UG Applied Mathematics Booster Test 3 - Types, Limitations and Tests -

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UG Applied Mathematics Booster Test 3 - Types, Limitations and Tests

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

UG Applied Mathematics Booster Test 3 - Types, Limitations and Tests

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QUESTION 1 OF 20

Assertion (A): Value Index keeps track of inventory, sales, and trading by measuring total value changes.
Reason (R): The Value Index evaluates the average value for a particular period in comparison with that of the base period.

Answer Review

1 Assertion (A): Value Index keeps track of inventory, sales, and trading by measuring total value changes.
Reason (R): The Value Index evaluates the average value for a particular period in comparison with that of the base period.

A Both A and R are false

B A is true, R is false

C Both A and R are true, and R is the correct explanation of A

D A is false, R is true

💡 Short Explanation

Value Index compares total values across periods It is useful in inventory and sales analysis Base year comparison explains its purpose

✅ Correct Answer Explanation

The Value Index measures the total value change between the current period and the base period. It is widely used for inventory, sales, exports, imports, and trading comparisons. The Reason correctly explains the Assertion because the Value Index works by comparing average or total values relative to a base period. Hence, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

❓ Why Other Options Are Incorrect

Option A → Both statements are actually true.
Option B → The Reason is also true.
Option D → Assertion is true, not false.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Match the definition of Value Index with its practical business application.

Final Logic:

Comparing values with a base period explains why Value Index tracks inventory and sales.

🧠 Memory Trick

"Value Index = Value Comparison"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Value Index –

2 Which of the following statements incorrectly represents the formulation or purpose of a Quantity Index?

A It is defined as \(I_{n}=\frac{\sum Q_{n}}{\sum Q_{0}}\times 100\) in simple aggregative terms

B It measures changes in the volume of goods produced, consumed, or sold

C The Index of Industrial Production (IIP) is a standard example of a Quantity Index

D It acts as a vector field measuring directional price inflations over a geographical area

💡 Short Explanation

Quantity Index measures physical quantities IIP is a standard example Vector field terminology is irrelevant

✅ Correct Answer Explanation

A Quantity Index measures changes in physical quantities such as production, consumption, or sales. The simple aggregative quantity formula is: \(I_{n}=\frac{\sum Q_{n}}{\sum Q_{0}}\times 100\) The Index of Industrial Production (IIP) is a well-known Quantity Index. Option D is incorrect because Quantity Indices do not involve vector fields or directional inflation mapping.

❓ Why Other Options Are Incorrect

Option A → Correct simple aggregative quantity formula.
Option B → Correct purpose of Quantity Index.
Option C → IIP is a classic example.

🎯 Strategy

Used

Odd One Out

Application:

Identify the option using unrelated mathematical jargon.

Final Logic:

Quantity Indices measure quantity change, not vector fields.

🧠 Memory Trick

"Quantity = Physical Volume"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Quantity Index –

3 A Price Index is fundamentally designed to capture relative price changes. Why is the Method of Least Squares sometimes applied in time series data alongside price indices?

A To find the straight-line equation that best fits the time series data of the price index, minimizing the sum of squares of deviations

B To calculate the definite integral of the index curve

C To find the exact geographical area of the market

D To convert the price index into a probability matrix

💡 Short Explanation

Least Squares finds trend lines It minimizes squared deviations Used in time series trend analysis

✅ Correct Answer Explanation

The Method of Least Squares is used in time series analysis to determine the best-fitting trend line. It minimizes the sum of squared deviations between actual and estimated values. This helps analyze long-term movements in price indices. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Least Squares is not an integration method.
Option C → It does not calculate market area.
Option D → It is unrelated to probability matrices.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Connect Least Squares with trend fitting in time series.

Final Logic:

Least Squares minimizes deviations for best-fit trends.

