Statistics Class 11 Chapter 5 - Index Numbers - Solved MCQs for All Exam Boards

"THE HOLY QURAN AND STATISTICS"
Surah Al-Jinn (72:28):
وَأَحْصَىٰ كُلَّ شَيْءٍ عَدَدًا

"And He has enumerated everything in numbers." (Allah perfectly counts and knows the exact measure of all creations).

(F.Sc. Part – I, Chapter 5: Index Numbers)

Q1. An index number computed for a single variable is called:

A. Simple index number   ✓ Correct Answer

B. Composite index number

C. Weighted composite index number

D. None

Explanation: An index based on only one item/variable is called a simple index number.

Q2. An index number computed for a group of related variables is called:

A. Simple index number

B. Composite index number   ✓ Correct Answer

C. Weighted composite index number

D. None

Explanation: When several related variables/items are combined into one index, it is called a composite index number.

Q3. An index number calculated for more than one item is called:

A. Composite   ✓ Correct Answer

B. Simple

C. Price relative

D. None

Explanation: Combining multiple items into a single index makes it a composite index number.

Q4. Chaining process is a method of converting the link relatives into:

A. Fixed base relatives   ✓ Correct Answer

B. Quantities

C. Prices

D. None

Explanation: Chaining multiplies successive link relatives together to convert them into fixed base relatives.

Q5. The chain relatives are the fixed base relatives computed from:

A. Fixed base relatives

B. Link relatives   ✓ Correct Answer

C. Both (a) and (b)

D. None

Explanation: Chain relatives are derived by successively multiplying (chaining) the link relatives.

Q6. The fixed base relatives computed from link relatives are called:

A. Chain relatives   ✓ Correct Answer

B. Link relatives

C. Fixed base relatives

D. None

Explanation: This chaining process itself produces what are called chain relatives.

Q7. The index number for the base year is:

A. 100   ✓ Correct Answer

B. Greater than 100

C. Less than 100

D. None

Explanation: By convention, the base year is always assigned an index value of 100.

Q8. The other name of quantity index number is:

A. Volume index number

B. Quantum index number

C. Value index number

D. Both (a) and (b)   ✓ Correct Answer

Explanation: Quantity index numbers are also known as volume index numbers or quantum index numbers — both terms apply.

Q9. Laspeyre's index number suggested using ___ as weights.

A. Base year quantity   ✓ Correct Answer

B. Current year quantity

C. Current year price

D. All

Explanation: Laspeyre's index uses base year quantities as fixed weights.

Q10. Paasche's index number suggested using ___ as weights.

A. Base year quantity

B. Current year quantity   ✓ Correct Answer

C. Current year price

D. All

Explanation: Paasche's index uses current year quantities as weights.

Q11. Laspeyre's index has:

A. Upward bias   ✓ Correct Answer

B. Downward bias

C. No bias

D. None

Explanation: Since it uses fixed base year quantities, Laspeyre's index tends to overstate price rises — an upward bias.

Q12. Paasche's index has a:

A. Upward bias

B. Downward bias   ✓ Correct Answer

C. No bias

D. None

Explanation: Using current year quantities, Paasche's index tends to understate price rises — a downward bias.

Q13. To make comparisons, link relatives are converted to:

A. Price relatives

B. Chain relatives   ✓ Correct Answer

C. Quantity relatives

D. Value relatives

Explanation: Link relatives are chained together (multiplied successively) to form chain relatives for comparison.

Q14. Link relatives are calculated using the:

A. Chain base method   ✓ Correct Answer

B. Fixed base method

C. Simple aggregative method

D. Aggregate expenditure method

Explanation: Link relatives — the ratio of each period's value to the immediately preceding period — are computed under the chain base method.

Q15. FBS stands for:

A. Federal Bureau of Statistics   ✓ Correct Answer

B. Football Statistics

C. First Book of Statistics

D. None

Explanation: FBS is the abbreviation for the Federal Bureau of Statistics (Pakistan).

Q16. The chain index for the base year is:

A. 100   ✓ Correct Answer

B. Greater than 100

C. Less than 100

D. None

Explanation: Just like any index number, the base year in a chain index is fixed at 100.

