Statistics MCQs

Question #1141

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Chain base index numbers are advantageous when:

A. Calculating weighted averages of quantities

B. Long-term trends with a stable base are needed

C. Data for the base period is unavailable

D. Short-term period-to-period changes are of primary interest

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Correct Answer: Option D

Explanation:
Chain base indices use the previous period as base, making them sensitive to recent changes and suitable for analyzing short-term fluctuations, though they complicate long-term comparisons.

This question belongs to: Accountancy and Statistics Statistics

Question #1142

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Laspeyres price index uses which quantity weights?

A. Geometric mean of quantities

B. Base period quantities

C. Current period quantities

D. Average of base and current quantities

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Correct Answer: Option B

Explanation:
Laspeyres index = Σ(p₁q₀)/Σ(p₀q₀) × 100, using base period quantities (q₀) as weights, which may overstate inflation if consumers substitute away from goods with rising prices.

This question belongs to: Accountancy and Statistics Statistics

Question #1143

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Paasche price index is calculated as:

A. √[Σ(p₁q₀)/Σ(p₀q₀) × Σ(p₁q₁)/Σ(p₀q₁)] × 100

B. Σ(p₁q₁)/Σ(p₀q₁) × 100

C. Σ(p₁q₀)/Σ(p₀q₀) × 100

D. Σ(p₁q₁)/Σ(p₀q₀) × 100

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Correct Answer: Option B

Explanation:
Paasche index = Σ(p₁q₁)/Σ(p₀q₁) × 100, using current period quantities (q₁) as weights, which may understate inflation due to substitution effects but reflects current consumption patterns.

This question belongs to: Accountancy and Statistics Statistics

Question #1144

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Which index number formula satisfies both time reversal and factor reversal tests?

A. Simple aggregative index

B. Laspeyres index

C. Fisher's ideal index

D. Paasche index

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Correct Answer: Option C

Explanation:
Fisher's ideal index, being the geometric mean of Laspeyres and Paasche indices, is the only common formula that satisfies both time reversal and factor reversal tests, ensuring mathematical consistency.

This question belongs to: Accountancy and Statistics Statistics

Question #1145

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Weighted index numbers are preferred over simple indices because they:

A. Account for the relative importance of different items in the basket

B. Are easier to calculate

C. Do not require quantity data

D. Always satisfy the circular test

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Correct Answer: Option A

Explanation:
Weighted indices assign weights (e.g., expenditure shares) to reflect the economic significance of items, providing a more realistic measure of overall change than simple indices that treat all items equally.

This question belongs to: Accountancy and Statistics Statistics

Question #1146

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The circular test is satisfied if an index allows comparison of period 2 with period 0 via period 1, i.e., P₀₁ × P₁₂ = P₀₂. Which index commonly fails this test?

A. Chain base index with fixed weights

B. Simple geometric mean index

C. Laspeyres index

D. Fisher's ideal index

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Correct Answer: Option C

Explanation:
Laspeyres index uses fixed base-period weights, so P₀₁ × P₁₂ ≠ P₀₂ in general due to weight rigidity, failing the circular test; Fisher's index satisfies it under certain conditions.

This question belongs to: Accountancy and Statistics Statistics

Question #1147

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Wholesale Price Index (WPI) in India primarily measures price changes for goods at which stage?

A. Retail sale to consumers

B. First point of bulk sale in the market

C. Factory gate before any distribution

D. Import at customs

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Correct Answer: Option B

Explanation:
WPI tracks price movements of goods traded in bulk at the wholesale level (first point of mass sale), reflecting producer and wholesale market inflation, distinct from consumer-focused CPI.

This question belongs to: Accountancy and Statistics Statistics

Question #1148

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Consumer Price Index (CPI) is most relevant for:

A. Calculating export competitiveness

B. Assessing changes in the cost of living for households

C. Setting wholesale trade policies

D. Measuring producer cost inflation

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Correct Answer: Option B

Explanation:
CPI measures average price changes paid by consumers for a basket of goods and services, directly indicating inflation's impact on household purchasing power and cost of living.

This question belongs to: Accountancy and Statistics Statistics

Question #1149

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Cost of Living Index is essentially a type of:

A. Producer Price Index

B. Consumer Price Index tailored to specific population groups

C. Export-Import Price Index

D. Wholesale Price Index

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Correct Answer: Option B

Explanation:
Cost of Living Index is a specialized CPI that reflects price changes for a consumption basket relevant to a particular demographic (e.g., industrial workers), used for wage adjustments and welfare analysis.

This question belongs to: Accountancy and Statistics Statistics

Question #1150

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If the CPI increased from 150 to 165 over a year, the inflation rate based on CPI is:

A. 15%

B. 16.5%

C. 65%

D. 10%

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Correct Answer: Option D

Explanation:
Inflation rate = [(New CPI - Old CPI) / Old CPI] × 100 = (165 - 150)/150 × 100 = 15/150 × 100 = 10%. This measures the percentage increase in the price level.

