UG Applied Mathematics Booster Test 3 - Methods of Index Numbers -

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UG Applied Mathematics Booster Test 3 - Methods of Index Numbers

⏱️ 30 Minutes

❓ 20 Questions

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

UG Applied Mathematics Booster Test 3 - Methods of Index Numbers

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QUESTION 1 OF 20

In a time series, a moving average smooths data. In contrast, the simple aggregative method directly assesses raw price summation. Compute the simple aggregative index if
∑p_0=359"and"∑p_n=515.
"Simple Aggregative Index"=(∑p_n)/(∑p_0 )×100

Answer Review

1 In a time series, a moving average smooths data. In contrast, the simple aggregative method directly assesses raw price summation. Compute the simple aggregative index if
∑p_0=359"and"∑p_n=515.
"Simple Aggregative Index"=(∑p_n)/(∑p_0 )×100

A 120.50

B 133.40

C 143.45

D 150.20

💡 Short Explanation

Additive price totals are compared Current sum is divided by base sum Result is expressed as a percentage

✅ Correct Answer Explanation

The Simple Aggregative Index formula is: \(P_{01}=\frac{\sum p_{n}}{\sum p_{0}}\times 100\) Substituting the values: \(P_{01}=\frac{515}{359}\times 100P_{01}=143.45\) Thus, Option C is correct. Option A and B underestimate the ratio, while Option D overestimates the computed percentage.

❓ Why Other Options Are Incorrect

Option A → Incorrect numerical computation of the ratio.
Option B → Does not match the correct percentage value.
Option D → Higher than the actual calculated index.

🎯 Strategy

Used

Substitution

Application:

Direct substitution into the standard aggregative formula gives the answer immediately.

Final Logic:

\(515\div 359\times 100=143.45\)

🧠 Memory Trick

"Current total over Base total"

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

2 Identify the incorrect statement regarding quantity summation in simple index formulation.

A It uses unweighted quantity sums.

B It expresses the aggregate of quantities in any year as a percentage.

C It lacks weighting mechanisms.

D It uses p_n Q_nas the numerator for summation.

💡 Short Explanation

Quantity summation uses only quantities No weights are applied Price–quantity products are absent

✅ Correct Answer Explanation

A simple quantity summation index uses: \(Q_{01}=\frac{\sum Q_{n}}{\sum Q_{0}}\times 100\) It does not involve price–quantity products such as \(p_{n}Q_{n}\). Hence, Option D is incorrect. Options A, B, and C correctly describe the unweighted quantity summation method.

❓ Why Other Options Are Incorrect

Option A → Correct because the method is unweighted.
Option B → Correct since the result is expressed as a percentage.
Option C → Correct because no weighting mechanism exists.

🎯 Strategy

Used

Elimination

Application:

Identify the option introducing weighted expenditure terms into an unweighted method.

Final Logic:

Simple quantity summation excludes \(p_{n}Q_{n}\).

🧠 Memory Trick

"Simple quantity = Quantities only"

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

3 Match the concepts related to absence or treatment of weights in index numbers.

List I (Concepts)	List II (Explanation)
1. Concealed Weights	a. High unit prices dominate the index due to lack of distinct quantity weights
2. Equal Importance	b. Individually calculated relatives disregard absolute quantities
3. Price Dominance Effect	c. All commodities are treated uniformly regardless of their significance
4. Ignoring Quantity Differences	d. Implicit weighting occurs due to differences in price magnitudes

A 1–a, 2–c, 3–d, 4–b

B 1–d, 2–c, 3–a, 4–b

C 1–b, 2–a, 3–c, 4–d

D 1–c, 2–d, 3–b, 4–a

💡 Short Explanation

Expensive goods create hidden weights Equal importance ignores significance Relative methods ignore quantity differences

✅ Correct Answer Explanation

Correct matching: • Concealed Weights → implicit weighting due to price magnitude → d • Equal Importance → all commodities treated equally → c • Price Dominance Effect → high-priced goods dominate → a • Ignoring Quantity Differences → relatives ignore actual quantities → b Therefore, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Swaps concealed weights and dominance effect.
Option C → Incorrect pairings throughout.
Option D → Misplaces nearly all conceptual matches.

🎯 Strategy

Used

Option Grouping

Application:

Associate each concept with its defining limitation or behavior.

Final Logic:

High prices create concealed weights while relatives ignore quantities.