Q17. The link relative is the percentage ratio of a given year's value with the:

A. First year value

B. Succeeding year value

C. Same year value

D. Preceding year value   ✓ Correct Answer

Explanation: By definition, a link relative compares a given year's value to the immediately preceding year's value.

Q18. Link relative = (Pₙ / ___) × 100:

A. Pₙ

B. Pₙ₋₁   ✓ Correct Answer

C. Pₙ₋₃

D. Pₙ₋₂

Explanation: Link relative uses the immediately preceding period's value, Pₙ₋₁, in the denominator.

Q19. The common way used to measure inflation in Pakistan is:

A. Price indicator

B. CPI   ✓ Correct Answer

C. WPI

D. None

Explanation: The Consumer Price Index (CPI) is the standard measure used to track inflation in Pakistan.

Q20. The inverse of the consumer price index number can be used to measure the:

A. Purchasing power of money   ✓ Correct Answer

B. Man power

C. Water power

D. Electric power

Explanation: Taking the reciprocal of CPI (×100) gives the purchasing power of money.

Q21. Indices used as a factor to cancel out the effect of inflation are:

A. GMI

B. WPI

C. CPI   ✓ Correct Answer

D. Both (a) and (b)

Explanation: CPI is commonly used to deflate nominal values and remove the effect of inflation.

Q22. The index number that measures changes in the producer's selling price is:

A. Whole sale price index number   ✓ Correct Answer

B. Consumer price index number

C. Sensitive Price Indicator

D. None

Explanation: The Wholesale Price Index (WPI) tracks prices at the producer/wholesale level.

Q23. The index number of import and export prices helps measure change in terms of:

A. Trade of the country   ✓ Correct Answer

B. Purchasing power of money

C. Inflation

D. None

Explanation: Import/export price indices are used to gauge changes in a country's trade position.

Q24. The geometric mean of the Laspeyre's and Paasche's index numbers is called:

A. Marshall's index number

B. Fisher's index number   ✓ Correct Answer

C. Pearson's index number

D. Walsh's index number

Explanation: Fisher's Ideal Index is defined as the geometric mean of the Laspeyre's and Paasche's indices.

Q25. A current year weighted index number is the:

A. Fisher's

B. Laspeyre's

C. Paasche's   ✓ Correct Answer

D. Marshall's

Explanation: Paasche's index uses current year quantities as weights, making it a current-year weighted index.

Q26. A base year weighted index number is the:

A. Paasche's

B. Laspeyre's   ✓ Correct Answer

C. Fisher's

D. Walsh's

Explanation: Laspeyre's index uses base year quantities as weights, making it a base-year weighted index.

Q27. Quantum index number is another name for:

A. Volume index number

B. Quantity index number

C. Value index number

D. Both (a) and (b)   ✓ Correct Answer

Explanation: Quantum index number is simply another term for the volume/quantity index number.

Q28. Laspeyre's price index number uses weights of:

A. Current year quantities

B. Current year prices

C. Base year quantities   ✓ Correct Answer

D. Base year prices

Explanation: Laspeyre's price index is weighted using base year quantities.

Q29. Paasche's price index number uses weights of:

A. Current year quantities   ✓ Correct Answer

B. Current year prices

C. Base year quantities

D. Base year prices

Explanation: Paasche's price index is weighted using current year quantities.

Q30. The chain base method is better than the fixed base method.

A. True   ✓ Correct Answer

B. False

C. Partially true

D. None

Explanation: The chain base method adapts weights over time, generally making it more responsive/accurate than a fixed base method.

Q31. Aggregate expenditure and Family Budget methods are used for computing:

A. Consumer price index number

B. Retail price index number

C. Cost of living price index number

D. All of these   ✓ Correct Answer

Explanation: Both methods are standard techniques for computing consumer price, retail price, and cost of living indices.

Q32. The most suitable average for index numbers is the:

A. Harmonic mean

B. Arithmetic mean

C. Geometric mean   ✓ Correct Answer

D. None

Explanation: The geometric mean is considered the most appropriate average for constructing index numbers, since it handles ratios well.

