistent with the calculation from period $1$ to $0$.

(C) Shifting the base period from $0$ to $1$ using the formula directly yields the reciprocal index (or $10000/Index$ for percentages).

(D) The formula is equally suitable for measuring price increases and decreases.

Question 10. Marshall-Edgeworth Index satisfies which of the following tests?

(A) Time Reversal Test

(B) Factor Reversal Test

(C) Circular Test

(D) Neither Time Reversal nor Factor Reversal Test (this is incorrect, it satisfies both)

Question 1. Which of the following are examples of time series data from an Indian context?

(A) Annual production of rice in India from $2000$ to $2020$.

(B) Monthly unemployment rate in India over the last $5$ years.

(C) Daily closing value of the Sensex.

(D) Literacy rates of different states in India in a particular year.

Question 2. The defining characteristic of time series data is that the observations are ordered by:

(A) Their magnitude (smallest to largest).

(B) The time at which they were recorded.

(C) Their frequency of occurrence.

(D) A spatial dimension (like geographic location).

Question 3. The main objectives of analyzing time series data include:

(A) Understanding the underlying patterns and components of the data.

(B) Forecasting future values of the series.

(C) Making informed decisions based on past and projected trends.

(D) Calculating the correlation between different variables at a single point in time.

Question 4. Time series analysis is widely used in which of the following fields?

(A) Economics and Finance (e.g., stock prices, inflation).

(B) Meteorology (e.g., temperature, rainfall data).

(C) Production and Operations (e.g., sales forecasting, quality control).

(D) Social Sciences (e.g., population growth, crime rates).

Question 5. Univariate time series analysis focuses on:

(A) A single variable observed over time.

(B) The relationship between multiple variables over time.

(C) Data where the time intervals are always equal.

(D) Predicting the value of one variable based on others.

Question 6. The significance of studying time series patterns lies in their ability to:

(A) Help in identifying past regularities or deviations from normal behaviour.

(B) Provide a basis for extrapolating future values (forecasting).

(C) Assist in planning and control processes in various domains.

(D) Prove cause-and-effect relationships definitively.

Question 7. Time series data can be collected at various frequencies, such as:

(A) Annually

(B) Quarterly

(C) Monthly

(D) Daily or even hourly/minutely

Question 8. When observing the annual sales figures of a large company in India over the last $20$ years, which of the following might be evident?

(A) A general upward or downward trend (Secular Trend).

(B) Fluctuations related to the overall business cycle (Cyclical Variation).

(C) Regular patterns repeating within each year (Seasonal Variation).

(D) Unpredictable spikes or drops (Irregular Variation).

Question 9. Cross-sectional data differs from time series data because:

(A) Cross-sectional data is collected at a single point in time.

(B) Cross-sectional data involves multiple subjects or entities (e.g., individuals, firms, regions).

(C) Time series data involves a single entity observed over multiple time points.

(D) Cross-sectional data is always measured in monetary units.

Question 10. Time series analysis helps in understanding factors influencing a variable over time. These factors are broadly categorized into components. Which of the following are considered components of a time series?

(A) Trend

(B) Seasonality

(C) Randomness

(D) Correlation

Question 11. The primary goal of analyzing time series components is often to:

(A) Isolate each component to understand its individual impact.

(B) Use the identified patterns to forecast future values.

(C) Adjust the data to remove the effect of certain components (e.g., seasonal adjustment).

(D) Identify relationships between different time series.

Question 12. Which of the following are considered desirable properties for time series data that are often assumed for certain analytical methods?

(A) Stationarity (statistical properties like mean and variance are constant over time).

(B) Independence of observations.

(C) Constant trend and seasonality.

(D) Homoscedasticity (constant variance).

Question 1. The Secular Trend in a time series represents:

(A) Short-term fluctuations.

(B) The underlying long-term direction or movement of the series.

(C) A smooth, regular pattern over an extended period.

(D) Fluctuations that repeat within a year.