🧠 Memory Trick

"Least Squares = Best Fit Line"

📚 Class XI – Statistics for Economics – Chapter: Correlation and Time Series – Topic: Least Squares Trend –

4 Which of the following correctly reflect the purpose of computing a Consumer Price Index (CPI)?
(i) It measures the movement in the general level of prices of consumer goods
(ii) It is primarily calculated by finding the probability of random variables
(iii) It is an example of a relative price index

A Only (i)

B (i) and (iii)

C Only (iii)

D All (i), (ii), and (iii)

💡 Short Explanation

CPI measures consumer price movement It is a relative price index Probability concepts are unrelated

✅ Correct Answer Explanation

Statement (i) is correct because CPI measures changes in consumer prices. Statement (iii) is also correct because CPI is a price relative index. Statement (ii) is incorrect because CPI calculation is not based on probability theory. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Ignores statement (iii).
Option C → Ignores statement (i).
Option D → Statement (ii) is false.

🎯 Strategy

Used

Elimination

Application:

Remove statements unrelated to index number construction.

Final Logic:

CPI measures price changes, not probability distributions.

🧠 Memory Trick

"CPI = Consumer Price Indicator"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Consumer Price Index –

5 Suppose a sample survey for an index has a 5% margin of error due to sampling limitations. If the calculated index value is 140, what is the theoretical range of the true index value based on this error margin?

A 130 to 150

B 140 exactly

C 135 to 145

D 133 to 147

💡 Short Explanation

5% of 140 = 7 Add and subtract margin Gives estimated range

✅ Correct Answer Explanation

Calculate 5% of 140: \(0.05\times 140=7\) Thus: \(140-7=133140+7=147\) So the possible range is 133 to 147. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A → Margin becomes ±10, not ±7.
Option B → Ignores sampling error.
Option C → Uses incorrect margin ±5.

🎯 Strategy

Used

Substitution

Application:

Directly compute 5% of the index value.

Final Logic:

True value lies within ±5% of 140.

🧠 Memory Trick

"5% of 140 = 7"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Sampling Errors and Limitations –

6 Arrange the following indices in ascending order of their typical values, given that the Laspeyres index tends to overestimate and the Paasche index underestimates the rise in the cost of living.
1. Fisher's Index
2. Laspeyres' Index
3. Paasche's Index

A 1, 2, 3

B 2, 1, 3

C 3, 1, 2

D 1, 3, 2

💡 Short Explanation

Paasche usually gives lower values Laspeyres gives higher values Fisher lies between them

✅ Correct Answer Explanation

Paasche Index generally underestimates the rise in cost of living. Laspeyres Index generally overestimates it. Fisher's Ideal Index is the geometric mean of both, so it lies between them. Thus: \(Paasche<Fisher<Laspeyres\) Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Places Fisher before Paasche incorrectly.
Option B → Laspeyres should not be smallest.
Option D → Fisher should not be smallest.

🎯 Strategy

Used

Option Grouping

Application:

Recall relative magnitude ordering of major weighted indices.

Final Logic:

Fisher balances Paasche and Laspeyres.

🧠 Memory Trick

"Paasche Low, Laspeyres High"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Comparison of Weighted Indices –

7 When plotting a time series graph of retail sales, the inclusion of outdated items in the index calculation will most likely:

A Perfectly smooth the moving average line

B Skew the secular trend component, making the trend line inaccurate for the current economy

C Transform the linear trend into a circular vector region

D Have zero effect on the amplitude of the cyclical component

💡 Short Explanation

Outdated items distort trends Trend line becomes unrealistic Current economy is misrepresented

✅ Correct Answer Explanation

Using outdated commodities causes the index to fail in representing present economic conditions. As a result, the secular trend component becomes distorted and misleading. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Outdated items do not improve smoothing.
Option C → Circular vector regions are irrelevant.
Option D → Outdated items can affect cyclical interpretation.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Relate outdated data to inaccurate economic trends.

Final Logic:

Old items distort current trend measurement.