🧠 Memory Trick

"Hidden prices = Hidden weights"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Defects of Unweighted Methods –

4 Arrange the steps mathematically to demonstrate the high value bias effect taking over a simple aggregate:
1. Calculate individual percentage price relatives for contrast.
2. Observe that the raw summation index favors the ₹148 item.
3. Compare the unweighted aggregate index result to the relatives average.
4. Add prices of a ₹3 item and a ₹148 item together.

A 1, 2, 3, 4

B 4, 2, 1, 3

C 3, 2, 1, 4

D 2, 3, 4, 1

💡 Short Explanation

Begin with raw aggregation Observe dominance of costly item Compare with relatives method

✅ Correct Answer Explanation

Logical order: 1. Add ₹3 and ₹148 together 2. Observe dominance of ₹148 in total 3. Calculate separate relatives for comparison 4. Compare aggregate and relatives average Thus, Option B correctly demonstrates high-value bias progression.

❓ Why Other Options Are Incorrect

Option A → Starts with relatives before aggregation.
Option C → Comparison should come last.
Option D → Observation cannot occur before summation.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Follow the natural mathematical flow from raw addition to analytical comparison.

Final Logic:

Aggregation must precede bias observation and comparison.

🧠 Memory Trick

"Add → Observe → Compare"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: High Value Bias in Aggregative Method –

5 A commodity's relative conversion index is 150. If the base period price was "₹" 40, what is the current period price?
"Price Relative"=p_n/p_0 ×100

A ₹100

B ₹125

C ₹60

D ₹200

💡 Short Explanation

Relative index equals 150 Base price equals ₹40 Solve for current price

✅ Correct Answer Explanation

Using the formula: \(\frac{p_{n}}{p_{0}}\times 100=150\) Substitute \(p_{0}=40\): \(\frac{p_{n}}{40}\times 100=150p_{n}=60\) Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Would produce relative 250.
Option B → Gives relative 312.5.
Option D → Gives relative 500.

🎯 Strategy

Used

Substitution

Application:

Rearrange the relative formula to find current price.

Final Logic:

\(150\%\)of 40 equals 60.

🧠 Memory Trick

"150% of 40 = 60"

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

6 Which of the following formulas represent a correct mean calculation for price indices?

A (∑p_n)/(∑p_0 )

B ∑p_n Q_0

C ∫(p_0)" " dp

D (∑(p_n/p_0 ⓜ×100))/N

💡 Short Explanation

Price relatives are averaged Divide total relatives by number of items Produces arithmetic mean index

✅ Correct Answer Explanation

The Simple Average of Price Relatives method is: \(P=\frac{\sum \left(\frac{p_{n}}{p_{0}},\ 100\right)}{N}\) This is exactly represented by Option D. Option A is a simple aggregative formula, not a mean of relatives.

❓ Why Other Options Are Incorrect

Option A → Aggregative method, not average relatives.
Option B → Weighted expenditure component only.
Option C → Irrelevant integral expression.

🎯 Strategy

Used

Option Grouping

Application:

Identify the formula explicitly averaging price relatives.

Final Logic:

Mean index requires summation divided by number of commodities.

🧠 Memory Trick

"Average relatives = Sum relatives ÷ N"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Simple Average of Relatives –

7 Assertion (A): The simple average of relatives properly incorporates varying quantity weights to balance items.
Reason (R): It explicitly uses p_n Q_nas value weights in its core formula.

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

Simple average ignores weights No value weighting exists Both statements are incorrect

✅ Correct Answer Explanation

The Assertion is false because the simple average of relatives gives equal importance to all items. The Reason is also false because \(p_{n}Q_{n}\)value weights are not used in the simple average method. Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Assertion itself is incorrect.
Option C → Neither statement is true.
Option D → Reason is also false.

🎯 Strategy

Used

Elimination

Application:

Recall that simple averages are unweighted methods.

Final Logic:

No quantity weights or value weights are included.

🧠 Memory Trick

"Simple relatives = Equal importance"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Defects of Simple Average Method –

8 Assertion (A): The simple average of relatives effectively gives equal probability or importance to each relative, heavily ignoring absolute quantities.
Reason (R): It mathematically utilizes moving averages to strictly smooth the index data.

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

Equal importance is a known flaw Quantities are ignored Moving averages are unrelated

✅ Correct Answer Explanation

The Assertion is true because simple average of relatives gives equal importance to every commodity regardless of quantity. The Reason is false because moving averages belong to time-series smoothing techniques, not simple average of relatives. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

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

🎯 Strategy

Used

Elimination

Application:

Separate index methods from time-series smoothing methods.