Question 2. Seasonal Variation refers to patterns in a time series that:

(A) Repeat regularly over periods longer than a year.

(B) Are caused by seasonal factors like climate, festivals, or school holidays.

(C) Have a fixed period, typically a year or a sub-period of a year (quarter, month, week, day).

(D) Represent the general upward or downward movement.

Question 3. Cyclical Variation is characterized by fluctuations that:

(A) Have a regular, repeating pattern with a fixed period within a year.

(B) Are associated with the phases of a business cycle (prosperity, recession, depression, recovery).

(C) Typically have a period longer than a year, but the period is generally not fixed or strictly regular.

(D) Are entirely unpredictable.

Question 4. Irregular Variation (also known as Random or Erratic variation) in a time series is caused by:

(A) Predictable events that repeat annually.

(B) Unexpected and unpredictable events.

(C) Factors that are difficult to identify or quantify systematically.

(D) Long-term economic changes.

Question 5. The Additive Model of time series decomposition is appropriate when:

(A) The magnitude of seasonal and cyclical fluctuations is relatively constant regardless of the level of the trend.

(B) The components are assumed to be independent of each other.

(C) The model is expressed as $Y = T + S + C + I$.

(D) The magnitude of fluctuations increases proportionally with the trend.

Question 6. The Multiplicative Model of time series decomposition is suitable when:

(A) The magnitude of seasonal and cyclical fluctuations tends to increase as the trend increases.

(B) The components are assumed to interact multiplicatively.

(C) The model is expressed as $Y = T \times S \times C \times I$.

(D) The series values are always positive.

Question 7. Identify which component is represented by the following examples in the Indian context:

(A) Increasing smartphone sales over the last decade: Secular Trend

(B) Peak demand for electricity during summer: Seasonal Variation

(C) Slowdown in economic growth during a global recession: Cyclical Variation

(D) A sudden spike in onion prices due to unexpected floods: Irregular Variation

Question 8. Decomposition of a time series helps in:

(A) Understanding the individual forces influencing the series.

(B) Removing specific components to analyze others more clearly (e.g., seasonal adjustment).

(C) Selecting appropriate forecasting methods.

(D) Converting the time series into cross-sectional data.

Question 9. Which component is typically smoothed out when a moving average with a period equal to the seasonality (e.g., a $12$-month moving average for monthly data) is applied?

(A) Secular Trend

(B) Seasonal Variation

(C) Irregular Variation

(D) Cyclical Variation is also smoothed to some extent

Question 10. Cyclical fluctuations are distinct from seasonal fluctuations because:

(A) Their period is usually longer than a year.

(B) Their period is not fixed or precisely predictable.

(C) They are generally related to broader economic conditions.

(D) They repeat at exact, predictable intervals.

Question 11. The Irregular component:

(A) Represents variations that are unpredictable and random.

(B) Is caused by unforeseen events like strikes, earthquakes, or sudden policy changes.

(C) Is usually the smallest component after removing trend, seasonal, and cyclical influences.

(D) Can be modeled and forecasted easily.

Question 12. When analyzing monthly sales data for woollen clothing in a cold climate region in India, which components would you expect to be significant?

(A) Seasonal Variation (higher sales in winter months)

(B) Secular Trend (if sales are growing or declining over years)

(C) Cyclical Variation (related to overall economic prosperity affecting discretionary spending)

(D) Irregular Variation (due to unexpected events like unseasonal weather or supply chain issues)

Question 13. In time series decomposition, the Trend-Cycle component is often estimated first, then seasonality is estimated, and finally the irregular component is the residual. This process helps in:

(A) Quantifying the contribution of each component to the observed series.

(B) Understanding the smoothed underlying movement and the regular periodic patterns.

(C) Identifying the unpredictable part of the series.

(D) Ensuring that the sum or product of components exactly equals the original series.

Question 1. Which methods are commonly used to estimate the Secular Trend in a time series?

