Assertion-Reason MCQs for Sub-Topics of Topic 14: Index Numbers & Time-Based Data

Question 1. Assertion (A): Index numbers are often called economic barometers.

Reason (R): They measure fluctuations and relative changes in economic phenomena over time or space, providing insights into the state of the economy.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): The base period for an index number is always the first year for which data is available.

Reason (R): The base period should be a period of economic stability and normality to serve as a reliable reference point.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): A price relative of 115 for a commodity in the current period (base=100) means the price has increased by 15% compared to the base period.

Reason (R): A price relative is calculated as $\frac{\text{Current Price}}{\text{Base Price}} \times 100$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Index numbers are useful for comparing the general price level between Delhi and Mumbai in the same year.

Reason (R): Index numbers can measure changes in a group of related variables over space.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): A quantity relative measures the change in the price of a single commodity.

Reason (R): A quantity relative is calculated as the ratio of the quantity in the current period to the quantity in the base period, multiplied by 100.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): Shifting the base of an index number series changes the relative comparison between the original base period and the current period.

Reason (R): Shifting the base expresses the entire series in relation to a new base period, changing the reference point for all comparisons.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): The Simple Aggregate Method for constructing a price index is affected by the units in which prices are quoted.

Reason (R): The Simple Aggregate Method sums the absolute prices in the current and base periods, making a change in units (e.g., per kg vs per quintal) affect the sum directly.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): The Simple Average of Price Relatives Method is not affected by the units in which prices are quoted.

Reason (R): Price relatives are ratios of prices, making them unitless before averaging.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): Simple index number methods are generally not suitable for constructing important indices like the Consumer Price Index (CPI).

Reason (R): Simple methods do not incorporate weights reflecting the relative importance of different commodities.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): In the Simple Aggregate Method, a commodity with a higher price will have a greater impact on the index calculation than a commodity with a lower price, even if their percentage price changes are similar.

Reason (R): The Simple Aggregate Method sums the absolute prices, so larger absolute price changes from expensive items contribute more to the sum.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): The Simple Average of Price Relatives (Arithmetic Mean) can be heavily influenced by extremely large price relatives.

Reason (R): The Arithmetic Mean is sensitive to extreme values, and a large percentage price increase for even a single commodity can result in a very large price relative.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): Simple Quantity Indices are constructed using methods analogous to simple price indices.

Reason (R): The Simple Aggregate Quantity Index is calculated as the ratio of the sum of current year quantities to the sum of base year quantities, multiplied by 100.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Weighted index numbers provide a more realistic measure of overall change in a group of commodities compared to simple index numbers.

Reason (R): Weighted index numbers assign importance to different commodities based on factors like their share in total expenditure or production.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Laspeyres Price Index tends to overstate the increase in the cost of living.

Reason (R): Laspeyres Index uses base period quantities as weights, which does not account for consumers substituting towards relatively cheaper goods in the current period.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): Paasche Price Index tends to understate the increase in the price level.

Reason (R): Paasche Index uses current period quantities as weights, implicitly reflecting the fact that consumers may have shifted consumption towards goods whose relative prices have increased less (or decreased).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Fisher's Ideal Index is the most commonly used index in official statistics in India.

Reason (R): Fisher's Ideal Index is considered theoretically superior as it satisfies both the Time Reversal and Factor Reversal Tests.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): The Weighted Average of Price Relatives method with base period value weights ($W = p_0 q_0$) is equivalent to the Laspeyres Price Index.

Reason (R): Substituting $W = p_0 q_0$ into the formula $\frac{\sum (\frac{p_1}{p_0}) W}{\sum W} \times 100$ results in $\frac{\sum (\frac{p_1}{p_0}) p_0 q_0}{\sum p_0 q_0} \times 100 = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$, which is the Laspeyres formula.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): Constructing weighted index numbers requires data on both prices (or quantities) and corresponding weights (usually quantities or values) for both the base and current periods.

Reason (R): The choice of weights (base period or current period) is what distinguishes methods like Laspeyres and Paasche.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): The Time Reversal Test checks if the index number formula is symmetrical with respect to time.

Reason (R): The test requires that $P_{01} \times P_{10} = 1$ (for index ratios) or $P_{01} \times P_{10} = 10000$ (for percentage indices), meaning going forward and then backward in time should result in the original state.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Laspeyres Price Index satisfies the Time Reversal Test.

Reason (R): Laspeyres Price Index uses base period quantities ($q_0$) as weights, and swapping time periods means the weights for $P_{10}$ would be $q_1$, not $q_0$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): Fisher's Ideal Index satisfies the Factor Reversal Test.

Reason (R): The Factor Reversal Test requires that $P_{01} \times Q_{01} = V_{01}$, and Fisher's formula is constructed specifically to satisfy this relationship by taking the geometric mean.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): The Circular Test is an important property for indices used for comparisons involving more than two periods or for chaining index numbers.

Reason (R): The Circular Test ensures consistency such that $P_{01} \times P_{12} = P_{02}$ (for ratios), meaning the direct index from 0 to 2 is the same as the chained index via period 1.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Laspeyres and Paasche indices generally fail the Circular Test.

Reason (R): The failure of the Circular Test implies that base shifting or chaining indices using these formulas may lead to different results compared to a direct calculation from the original base to the final period.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): The Simple Aggregate Price Index does not satisfy the Time Reversal Test.