Final Logic:

Equal importance is true, moving averages are irrelevant here.

🧠 Memory Trick

"Relatives ignore quantity"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Limitation of Average Relatives Method –

9 Assertion (A): Taking a cross-sectional weighted aggregate provides a much better and more accurate comparison than simple aggregates.
Reason (R): The allotment of vector quantities as weights enables commodities of greater importance to have more impact.

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

Weighted methods improve realism Important commodities get larger influence Reason correctly explains assertion

✅ Correct Answer Explanation

The Assertion is true because weighted indices provide more accurate economic comparisons. The Reason is also true because assigning weights based on importance ensures significant commodities affect the index more strongly. Thus, the Reason correctly explains the Assertion.

❓ Why Other Options Are Incorrect

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

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Link weighted importance with improved index accuracy.

Final Logic:

Weighted influence produces realistic economic comparison.

🧠 Memory Trick

"More important goods = More weight"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Weighted Aggregative Method –

10 Assertion (A): The unweighted aggregative index acts as a perfect economic integral and is the most accurate method.
Reason (R): Taking the fixed quantity of usage into account in a weighted index helps find a mathematically precise index, resisting unit-based dominance.

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

Unweighted methods are biased Weighted methods resist dominance effects Fixed quantities improve accuracy

✅ Correct Answer Explanation

The Assertion is false because unweighted aggregative indices are not the most accurate; they suffer from concealed weight bias. The Reason is true because weighted indices use quantities to reduce dominance by high-priced commodities. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A → Reason is actually true.
Option B → Assertion is false.
Option C → Assertion is not true.

🎯 Strategy

Used

Elimination

Application:

Recall the defects of unweighted methods and advantages of weighting.

Final Logic:

Weighted indices are more accurate than unweighted aggregates.

🧠 Memory Trick

"Weights reduce bias"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Weighted vs Unweighted Methods –

📄 Passage

"It is essential to test the consistency of a good index number using methods such as the Time Reversal Test. If the time subscripts (0 and 1) of a price or quantity index number are interchanged, then the resulting relative should be the reciprocal of the original. The Laspeyres method does not satisfy this condition."

Based on the passage, the base year weights structure of the Laspeyres method causes it to fail the Time Reversal Test. This is mathematically expressed as:

A P_01×P_10≠1

B P_01+P_10=1

C P_01×P_10=1

D P_01/P_10 =0

💡 Short Explanation

Time reversal requires reciprocal consistency Laspeyres method fails this condition Product of reverse indices is not 1

✅ Correct Answer Explanation

The Time Reversal Test requires: \(P_{01}\times P_{10}=1\) Laspeyres index uses fixed base-year quantities as weights. Due to this fixed weighting structure, reversing time subscripts does not produce reciprocal consistency. Hence: \(P_{01}\times P_{10}\neq 1\) Therefore, Option A is correct. Option C represents the condition for satisfying the test, which Laspeyres fails.

❓ Why Other Options Are Incorrect

Option B → Addition of indices is unrelated to the Time Reversal Test.
Option C → This is the ideal condition, not the Laspeyres failure condition.
Option D → Division equal to zero has no relevance here.

🎯 Strategy

Used

Elimination

Application:

Recall the standard Time Reversal condition and identify the failure form.

Final Logic:

Since Laspeyres fails the test, the product cannot equal 1.

🧠 Memory Trick

"Time reversal ⇒ Product = 1"

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

📄 Passage

Regarding the overestimation issue, if data calculation shows
"Laspeyres"=403"andPaasche"=381,
this mathematical gap primarily indicates:

A Paasche method inherently overestimates usage

B Laspeyres value is higher because it strictly retains base weights, often overestimating the rise as consumers shift habits

C Both are exactly equal in real terms

D The Fisher test is mathematically flawed

💡 Short Explanation

Laspeyres uses base-year weights Consumer substitution is ignored This creates upward bias

✅ Correct Answer Explanation

Laspeyres Index uses base-period quantities: \(L=\frac{\sum p_{n}Q_{0}}{\sum p_{0}Q_{0}}\times 100\) Consumers generally reduce consumption of items whose prices rise sharply. Since Laspeyres continues using old base-year quantities, it ignores this adjustment and often overestimates the rise in cost of living. Since \(403>381\), the Laspeyres estimate is higher than the Paasche estimate. Therefore, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Paasche usually underestimates rather than overestimates.
Option C → The values are clearly unequal.
Option D → Fisher's method is not flawed here.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Compare behavior of base-weight and current-weight methods.