(A) Freehand Curve Method

(B) Method of Semi-Averages

(C) Moving Average Method

(D) Method of Least Squares

Question 2. The Freehand Curve Method of measuring trend involves:

(A) Plotting the time series data.

(B) Drawing a smooth curve that appears to follow the general direction of the data.

(C) Using mathematical equations to fit the curve.

(D) Being highly subjective, depending on the individual drawing the curve.

Question 3. The Method of Semi-Averages:

(A) Divides the data into two equal halves.

(B) Calculates the average for each half.

(C) Fits a straight line through the two semi-averages plotted at the mid-points of their respective periods.

(D) Can be used to fit non-linear trends easily.

Question 4. The Moving Average Method is used for trend estimation and smoothing. The length of the moving average period (e.g., $3$-year MA, $5$-year MA) affects:

(A) How much of the short-term fluctuations are smoothed out.

(B) The number of data points for which a moving average can be calculated at the beginning and end of the series.

(C) Whether the moving average is centered or not.

(D) The underlying secular trend itself.

Question 5. Which method is considered the most objective for fitting a trend line because it minimizes the sum of the squared vertical distances between the observed values and the trend line?

(A) Freehand Curve Method

(B) Method of Semi-Averages

(C) Moving Average Method

(D) Method of Least Squares

Question 6. The Method of Least Squares can be used to fit different types of trend curves, including:

(A) Linear trend ($Y_t = a + bT$)

(B) Parabolic trend ($Y_t = a + bT + cT^2$)

(C) Exponential trend ($Y_t = ab^T$ or $\log Y_t = \log a + T \log b$)

(D) Seasonal patterns directly.

Question 7. When fitting a linear trend using the Method of Least Squares and shifting the origin of time to the middle of the series (so $\sum T = 0$), the normal equations simplify, allowing easy calculation of the coefficients. In this case:

(A) The value of $a$ is the trend value at the origin.

(B) The value of $a$ is $\frac{\sum Y}{n}$.

(C) The value of $b$ is the average rate of change per unit of time.

(D) The value of $b$ is $\frac{\sum YT}{\sum T^2}$.

Question 8. Consider the data for a time series for years $2018$, $2019$, $2020$, $2021$, $2022$. If we apply the Method of Least Squares for a linear trend and shift the origin to $2020$, what are the assigned values of T?

(A) $-2$, $-1$, $0$, $1$, $2$

(B) $1$, $2$, $3$, $4$, $5$

(C) $2018$, $2019$, $2020$, $2021$, $2022$

(D) $-2.5$, $-1.5$, $-0.5$, $0.5$, $1.5$

Question 9. The Moving Average Method is effective in eliminating or smoothing out which components of a time series, assuming the period of the moving average matches the period of the component?

(A) Secular Trend (if the period is long enough)

(B) Seasonal Variation

(C) Irregular Variation

(D) Cyclical Variation (smoothed, but not eliminated)

Question 10. Limitations of the Moving Average Method include:

(A) Loss of data points at the beginning and end of the series.

(B) It does not provide a mathematical equation for the trend, making extrapolation difficult.

(C) The choice of the period of the moving average can be arbitrary if the length of cycles or seasonality is unknown.

(D) It is highly subjective.

Question 11. When fitting a parabolic trend $Y_t = a + bT + cT^2$ using the Method of Least Squares:

(A) The coefficient $c$ indicates the rate of acceleration or deceleration of the trend.

(B) If $c > 0$, the curve opens upwards (U-shape).

(C) If $c < 0$, the curve opens downwards (inverted U-shape).

(D) This method is only applicable if the trend is perfectly symmetric.

Question 12. Compared to the Method of Least Squares, the Method of Semi-Averages is:

(A) Simpler to calculate.

(B) Less sensitive to extreme values.

(C) More objective.

(D) Only suitable for strictly linear trends.

Question 1. The Consumer Price Index (CPI) in India is used for which of the following purposes?

(A) As a primary measure of retail inflation.

(B) To calculate Dearness Allowance (DA) for government employees and pensioners.

(C) For adjusting wages and salaries in various sectors.