Reason (R): In the Simple Aggregate Price Index, $\frac{\sum p_1}{\sum p_0} \times \frac{\sum p_0}{\sum p_1} = 1$, thus satisfying the Time Reversal Test.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Time series data must always be collected at equally spaced time intervals.

Reason (R): Analysis of time series data is simpler when observations are collected at equal intervals, but it is not a strict requirement for all time series analysis techniques.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Analyzing the past behavior of a time series is crucial for forecasting its future values.

Reason (R): Time series analysis aims to identify patterns and components in historical data that can be extrapolated into the future, assuming these patterns will continue.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): Cross-sectional data is a type of time series data.

Reason (R): Cross-sectional data involves observations collected for multiple entities at a single point in time, whereas time series data involves observations for a single entity over successive points in time.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Univariate time series analysis studies the relationship between two or more variables over time.

Reason (R): Univariate time series analysis focuses on a single variable observed at successive points in time.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Time series analysis is useful for understanding the impact of festivals on sales figures in India.

Reason (R): The impact of festivals like Diwali or Eid constitutes a seasonal component in sales data, which time series analysis can identify and quantify.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Secular trend is the long-term movement in a time series.

Reason (R): It represents the gradual and smooth change in the series over a considerable period due to factors like population growth, technological advancements, etc.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Seasonal variation in a time series is always caused by weather changes.

Reason (R): Seasonal variation repeats within a fixed period (like a year) and can be caused by factors like weather, festivals, customs, and administrative rules.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): Cyclical variations have a regular and predictable period, typically lasting exactly one year.

Reason (R): Cyclical variations are associated with economic cycles and have periods longer than a year, which are not strictly fixed or regular.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Irregular variations are random fluctuations in a time series that cannot be explained by trend, seasonality, or cyclical movements.

Reason (R): These variations are caused by unforeseen events like strikes, natural disasters, or sudden policy changes.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): The Additive Model of time series decomposition is suitable when the magnitude of seasonal fluctuations is constant over time.

Reason (R): In the Additive Model, the components are summed ($Y = T + S + C + I$), implying that the variations are absolute amounts added to the trend.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): The Multiplicative Model is preferred when seasonal variations increase proportionally with the level of the time series.

Reason (R): In the Multiplicative Model ($Y = T \times S \times C \times I$), the seasonal component is a factor that scales the trend, allowing its impact to grow as the trend increases.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): The Freehand Curve Method is an objective method for estimating trend.

Reason (R): In the Freehand Curve Method, the trend line is drawn subjectively by visually inspecting the plotted data.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): The Method of Semi-Averages divides the time series data into two equal parts and calculates the geometric mean of each part.

Reason (R): The Method of Semi-Averages uses the arithmetic mean of each equal half of the data to fit a straight line trend.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): A major advantage of the Moving Average Method is that it provides a mathematical equation for the trend, useful for extrapolation.

Reason (R): The Moving Average Method is primarily a smoothing technique and does not result in a specific algebraic expression for the trend line.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): The Method of Least Squares provides the best fit for a trend line in the sense of minimizing the sum of squared errors.

Reason (R): The least squares principle finds the line (or curve) that minimizes the vertical distances between the observed data points and the fitted line (or curve).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): When fitting a linear trend $Y = a + bT$ using Least Squares with the origin at the middle year, the coefficient 'a' represents the average value of Y over the entire period.

Reason (R): With the origin at the middle year (and $\sum T = 0$), the normal equation $\sum Y = na + b \sum T$ simplifies to $\sum Y = na$, so $a = \frac{\sum Y}{n} = \bar{Y}$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): A parabolic trend $Y_t = a + bT + cT^2$ is suitable for a time series where the rate of growth is accelerating or decelerating.

Reason (R): The coefficient 'c' in the parabolic trend equation measures the rate of change of the slope (acceleration or deceleration).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): The Consumer Price Index (CPI) measures inflation at the wholesale level.

Reason (R): CPI measures the change in the retail prices of a basket of goods and services consumed by households.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Wholesale Price Index (WPI) is often used as a leading indicator of inflation in CPI.

Reason (R): Price changes at the wholesale level often get passed on to consumers at the retail level after a time lag.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): The Index of Industrial Production (IIP) measures changes in the volume of industrial production in India.

Reason (R): IIP is a key indicator used to assess the growth or decline in the output of the manufacturing, mining, and electricity sectors.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): One limitation of using index numbers is the difficulty in accounting for changes in the quality of goods over time.

Reason (R): If the quality of a product improves, a constant price might represent a decrease in the price per unit of quality, which is hard to capture in standard index number calculations.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): CPI is widely used in India for adjusting wages and salaries (Dearness Allowance).

Reason (R): Adjusting nominal wages by CPI helps maintain the real purchasing power of employees' income against inflation.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): Deflating a nominal value using a price index converts it into real terms.

Reason (R): Dividing a nominal value by a price index (and multiplying by 100 if the index base is 100) removes the effect of price changes, expressing the value in terms of the base period's purchasing power.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 7. Assertion (A): The basket of goods and services used for calculating CPI remains fixed permanently.

Reason (R): The basket and weights are revised periodically to reflect changes in consumer spending patterns, introduction of new products, etc., to maintain relevance.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 8. Assertion (A): WPI is considered more relevant than CPI for measuring the impact of inflation on the common household budget.

Reason (R): WPI tracks prices at the wholesale level, while CPI tracks prices at the retail level where consumers actually purchase goods and services.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.