Final Logic:

Fixed base weights create upward bias in Laspeyres.

🧠 Memory Trick

"Laspeyres locks old habits"

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

13 The expenditure area computed using current year weights defines the components of the Paasche index. In the Paasche index formula, the denominator utilizes:

A ∑p_0 Q_0

B ∑p_n Q_0

C ∑p_0 Q_n

D ∑p_n Q_n

💡 Short Explanation

Paasche uses current-year quantities Current quantities appear in numerator and denominator Base prices remain in denominator

✅ Correct Answer Explanation

The Paasche Price Index formula is: \(P=\frac{\sum p_{n}Q_{n}}{\sum p_{0}Q_{n}}\times 100\) The denominator therefore contains: \(\sum p_{0}Q_{n}\) Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Used in Laspeyres denominator.
Option B → Not a standard denominator expression.
Option D → This forms the numerator.

🎯 Strategy

Used

Substitution

Application:

Recall the standard Paasche formula directly.

Final Logic:

Current quantities appear in both numerator and denominator.

🧠 Memory Trick

"Paasche = Present quantities"

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

14 When the Paasche curve exhibits its underestimation issue ("Paasche" ⓜ<"Laspeyres" ), the economic interpretation suggests:

A Quantity usage has exponentially decreased everywhere

B Market prices universally dropped to zero

C There are severe integral errors in the raw data

D Usage has increased faster in the lower-priced sectors as consumers adapt to current needs

💡 Short Explanation

Paasche uses current weights Consumers shift toward cheaper goods This lowers measured inflation

✅ Correct Answer Explanation

Paasche Index uses current-year quantities, reflecting consumer adaptation: \(P=\frac{\sum p_{n}Q_{n}}{\sum p_{0}Q_{n}}\times 100\) When consumers buy more relatively cheaper goods, the measured increase in cost of living becomes lower. Hence, Paasche generally underestimates inflation compared to Laspeyres. Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A → Exponential decrease is not implied.
Option B → Prices do not fall to zero.
Option C → The issue is economic weighting, not data integration errors.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Link current-weight adjustment with consumer substitution behavior.

Final Logic:

Consumers shift toward cheaper items, lowering the index.

🧠 Memory Trick

"Paasche follows present choices"

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

15 Utilizing the geometric mean concept, if the Laspeyres index (L)=114.9and the Paasche index (P)=113.2, the Fisher index is logically structured as:

A √(114.9×113.2)

B (114.9+113.2)/2

C 114.9×113.2

D (114.9)/(113.2)

💡 Short Explanation

Fisher uses geometric mean Combines Laspeyres and Paasche Formula involves square root

✅ Correct Answer Explanation

Fisher's Ideal Index is defined as: \(F=\sqrt{LP}\) Substituting: \(F=\sqrt{114.9\times 113.2}\) Thus, Option A correctly represents the Fisher Index structure.

❓ Why Other Options Are Incorrect

Option B → Arithmetic mean, not geometric mean.
Option C → Missing square root.
Option D → Ratio formula is incorrect.

🎯 Strategy

Used

Option Grouping

Application:

Identify the formula containing the geometric mean operation.

Final Logic:

Fisher Index always uses square root of \(L\times P\).

🧠 Memory Trick

"Fisher = √(L×P)"

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

16 The Fisher index stands as the ideal index concept because its formulation allows it to mathematically satisfy:

A The unit test only, while failing all others

B The time-reversal test (and unit test), proving P_01×P_10=1

C Neither the time-reversal test nor the unit test

D The circular test exclusively

💡 Short Explanation

Fisher passes major adequacy tests Time reversal condition is satisfied Hence called ideal index

✅ Correct Answer Explanation

Fisher's Index satisfies important tests of adequacy, especially: \(P_{01}\times P_{10}=1\) This fulfills the Time Reversal Test. Because Fisher combines Laspeyres and Paasche geometrically, it balances their biases and becomes the "Ideal Index." Thus, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Fisher satisfies more than just unit test.
Option C → Completely incorrect.
Option D → Circular test alone is insufficient.

🎯 Strategy

Used

Elimination

Application:

Recall why Fisher is termed ideal.

