Case Study / Scenario-Based MCQs for Sub-Topics of Topic 14: Index Numbers & Time-Based Data

Question 1. An economist is studying the change in the general price level in Mumbai over the last decade (2015-2025). To do this effectively, they decide to construct a price index. Which of the following is the *most* appropriate definition for the statistical device they will use?

(A) A measure of the absolute increase in the cost of goods.

(B) A list of prices for essential commodities.

(C) A statistical device used to measure relative changes in the price of a group of related items over time.

(D) A graphical representation of price fluctuations.

Question 2. A retail chain operating across India wants to compare the sales performance of its clothing division in different regions during the recent festive season compared to the previous year. They decide to calculate a sales index for each region, taking the previous year's festive season sales as the base. What is the primary purpose of using an index number in this scenario?

(A) To calculate the total sales revenue for the current year.

(B) To identify the most profitable region in terms of absolute sales.

(C) To measure the relative change in sales in each region compared to the base period, allowing for easy comparison of performance across regions.

(D) To forecast sales for the next festive season.

Question 3. The Government of India is planning to revise the base year for a major economic index. They are considering using the year 2020-21 as the new base. Which of the following would be a key consideration for choosing this specific period as the base?

(A) It must be the most recent year with available data.

(B) It should ideally be a period of relative economic stability, free from major shocks.

(C) It must have the highest values recorded in the time series.

(D) Any year can be chosen as a base period arbitrarily.

Question 4. A farmer is tracking the price of fertilizers. In 2022 (base period), the price was $\textsf{₹}1500$ per bag. In 2024 (current period), the price increased to $\textsf{₹}1800$ per bag. What is the price relative for fertilizer in 2024, taking 2022 as the base?

(A) $\textsf{₹}300$

(B) $\frac{1500}{1800} \times 100 = 83.33$

(C) $\frac{1800}{1500} \times 100 = 120$

(D) $1800 - 1500 = 300$

Question 5. A manufacturing company is analyzing its production output of steel pipes. In 2019, they produced 5000 tonnes. In 2023, they produced 6500 tonnes. Using 2019 as the base year, what is the quantity relative for steel pipe production in 2023?

(A) $6500 - 5000 = 1500$ tonnes

(B) $\frac{5000}{6500} \times 100 \approx 76.92$

(C) $\frac{6500}{5000} = 1.3$

(D) $\frac{6500}{5000} \times 100 = 130$

Question 1. A small market researcher wants to create a simple price index for fruits sold in a local market, including apples (sold per kg) and bananas (sold per dozen). Base Year (2022) prices: Apples $\textsf{₹}100$/kg, Bananas $\textsf{₹}60$/dozen. Current Year (2023) prices: Apples $\textsf{₹}120$/kg, Bananas $\textsf{₹}75$/dozen. If they use the Simple Aggregate Method, what index will they get for 2023 (base 2022)?

(A) $\frac{120+75}{100+60} \times 100 = \frac{195}{160} \times 100 \approx 121.88$

(B) $\frac{100+60}{120+75} \times 100 = \frac{160}{195} \times 100 \approx 82.05$

(C) $\frac{1}{2} \left(\frac{120}{100} \times 100 + \frac{75}{60} \times 100\right) = \frac{1}{2}(120 + 125) = 122.5$

(D) This method is not suitable due to different units, leading to a potentially misleading result.

Question 2. Using the same fruit price data from Question 1, if the market researcher uses the Simple Average of Price Relatives Method (Arithmetic Mean), what index will they get for 2023 (base 2022)?

(A) $\frac{195}{160} \times 100 \approx 121.88$

(B) $\frac{120+75}{2} = 97.5$

(C) Price relative for Apples = $\frac{120}{100} \times 100 = 120$. Price relative for Bananas = $\frac{75}{60} \times 100 = 125$. Average = $\frac{120+125}{2} = 122.5$.

(D) Average of price ratios: $\frac{1.2 + 1.25}{2} \times 100 = 1.225 \times 100 = 122.5$.

Question 3. A school canteen manager wants a quick estimate of the price change for three snack items: Samosa, Pakora, and Biscuit. Base Year (2021) prices: Samosa $\textsf{₹}10$, Pakora $\textsf{₹}15$, Biscuit $\textsf{₹}5$. Current Year (2023) prices: Samosa $\textsf{₹}12$, Pakora $\textsf{₹}18$, Biscuit $\textsf{₹}6$. Using the Simple Aggregate Method, what is the index for 2023 (base 2021)?