🧠 Memory Trick

"Old data → Wrong trend"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Selection of Commodities –

8 Match the data-related issues to their consequences in index number construction:

List I	List II
1. Too short a base period	a. Highly unreliable prices
2. War or natural calamity in base year	b. Erratic boom or depression effects
3. Random sampling without judgment	c. Results are highly sensitive and flawed in unweighted aggregates
4. Concealed weights due to high unit price	d. Results may not be perfectly approximate for relevant commodities

A 1–a, 2–b, 3–d, 4–c

B 1–c, 2–b, 3–a, 4–d

C 1–b, 2–a, 3–d, 4–c

D 1–d, 2–c, 3–b, 4–a

💡 Short Explanation

Short base periods are unreliable War years distort prices Concealed weights bias aggregates

✅ Correct Answer Explanation

Correct matching: Too short a base period → highly unreliable prices War or calamity → boom/depression effects Random sampling → poor approximation Concealed weights → flawed unweighted results Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Incorrectly swaps concealed weights and short-period effects.
Option C → Misplaces war-year effect.
Option D → Most pairings are incorrect.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Match each data issue with its known statistical consequence.

Final Logic:

Each flaw produces a specific distortion.

🧠 Memory Trick

"War distorts, short base weakens"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Problems in Construction –

9 Assertion (A): The adequacy of an index number is tested solely by measuring the area under its time series integral.
Reason (R): If the probability of error is zero, the unit test is automatically skipped.

A Both A and R are false

B A is true, R is false

C Both A and R are true, and R is the correct explanation of A

D A is false, R is true

💡 Short Explanation

Adequacy uses statistical tests Integrals are unrelated Unit Test cannot be skipped automatically

✅ Correct Answer Explanation

Adequacy of index numbers is checked through tests like: Unit Test Time Reversal Test Factor Reversal Test It is not determined by area under integrals. Also, the Unit Test is not skipped merely because error probability is low. Hence, both Assertion and Reason are false.

❓ Why Other Options Are Incorrect

Option B → Assertion is false.
Option C → Both statements are false.
Option D → Reason is also false.

🎯 Strategy

Used

Elimination

Application:

Remove unrelated calculus and probability terminology.

Final Logic:

Adequacy relies on formal consistency tests.

🧠 Memory Trick

"Adequacy = Tests, not integrals"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Tests of Adequacy –

10 Which of the following equations correctly represent the consistency checks of the Time Reversal Test and the fundamental failure of the Laspeyres method?
(i) \(\frac{\sum p_{1}q_{0}}{\sum p_{0}q_{0}}\times \frac{\sum p_{0}q_{1}}{\sum p_{1}q_{1}}\neq 1\)
(ii) \(p_{01}\times p_{10}=1\)
(iii) \(\int p_{01} dx=1\)

A Only (i)

B Both (i) and (ii)

C Both (ii) and (iii)

D All (i), (ii), and (iii)

💡 Short Explanation

Time Reversal requires reciprocal relation Laspeyres fails this condition Integration is unrelated

✅ Correct Answer Explanation

Statement (ii) correctly defines the Time Reversal Test: \(p_{01}\times p_{10}=1\) Statement (i) correctly shows Laspeyres failure mathematically. Statement (iii) is unrelated to adequacy testing. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Ignores the standard Time Reversal equation.
Option C → Statement (iii) is false.
Option D → Integration equation is incorrect.

🎯 Strategy

Used

Option Grouping

Application:

Combine conceptual and formula-based conditions.

Final Logic:

Time Reversal uses reciprocal multiplication, not integration.

🧠 Memory Trick

"Reverse × Reverse = 1"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Time Reversal Test –

11 If wheat is priced in ₹/quintal and milk is priced in ₹/litre, which of the following index calculations will not be affected by the disparity in these units?

A Unweighted aggregate price index

B Simple aggregative index

C Simple average of relatives method

D Simple aggregate volume area

💡 Short Explanation

Unit Test checks independence from measurement units Relative methods reduce unit problems Simple average of relatives uses percentages

✅ Correct Answer Explanation

The Simple Average of Relatives Method converts prices into percentage relatives before averaging. Since percentages are unit-free, the method becomes independent of units like kg or litre. Thus, it is not affected by disparity in measurement units and satisfies the Unit Test better than simple aggregative methods. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Unweighted aggregate price index directly sums prices and is affected by units.
Option B → Simple aggregative index fails the Unit Test because units influence totals.
Option D → "Simple aggregate volume area" is not a standard unit-independent index method.