(D) As a measure of changes in wholesale prices.

Question 2. The Wholesale Price Index (WPI) in India is primarily used for:

(A) Tracking inflation at the producer or wholesale level.

(B) Monitoring price movements of industrial raw materials and intermediate goods.

(C) Deflating national income estimates at the wholesale stage.

(D) Measuring the cost of living for urban households.

Question 3. The Index of Industrial Production (IIP) is an important economic indicator that measures:

(A) Changes in the volume of production in the industrial sector.

(B) Short-term fluctuations in industrial output.

(C) The price level of industrial goods.

(D) Growth in different sectors like manufacturing, mining, and electricity.

Question 4. What are some common limitations faced in the construction and interpretation of all types of index numbers (including CPI, WPI, IIP)?

(A) Problems in selecting a truly representative basket of items.

(B) Challenges in accurately accounting for quality changes over time.

(C) The fixed nature of weights used in many weighted index formulas may not reflect changing consumption patterns.

(D) They always perfectly reflect the experience of every individual or business.

Question 5. CPI (Combined) in India is currently published by the National Statistical Office (NSO) and includes price data for:

(A) Both urban and rural areas.

(B) A wide range of goods and services consumed by households.

(C) Only manufactured products.

(D) Wholesale markets exclusively.

Question 6. WPI is often considered a leading indicator of inflation because:

(A) Price changes at the wholesale level often precede changes at the retail level.

(B) It directly measures consumer spending.

(C) It reflects input costs for producers.

(D) It includes services, which quickly reflect inflationary pressures.

Question 7. The Index of Industrial Production (IIP) base year is revised periodically. Revising the base year and the basket of items for IIP helps to:

(A) Reflect the changing structure of the industrial sector.

(B) Incorporate new industrial products and technologies.

(C) Make the index more representative and relevant.

(D) Increase the absolute value of the index.

Question 8. Shifting the base of an index number series is a technique used to:

(A) Compare two or more index series with different base periods.

(B) Make the index number calculation easier.

(C) Express the index relative to a more recent or relevant base year.

(D) Eliminate the impact of inflation.

Question 9. Deflating a nominal value (like income or GDP) using a price index results in a 'real' value, which represents:

(A) The value in terms of constant purchasing power (based on the base period prices).

(B) The value adjusted for inflation.

(C) The actual monetary value received in the current period.

(D) The value in units of the base period currency value.

Question 10. Consider the limitations of index numbers. The 'substitution bias' is a limitation of fixed-weight indices (like Laspeyres-type CPI) because:

(A) It assumes consumers continue to buy the same basket of goods even if relative prices change.

(B) Consumers often substitute away from goods whose relative prices have increased towards relatively cheaper goods.

(C) The index may overstate the actual increase in the cost of maintaining a certain level of well-being.

(D) It is impossible to measure changes in consumption patterns.

Question 11. The base year for the current WPI series in India is $2011-12$. This means:

(A) The average WPI for the year $2011-12$ is set to $100$.

(B) The quantities or values used as weights are typically derived from data around $2011-12$.

(C) WPI values for subsequent years are compared to the price level in $2011-12$.

(D) The index can only measure price changes starting from $2011-12$.

Question 12. Real income can be calculated by dividing nominal income by the CPI (expressed as a ratio, e.g., $1.20$ for an index of $120$). If a person's nominal income increased by $15\%$ and the CPI increased by $10\%$, which statements are true about their real income?

(A) Real income has increased.

(B) The increase in nominal income is partially offset by inflation.

(C) The approximate increase in real income is $15\% - 10\% = 5\%$.

(D) The real income change depends only on the CPI.

Question 13. The choice between using WPI and CPI depends on the purpose of the analysis. Which index is more appropriate for measuring the impact of price changes on the common person?

(A) WPI (as it reflects producer costs)

(B) CPI (as it reflects retail prices paid by consumers)

(C) Both are equally relevant.

(D) Neither index is specifically designed for common person's budget.