(A) $\frac{10+15+5}{12+18+6} \times 100 = \frac{30}{36} \times 100 \approx 83.33$

(B) $\frac{12+18+6}{10+15+5} \times 100 = \frac{36}{30} \times 100 = 120$

(C) $\frac{1}{3} (\frac{12}{10} + \frac{18}{15} + \frac{6}{5}) \times 100 = \frac{1}{3}(1.2 + 1.2 + 1.2) \times 100 = 1.2 \times 100 = 120$

(D) $(1.2 \times 1.2 \times 1.2)^{1/3} \times 100 = 1.2 \times 100 = 120$

Question 4. Consider the scenario where the price of a luxury car accessory increases from $\textsf{₹}1,00,000$ to $\textsf{₹}1,20,000$, while the price of a common spare part increases from $\textsf{₹}100$ to $\textsf{₹}120$. A simple price index method is used combining these two items. Which simple method would give significantly more weight to the price increase of the luxury accessory purely based on its absolute price?

(A) Simple Aggregate Method

(B) Simple Average of Price Relatives Method

(C) Both methods would give them equal weight.

(D) Neither method is appropriate for this data.

Question 5. A researcher calculates a Simple Aggregate Price Index for a small basket of goods and gets a value of 118 for the current year. They then realize one commodity's price was quoted in tonnes in the base year and quintals in the current year, affecting the sum of prices. Which limitation of the Simple Aggregate Method is highlighted here?

(A) It does not account for the relative importance of items.

(B) It is affected by the choice of the base period.

(C) It is affected by the units of measurement of prices.

(D) It is difficult to calculate.

Question 1. A government statistical agency is constructing the Consumer Price Index (CPI) which reflects the price changes for a basket of goods and services typically consumed by urban households. CPI uses fixed weights based on household expenditure surveys from a base period. Which weighted index formula does this construction method most closely resemble?

(A) Paasche Price Index

(B) Laspeyres Price Index

(C) Marshall-Edgeworth Index

(D) Simple Aggregate Method

Question 2. An industry association wants to measure the price change for raw materials used by its members. They collect data on prices and quantities purchased in the base year (2020) and current year (2023). They calculate a price index using current year quantities as weights. Which index formula are they using?

(A) Laspeyres Price Index

(B) Weighted Average of Price Relatives

(C) Paasche Price Index

(D) Fisher's Ideal Index

Question 3. A researcher is comparing the average price change of essential food items between 2015 and 2020. They calculate a Laspeyres Price Index and a Paasche Price Index for this period. They want to use a single index that represents a balance between these two, and is considered theoretically robust. Which index would be most suitable?

(A) Simple Average of the two indices

(B) Marshall-Edgeworth Index

(C) Fisher's Ideal Index

(D) Weighted Average of Price Relatives

Question 4. Consider calculating a price index for a new product category that has grown significantly in sales volume since the base year. Using the Paasche Price Index for this category might result in a lower price index compared to Laspeyres, even if prices have increased. This is because Paasche uses current quantities, which would include the higher current volume of this product. This illustrates which potential bias in Paasche index?

(A) Overstatement of price change

(B) Understatement of price change (due to shifting consumption/production towards items with relatively lower price increases)

(C) Unit of measurement bias

(D) Base period bias

Question 5. An economist needs to calculate a consistent price index for a basket of goods over several years, say 2018, 2019, 2020, 2021. They want an index that uses weights that reflect the importance of commodities in both the base and current periods for each calculation step (e.g., 2018 to 2019, 2019 to 2020, etc.). Which index formula is designed to average the quantity weights from both periods?

(A) Laspeyres Price Index

(B) Paasche Price Index

(C) Fisher's Ideal Index (while theoretically good, its calculation for chained index is more involved than ME)

(D) Marshall-Edgeworth Index

Question 1. A statistician calculates a price index from 2020 to 2023 ($P_{2020 \to 2023}$) and then calculates another index from 2023 back to 2020 ($P_{2023 \to 2020}$). They find that the product of these two indices (when treated as ratios) is approximately 1. Which test of adequacy does this result suggest the index formula satisfies?

(A) Factor Reversal Test

(B) Circular Test

(C) Time Reversal Test

(D) Unit Test

Question 2. A researcher constructs both a price index ($P_{01}$) and a quantity index ($Q_{01}$) for a basket of goods from period 0 to period 1. They calculate the total value change for the same basket using $V_{01} = \frac{\sum p_1 q_1}{\sum p_0 q_0}$. They find that the product of their price and quantity indices ($P_{01} \times Q_{01}$) is equal to the value index ($V_{01}$) when treated as ratios. Which test of adequacy does their chosen index formula satisfy?

(A) Time Reversal Test

(B) Factor Reversal Test

(C) Circular Test

(D) Additivity Test

Question 3. A government agency uses a specific index number formula for its official price index. They need to publish a continuous series that requires linking indices across multiple base year revisions (e.g., combining a series based on 2011-12 with one based on 2016). They observe that chaining the indices using their formula ($P_{01} \times P_{12}$) does not give the same result as calculating the index directly from the original base to the final period ($P_{02}$). Which test of adequacy does their formula likely fail?