🎯 Strategy

Used

Odd One Out

Application:

Identify the method based on percentage relatives rather than raw summation.

Final Logic:

Percentage relatives remove unit dependence.

🧠 Memory Trick

"Relatives remove units"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Unit Test –

12 A manufacturer uses the simple aggregative index. The price of Commodity A rises from ₹10 to ₹15, and Commodity B rises from ₹1000 to ₹1050. The sums are:
\(\sum p_{0}=1010,\sum p_{1}=1065Index=\frac{1065}{1010}\times 100\approx 105.4\)
This demonstrates a limitation of the method because:

A The probability of calculating 1065/1010 is zero

B It perfectly satisfies the unit test

C The integral of the price is negative

D The high unit price of Commodity B conceals the significant 50% relative increase in Commodity A

💡 Short Explanation

High-priced items dominate totals Relative increases become hidden Simple aggregative method has concealed weights

✅ Correct Answer Explanation

Commodity A increased by 50%, but Commodity B increased only slightly. However, because Commodity B has a very high price level, it dominates the aggregate sum. As a result, the overall index shows only about 5.4% growth. This demonstrates the concealed weight problem in the Simple Aggregative Method. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A → Probability is irrelevant.
Option B → The method actually fails the Unit Test.
Option C → No integration or negative area is involved.

🎯 Strategy

Used

Dimensional/Unit Analysis

Application:

Compare relative percentage change with absolute price magnitude.

Final Logic:

High-priced commodities dominate unweighted totals.

🧠 Memory Trick

"Big prices hide big changes"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Limitations of Simple Aggregative Method –

13 Arrange the steps to prove that Fisher's Ideal Index satisfies the time-reversal test:
1. Substitute formulas:
\(\sqrt{\frac{\sum p_{1}q_{0}}{\sum p_{0}q_{0}}\times \frac{\sum p_{1}q_{1}}{\sum p_{0}q_{1}}}\times \sqrt{\frac{\sum p_{0}q_{1}}{\sum p_{1}q_{1}}\times \frac{\sum p_{0}q_{0}}{\sum p_{1}q_{0}}}\)
1. Write the formula for \(P_{01}\)using Fisher's method
2. Cancel out reciprocal terms under the square root
3. Write the formula for \(P_{10}\)by interchanging subscripts 0 and 1

A 2, 1, 4, 3

B 2, 4, 1, 3

C 1, 2, 3, 4

D 4, 2, 1, 3

💡 Short Explanation

Start with forward index Then write backward index Substitute and simplify reciprocals

✅ Correct Answer Explanation

To prove Fisher's Index satisfies the Time Reversal Test: Step 1 → Write \(P_{01}\) Step 2 → Write \(P_{10}\) Step 3 → Substitute both expressions Step 4 → Cancel reciprocal terms This finally gives: \(P_{01}\times P_{10}=1\) Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Substitution occurs after both formulas are written.
Option C → Formula substitution cannot begin before defining indices.
Option D → Reverse sequence is logically incorrect.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Follow the logical mathematical proof sequence.

Final Logic:

Define → interchange → substitute → simplify.

🧠 Memory Trick

"Forward → Reverse → Multiply → Cancel"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Fisher's Time Reversal Test –

14 Which statement is false regarding the reciprocal property in the Time Reversal Test?

A The reciprocal property implies that \(p_{01}\)and \(p_{10}\)must be equal vectors

B It states that if the time subscripts are interchangeable, the resulting relative should be the reciprocal of the original

C \(p_{01}\times p_{10}=1\) mathematically defines it

D The Marshall–Edgeworth method successfully fulfills this reciprocal property

💡 Short Explanation

Reciprocal does not mean equal Product must equal 1 Equality of vectors is unrelated

✅ Correct Answer Explanation

The Time Reversal Test states that the backward index should be the reciprocal of the forward index. Thus: \(p_{01}\times p_{10}=1\) This does not imply equality of vectors. Hence, Option A is false and therefore correct.