Final Logic:

Fisher satisfies key adequacy tests including time reversal.

🧠 Memory Trick

"Fisher passes reversal"

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

17 The expression
∑p_n (Q_0+Q_n)
serves as the numerator for evaluating the average weights method in which index?

A Laspeyres Index

B Paasche Index

C Marshall–Edgeworth Index

D Fisher's Ideal Index

💡 Short Explanation

Uses combined quantities Average weighting approach Base and current quantities are added

✅ Correct Answer Explanation

Marshall–Edgeworth Index uses average quantities as weights: \(ME=\frac{\sum p_{n}(Q_{0}+Q_{n})}{\sum p_{0}(Q_{0}+Q_{n})}\times 100\) The numerator therefore is: \(\sum p_{n}(Q_{0}+Q_{n})\) Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Uses only base quantities.
Option B → Uses only current quantities.
Option D → Fisher uses geometric mean.

🎯 Strategy

Used

Substitution

Application:

Recall the combined-weight formula directly.

Final Logic:

Sum of base and current quantities identifies Marshall–Edgeworth.

🧠 Memory Trick

"Marshall mixes both quantities"

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

18 Unlike the Laspeyres index, which uses base weights exclusively, the Marshall–Edgeworth index features combined period weights. This means it explicitly uses:

A Only the current year quantities

B Only the base year quantities

C A 4-year continuous moving average

D Both base and current year quantities summed together

💡 Short Explanation

Combined weighting system Base and current quantities are added Produces balanced weighting

✅ Correct Answer Explanation

Marshall–Edgeworth Index uses: \(Q_{0}+Q_{n}\) as combined weights. This incorporates both base-year and current-year quantities. Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A → Describes Paasche only.
Option B → Describes Laspeyres only.
Option C → Moving averages are unrelated.

🎯 Strategy

Used

Odd One Out

Application:

Identify the only option involving combined-period weights.

Final Logic:

Marshall–Edgeworth merges both periods' quantities.

🧠 Memory Trick

"Marshall merges both"

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

19 When computing relatives with weights, the value weight parameter explicitly formulated as
p_0 Q_0
is predominantly utilized in the:

A Weighted average of relatives method

B Unweighted simple average method

C Basic quantity index method

D Raw value index method

💡 Short Explanation

Base-year value weights are used Weighted relatives improve realism Expenditure weights influence averages

✅ Correct Answer Explanation

The Weighted Average of Relatives method commonly uses value weights: \(p_{0}Q_{0}\) These represent base-year expenditures and help assign importance to commodities. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Unweighted method uses no weights.
Option C → Quantity index differs conceptually.
Option D → Not the standard weighted relatives formulation.

🎯 Strategy

Used

Option Grouping

Application:

Associate expenditure weights with weighted relatives.

Final Logic:

\(p_{0}Q_{0}\)are standard value weights.

🧠 Memory Trick

"Value weights = p₀Q₀"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Weighted Average of Relatives –

20 The weighted average of relatives provides improved accuracy and is mathematically identical in its final calculation to which aggregative method when utilizing base value weights (p_0 Q_0 )?

A Simple aggregative index

B Laspeyres index (since p_n/p_0 ×p_0 Q_0=p_n Q_0)

C Paasche index

D Fisher's Ideal index

💡 Short Explanation

Base value weights simplify expression Formula transforms into Laspeyres form Both methods become equivalent

✅ Correct Answer Explanation

Weighted relatives formula: \(\frac{\sum \left(\frac{p_{n}}{p_{0}},\ p_{0}Q_{0}\right)}{\sum p_{0}Q_{0}}\times 100\) Simplifies to: \(\frac{\sum p_{n}Q_{0}}{\sum p_{0}Q_{0}}\times 100\) which is exactly the Laspeyres Index formula. Therefore, Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Simple aggregative method uses no weights.
Option C → Paasche uses current quantities.
Option D → Fisher uses geometric mean.

🎯 Strategy

Used

Substitution

Application:

Algebraic simplification directly reveals equivalence.

Final Logic:

\(\frac{p_{n}}{p_{0}}\times p_{0}Q_{0}=p_{n}Q_{0}\)

🧠 Memory Trick

"Weighted relatives → Laspeyres form"

📚 Class XI – Statistics for Economics – Chapter: Index Numbers – Topic: Weighted Average of Relatives –

UG Applied Mathematics Booster Test 3 - Methods of Index Numbers

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