(A) Time Reversal Test

(B) Factor Reversal Test

(C) Circular Test

(D) Economic Test

Question 4. The Fisher's Ideal Index is often cited as the "ideal" index because it is constructed to possess certain desirable theoretical properties. Which key tests of adequacy are satisfied by Fisher's Ideal Index?

(A) Only Time Reversal Test

(B) Only Factor Reversal Test

(C) Both Time Reversal Test and Factor Reversal Test

(D) Circular Test

Question 5. Consider the Simple Aggregate Price Index. If prices of two goods in Period 0 are $(\textsf{₹}10, \textsf{₹}20)$ and in Period 1 are $(\textsf{₹}30, \textsf{₹}15)$. $P_{01} = \frac{30+15}{10+20} \times 100 = 150$. $P_{10} = \frac{10+20}{30+15} \times 100 = 66.67$. $P_{01} \times P_{10} \neq 10000$. Which test is explicitly shown to be failed here by the Simple Aggregate Method?

(A) Factor Reversal Test

(B) Time Reversal Test

(C) Circular Test

(D) This method satisfies all tests.

Question 1. A data analyst at an e-commerce company in India is examining the number of online orders received each day over the past two years. They want to understand the trends and patterns in this data. What type of data is the number of online orders recorded daily?

(A) Cross-sectional data

(B) Panel data

(C) Time series data

(D) Spatial data

Question 2. An economist is studying India's Gross Domestic Product (GDP) growth rate reported quarterly over the last two decades. They observe fluctuations and potential long-term movements. What is the primary objective of analyzing this GDP time series?

(A) To compare India's GDP with other countries in a specific quarter.

(B) To understand the underlying patterns in GDP growth and possibly forecast future growth rates.

(C) To determine the literacy rate of different states based on GDP.

(D) To calculate the average GDP over the entire period.

Question 3. The manager of a hydro-power plant in North India is studying the daily water levels of a reservoir over the past 5 years. The data is recorded sequentially by date. This data is a time series. What is the defining characteristic of this data that makes it a time series?

(A) It involves a single variable (water level).

(B) It is measured in a physical unit (meters).

(C) The observations are ordered according to time (day).

(D) It is collected from a single location (the reservoir).

Question 4. A financial analyst is examining the closing stock prices of a major Indian company listed on the BSE, recorded every minute during trading hours. This high-frequency data is a time series. What type of time series analysis would be most directly applied to study just this single stock price over time?

(A) Cross-sectional analysis

(B) Multivariate time series analysis

(C) Univariate time series analysis

(D) Regression analysis

Question 5. A government health department is tracking the number of reported dengue cases in a city on a weekly basis for the last 10 years. They observe that cases typically increase during the monsoon season. Time series analysis is valuable here because it helps them:

(A) Understand the geographical spread of the disease.

(B) Identify and quantify the seasonal pattern of dengue cases.

(C) Determine the average number of cases over the entire period.

(D) Find a correlation with air quality levels.

Question 1. The Ministry of Statistics and Programme Implementation (MoSPI) in India observes that the overall life expectancy in India has been steadily increasing over the past several decades. This long-term, smooth upward movement in the time series data for life expectancy represents which component?

(A) Seasonal Variation

(B) Cyclical Variation

(C) Irregular Variation

(D) Secular Trend

Question 2. The sales data for woollen garments in India shows a significant peak every year during the winter months (October to February). This regular pattern occurring within a fixed period (a year) is an example of which time series component?

(A) Secular Trend

(B) Cyclical Variation

(C) Seasonal Variation

(D) Irregular Variation

Question 3. An analysis of India's GDP growth rate over several decades shows periods of boom followed by periods of slowdown or recession, typically lasting for more than a year but with no fixed duration. These wavelike fluctuations related to the overall state of the economy represent which component?

(A) Secular Trend

(B) Seasonal Variation

(C) Irregular Variation

(D) Cyclical Variation

Question 4. A sudden and unexpected drop in tourism revenue in a particular month in India due to a terrorist attack or a major transport strike is most likely attributable to which time series component?

(A) Secular Trend

(B) Seasonal Variation

(C) Cyclical Variation

(D) Irregular Variation

Question 5. An analyst is looking at quarterly sales data for automobiles in India. They observe that sales are consistently highest in the festive quarter (Q3/Q4) each year and lowest in Q1. They also notice that the magnitude of these seasonal peaks seems to be increasing proportionally with the overall growth in the automobile market over the last decade. Which model would be more appropriate to represent this time series?

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

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

(C) Both models are equally suitable.

(D) Neither model can represent this type of variation.