❓ Why Other Options Are Incorrect

Option B → Correct definition of reciprocal property.
Option C → Correct mathematical condition.
Option D → Marshall–Edgeworth satisfies this property.

🎯 Strategy

Used

Elimination

Application:

Remove statements matching the standard Time Reversal definition.

Final Logic:

Reciprocal relation is not vector equality.

🧠 Memory Trick

"Reciprocal ≠ Equal"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Time Reversal Test –

15 Using Fisher's formula, if the Laspeyres index is calculated as
\(\frac{435}{359}\times 100\)
and the Paasche index is
\(\frac{623}{515}\times 100,\)
what happens when computing the backward index \(p_{10}\)?

A The integral of the values reduces to 0

B The values form a moving average of 1

C The probabilities invert

D The terms interchange such that \(p_{10}\)is the square root of the inverted products, satisfying \(p_{01}\times p_{10}=1\)

💡 Short Explanation

Fisher uses reciprocal symmetry Backward index inverts ratios Product becomes 1

✅ Correct Answer Explanation

In Fisher's method, reversing time subscripts interchanges numerator and denominator terms. Thus, the backward index becomes the reciprocal form of the forward index. Therefore: \(p_{01}\times p_{10}=1\) Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A → No integration occurs.
Option B → Moving averages are unrelated.
Option C → Probability inversion is irrelevant.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Apply reciprocal logic of Fisher's method.

Final Logic:

Interchanging subscripts produces reciprocal indices.

🧠 Memory Trick

"Reverse Fisher → Invert fractions"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Fisher's Ideal Index –

16 Why specifically does the Laspeyres method fail the Time Reversal Test?
(i) When computing \(p_{10}\), the weight remains the base year quantity (i.e., \(q_{1}\)relative to the new base 1), disrupting the reciprocal fraction
(ii) \(\frac{\sum p_{1}q_{0}}{\sum p_{0}q_{0}}\times \frac{\sum p_{0}q_{1}}{\sum p_{1}q_{1}}\neq 1\)
(iii) It utilizes vector calculus which disrupts the time symmetry

A Only (i)

B Only (ii)

C Both (i) and (ii)

D All (i), (ii), and (iii)

💡 Short Explanation

Laspeyres keeps fixed weights Reciprocal condition fails Vector calculus is irrelevant

✅ Correct Answer Explanation

Statement (i) is correct because fixed quantity weights disrupt reciprocity when time is reversed. Statement (ii) correctly represents the failure mathematically: \(\frac{\sum p_{1}q_{0}}{\sum p_{0}q_{0}}\times \frac{\sum p_{0}q_{1}}{\sum p_{1}q_{1}}\neq 1\) Statement (iii) is false because vector calculus has no role here. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Ignores the mathematical condition.
Option B → Ignores conceptual explanation.
Option D → Vector calculus statement is false.

🎯 Strategy

Used

Option Grouping

Application:

Combine conceptual and formula-based reasoning.

Final Logic:

Laspeyres fails because reciprocal symmetry breaks.

🧠 Memory Trick

"Fixed weights break reversal"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Failure of Laspeyres in Time Reversal –

17 Match the test to its defining core concept:

List I	List II
1. Unit Test	a. p₀₁ × p₁₂ × p₂₀ = 1
2. Time Reversal Test	b. Interchangeability of prices and quantities
3. Factor Reversal Test	c. Independence from units such as kg, litres, etc.
4. Circular Test	d. p₀₁ × p₁₀ = 1

A 1–a, 2–b, 3–c, 4–d

B 1–d, 2–c, 3–a, 4–b

C 1–c, 2–d, 3–b, 4–a

D 1–b, 2–a, 3–d, 4–c

💡 Short Explanation

Unit Test checks unit independence Time Reversal checks reciprocity Circular Test checks multi-period consistency

✅ Correct Answer Explanation

Correct matching: Unit Test → independence from units Time Reversal Test → \(p_{01}\times p_{10}=1\) Factor Reversal Test → interchange of price and quantity Circular Test → \(p_{01}\times p_{12}\times p_{20}=1\) Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Incorrect matching of all concepts.
Option B → Unit Test and Time Reversal swapped.
Option D → Circular and Factor tests mismatched.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Match each adequacy test with its standard condition.