This question belongs to: Accountancy and Statistics Statistics

Question #1151

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Assertion (A): Fisher's index is called 'ideal' because it satisfies important mathematical tests. Reason (R): It is the geometric mean of Laspeyres and Paasche indices, balancing their biases.

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

B. A is false but R is true

C. A is true but R is false

D. Both A and R are true, but R is not the correct explanation of A

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Correct Answer: Option A

Explanation:
Fisher's index earns the 'ideal' designation by satisfying time reversal and factor reversal tests, achieved through its geometric mean formulation that mitigates the upward bias of Laspeyres and downward bias of Paasche.

This question belongs to: Accountancy and Statistics Statistics

Question #1152

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A census is characterized by:

A. Continuous registration of vital events only

B. Estimation based on survey data

C. Complete enumeration of every individual in a population at a specific time

D. Sampling only 10% of the population

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Correct Answer: Option C

Explanation:
A census involves counting and collecting demographic, social, and economic data from every member of a population within a defined territory at a particular reference time, ensuring comprehensive coverage.

This question belongs to: Accountancy and Statistics Statistics

Question #1153

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Which of the following is NOT a typical function of a national census?

A. Providing data for political representation (e.g., delimitation)

B. Conducting real-time monitoring of daily births and deaths

C. Informing public policy and resource allocation

D. Establishing baseline data for demographic research

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Correct Answer: Option B

Explanation:
Censuses are periodic (e.g., decennial) and not designed for real-time vital event tracking; continuous registration systems (e.g., civil registration) handle daily birth/death recording.

This question belongs to: Accountancy and Statistics Statistics

Question #1154

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If a country's population grows from 50 million to 55 million in 10 years, the average annual growth rate (approximate) is:

A. 2.0%

B. 0.5%

C. 1.5%

D. 1.0%

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Correct Answer: Option D

Explanation:
Using the rule of 70 or simple approximation: Growth rate ≈ [(Final/Initial)^(1/t) - 1] × 100 = [(55/50)^(0.1) - 1] × 100 ≈ (1.1^0.1 - 1)×100 ≈ (1.0096 - 1)×100 ≈ 0.96% ≈ 1.0% per annum.

This question belongs to: Accountancy and Statistics Statistics

Question #1155

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Which feature is essential for a census to be considered 'de jure'?

A. Counting people at their usual place of residence

B. Counting people where they are found on census night

C. Conducting the census digitally

D. Including only citizens in the count

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Correct Answer: Option A

Explanation:
De jure census counts individuals at their usual or legal residence, regardless of location on census day, providing data for administrative and planning purposes based on habitual residence.

This question belongs to: Accountancy and Statistics Statistics

Question #1156

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Vital statistics primarily concern data on:

A. Life events such as births, deaths, marriages, and divorces

B. Economic production and consumption

C. Housing conditions and amenities

D. Educational attainment and literacy

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Correct Answer: Option A

Explanation:
Vital statistics systematically record and analyze key life events (births, deaths, marriages, etc.) through civil registration systems, forming the basis for demographic and health indicators.

This question belongs to: Accountancy and Statistics Statistics

Question #1157

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The primary use of vital statistics is to:

A. Calculate national income

B. Assess environmental quality

C. Determine electoral constituencies

D. Monitor population health, plan services, and inform policy

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Correct Answer: Option D

Explanation:
Vital statistics provide critical inputs for public health planning, evaluating healthcare interventions, forecasting population trends, and formulating social policies related to fertility, mortality, and family welfare.

This question belongs to: Accountancy and Statistics Statistics

Question #1158

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Crude Birth Rate (CBR) is defined as:

A. Number of births per 1,000 married women

B. Number of births per 100 women of childbearing age

C. Number of live births per 1,000 mid-year population

D. Total births divided by total deaths

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Correct Answer: Option C

Explanation:
CBR = (Number of live births in a year / Mid-year population) × 1,000. It is a simple, widely used measure of fertility, though it does not account for age structure.

This question belongs to: Accountancy and Statistics Statistics

Question #1159

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General Fertility Rate (GFR) improves upon CBR by:

A. Adjusting for infant mortality

B. Using mid-year population of both sexes

C. Including stillbirths in the numerator

D. Restricting the denominator to women aged 15-49 years

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Correct Answer: Option D

Explanation:
GFR = (Live births / Women aged 15-49) × 1,000, focusing on the biologically relevant population for childbearing, making it a more refined fertility measure than CBR.

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Question #1160

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Age-Specific Fertility Rate (ASFR) for age group 20-24 is calculated as:

A. Births to women 20-24 / Married women 20-24 × 1,000

B. Total births / Women 20-24 × 1,000

C. Births to women 20-24 / Total population × 1,000

D. Births to women 20-24 / Total women 20-24 × 1,000

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Correct Answer: Option D

Explanation:
ASFR isolates fertility behavior within specific age groups: (Number of births to women in age group / Mid-year population of women in that age group) × 1,000, enabling detailed fertility pattern analysis.

This question belongs to: Accountancy and Statistics Statistics

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