Question 1. A historian is examining data on the production of handloom textiles in a region of India over the last 100 years. The data is available annually. They plot the data on a graph and draw a smooth curve visually to represent the long-term decline in production. Which method are they using to estimate the trend?

(A) Method of Semi-Averages

(B) Moving Average Method

(C) Method of Least Squares

(D) Freehand Curve Method

Question 2. A student is analyzing the annual production of sugarcane in Uttar Pradesh for the last 10 years. They divide the data into two equal halves, calculate the average production for each half, plot these averages at the mid-points of the respective periods, and draw a straight line connecting them. Which method are they using to measure the trend?

(A) Freehand Curve Method

(B) Method of Semi-Averages

(C) Moving Average Method

(D) Method of Least Squares

Question 3. A statistical department is calculating the trend for monthly data on electricity consumption in a city. They use a 12-month moving average to smooth out the seasonal pattern and irregular fluctuations, revealing the underlying trend and cyclical components. What is the primary purpose of using a moving average in this context?

(A) To fit a mathematical equation to the data.

(B) To forecast future electricity consumption.

(C) To eliminate the short-term fluctuations and highlight the smoother, longer-term movements.

(D) To calculate the average consumption over the entire period.

Question 4. A financial analyst is modeling the long-term trend in the annual profits of a company that has shown consistent growth but with some variability. They want to find an objective trend line that best fits the historical profit data. Which method is most suitable for finding the "best fit" trend line by minimizing the deviations?

(A) Freehand Curve Method

(B) Method of Semi-Averages

(C) Moving Average Method

(D) Method of Least Squares

Question 5. The annual number of internet subscribers in India showed a rapid increase in the initial years, but the rate of increase has slowed down more recently, suggesting a potential saturation. If an analyst wants to fit a curved trend line that captures this increasing trend but with a decreasing rate of increase, which method and type of curve might be appropriate using the Method of Least Squares?

(A) Fitting a linear trend ($Y=a+bT$).

(B) Fitting a parabolic trend ($Y=a+bT+cT^2$) with $c<0$.

(C) Fitting a parabolic trend ($Y=a+bT+cT^2$) with $c>0$.

(D) Using the Moving Average Method with a long period.

Question 1. A retired government employee in India receives a monthly pension. This pension is adjusted periodically based on the Dearness Allowance (DA). The DA calculation is linked to a specific index that reflects the change in the cost of living for consumers. Which index is primarily used for this purpose?

(A) Wholesale Price Index (WPI)

(B) Index of Industrial Production (IIP)

(C) Consumer Price Index (CPI)

(D) Agricultural Price Index

Question 2. The Reserve Bank of India (RBI) uses inflation data as a key factor in formulating its monetary policy (e.g., setting interest rates). For this purpose, RBI primarily tracks the inflation measured by which index?

(A) Wholesale Price Index (WPI)

(B) Consumer Price Index (CPI)

(C) Index of Industrial Production (IIP)

(D) Gross Domestic Product (GDP) Deflator

Question 3. A manufacturing company in India is assessing inflationary pressures on its input costs, such as raw materials and intermediate goods purchased from other businesses. Which index would be most relevant for them to track these price changes?

(A) Consumer Price Index (CPI)

(B) Wholesale Price Index (WPI)

(C) Index of Industrial Production (IIP)

(D) Retail Price Index

Question 4. An economic analyst wants to measure the performance of the industrial sector in India, specifically focusing on changes in the output volume of factories and mines over short periods (e.g., month-to-month). Which index is specifically designed for this purpose?

(A) Consumer Price Index (CPI)

(B) Wholesale Price Index (WPI)

(C) Index of Industrial Production (IIP)

(D) Producer Price Index (PPI)

Question 5. A person's annual salary in 2018 was $\textsf{₹}8,00,000$. The CPI for 2018, with base year 2016=100, was 115. To understand their purchasing power compared to 2016, they want to calculate their "real" salary in 2018 based on 2016 prices. What is the approximate real salary?

(A) $\textsf{₹}8,00,000 \times \frac{115}{100} = \textsf{₹}9,20,000$

(B) $\textsf{₹}8,00,000 \times \frac{100}{115} \approx \textsf{₹}6,95,652$

(C) $\textsf{₹}8,00,000 \times 115 = \textsf{₹}9,20,00,000$

(D) $\textsf{₹}8,00,000 - 115 = \textsf{₹}7,99,885$

Question 6. A statistical office is updating the basket of goods and services used for calculating the CPI. This revision is necessary because consumer spending patterns change over time with changes in income, technology, and availability of new products. Which limitation of index numbers is this revision process aimed at addressing?

(A) Difficulty in obtaining accurate data.

(B) Changes in the quality of goods.

(C) The fixed nature of the basket and weights in a Laspeyres-type index failing to capture changing consumption patterns (substitution bias).

(D) The problem of choosing a base year.