Final Logic:

Each adequacy test has a unique defining property.

🧠 Memory Trick

"Unit–Units, Time–Reciprocal, Circular–Cycle"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Tests of Adequacy – –334

18 Assertion (A): The Circular Test is an extension of the Time Reversal Test across multiple periods.
Reason (R): If a test satisfies the Circular Test, the probability of it being a simple aggregative method is exactly 0 because only integrals satisfy it.

A Both A and R are false

B A is true, R is false

C Both A and R are true, and R is the correct explanation of A

D A is false, R is true

💡 Short Explanation

Circular Test extends reciprocity Integrals are unrelated Probability statement is incorrect

✅ Correct Answer Explanation

Assertion (A) is true because the Circular Test extends the Time Reversal idea across several periods. The Reason (R) is false because integrals have no connection with satisfying the Circular Test. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Assertion is true.
Option C → Reason is false.
Option D → Assertion is not false.

🎯 Strategy

Used

Elimination

Application:

Separate correct adequacy-test logic from unrelated mathematical jargon.

Final Logic:

Circular Test concerns chained indices, not integrals.

🧠 Memory Trick

"Circular = Multi-time reversal"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Circular Test –

19 To accurately evaluate trend data alongside an index, a 4-year moving average is calculated. If the 4-year moving totals are 1730 and 1762, what is their centered average?

A 436.5

B 438.5

C 441.5

D 443.0

💡 Short Explanation

First compute moving averages Then average adjacent values Gives centered moving average

✅ Correct Answer Explanation

First moving average: \(\frac{1730}{4}=432.5\) Second moving average: \(\frac{1762}{4}=440.5\) Centered moving average: \(\frac{432.5+440.5}{2}=436.5\) Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Arithmetic mistake.
Option C → Incorrect averaging.
Option D → Equals only the second average approximately.

🎯 Strategy

Used

Substitution

Application:

Compute both moving averages and center them.

Final Logic:

Average of adjacent 4-year moving averages gives centered value.

🧠 Memory Trick

"Center = Average of averages"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Moving Averages – 341

20 In the evaluation and comparison of index number methods, which statement is objectively false?

A Paasche's index uses current period quantities as weights

B Laspeyres' index tends to overestimate the rise in the cost of living

C Fisher's Ideal index is the geometric mean of Laspeyres and Paasche

D Marshall–Edgeworth's method evaluates indices by calculating the definite integral of base year quantities alone

💡 Short Explanation

Marshall–Edgeworth uses combined quantities No definite integral involved Fisher uses geometric mean

✅ Correct Answer Explanation

Marshall–Edgeworth Index uses both base year and current year quantities together as weights. Its formula is: \(I_{ME}=\frac{\sum p_{n}(Q_{0}+Q_{n})}{\sum p_{0}(Q_{0}+Q_{n})}\times 100\) It does not use definite integration. Hence, Option D is false and therefore correct.

❓ Why Other Options Are Incorrect

Option A → Correct definition of Paasche Index.
Option B → Laspeyres generally overestimates cost rise.
Option C → Fisher is the geometric mean of Laspeyres and Paasche.

🎯 Strategy

Used

Odd One Out

Application:

Identify the statement introducing unrelated calculus terminology.

Final Logic:

Marshall–Edgeworth is a weighted average method, not an integral method.

🧠 Memory Trick

"ME mixes quantities, not integrals"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Marshall–Edgeworth Index –

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