Q33. The common way used to measure inflation in Pakistan is through the:

A. Consumer price index number   ✓ Correct Answer

B. Retail price index number

C. Cost of living price index number

D. All of these

Explanation: CPI is the standard, widely-used method to measure and track inflation in Pakistan.

Q34. The aggregative expenditure method as the base year weighted index number is given by:

A. Laspeyre   ✓ Correct Answer

B. Paasche

C. Fisher

D. Pearson

Explanation: The base-year weighted version of the aggregative expenditure method is Laspeyre's formula.

Q35. Laspeyre's index number gives more weight to the commodities whose prices have:

A. Increased   ✓ Correct Answer

B. Decreased

C. Not changed

D. None

Explanation: Since it uses fixed base year quantities, Laspeyre's index effectively over-weights commodities with rising prices.

Q36. Paasche's index number gives less weight to the commodities whose prices have:

A. Decreased

B. Increased   ✓ Correct Answer

C. Not changed

D. None

Explanation: Paasche's index, using current-year quantities, systematically under-weights commodities whose prices rose.

Q37. The index number of Pakistan's exports is a:

A. Composite index number   ✓ Correct Answer

B. Simple index number

C. Consumer price index number

D. None

Explanation: Since exports include many different commodities combined into one index, it is a composite index number.

Q38. The value index number, V₀ₙ, is given by:

A. ΣPₙq₀ / ΣP₀q₀

B. ΣPₙqₙ / ΣP₀q₀   ✓ Correct Answer

C. ΣPₙqₙ / ΣPₙqₙ

D. ΣP₀q₀ / ΣPₙqₙ

Explanation: The value index compares the total current value (price × quantity, both current year) to the base year value.

Q39. In the family budget method, the weights are:

A. Quantity

B. Price

C. Value   ✓ Correct Answer

D. Volume

Explanation: The family budget method uses values (expenditure) of items as weights.

Q40. In the aggregative expenditure method, the weights are:

A. Value

B. Price

C. Quantity   ✓ Correct Answer

D. Volume

Explanation: The aggregative expenditure method uses quantities as the weights applied to prices.

Q41. Value is equal to price multiplied by:

A. Value

B. Price

C. Quantity   ✓ Correct Answer

D. None

Explanation: By definition, Value = Price × Quantity.

Q42. The aggregative expenditure method is given by:

A. Paasche

B. Laspeyer

C. Fisher

D. All of these   ✓ Correct Answer

Explanation: Both Laspeyre's and Paasche's formulas (and their combination, Fisher's) are variants of the aggregative expenditure method.

Q43. The aggregative expenditure method is:

A. Base year weighted

B. Current year weighted

C. Both (a) and (b)   ✓ Correct Answer

D. None

Explanation: Depending on which quantities are used as weights, the aggregative expenditure method can be either base-year weighted (Laspeyre) or current-year weighted (Paasche).

Q44. CPI was computed in Pakistan for the first time in:

A. 1947

B. 1960   ✓ Correct Answer

C. 1950

D. 1970

Explanation: Pakistan's Consumer Price Index was first computed in 1960.

Q45. The index that indicates change in the producer's selling price is the:

A. Wholesale price index   ✓ Correct Answer

B. Consumer price index

C. Retail price index

D. Cost of living index

Explanation: The Wholesale Price Index reflects prices received by producers/sellers, unlike the consumer-focused CPI.

Q46. The purchasing power of the rupee is given by:

A. (1/CPI) × 100   ✓ Correct Answer

B. CPI × 100

C. (WPI/CPI) × 100

D. None

Explanation: Purchasing power of money = (1/CPI) × 100, since it's the inverse relationship with the price index.

Q47. If CPI = 123.4, the purchasing power of the rupee is:

A. 100

B. 12340

C. 123400

D. 0.81   ✓ Correct Answer

Explanation: Purchasing power = (1/123.4) × 100 ≈ 0.81.

Q48. Chain indices are just the price relatives computed by taking:

A. The first year as base   ✓ Correct Answer

B. The middle year as base

C. The average of the years as base

D. None

Explanation: In the chain base method, relatives are ultimately linked back to the original (first year) base period through successive chaining.


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