৪৯তম বিসিএস ⎯ পরিসংখ্যান [৯৮১]

An index number is a statistical tool used to show relative changes over time or between different locations. It summarizes changes in variables such as prices, quantities, or production, often using a base year as a reference. Option A is incorrect because index numbers show relative change, not absolute change. Option C and D are too narrow; index numbers are not limited to population or single commodity prices.

When comparing countries, differences in economic structure, consumption patterns, and selected commodities can distort index numbers. Option B is incorrect; index numbers are not automatically standardized internationally. Option C is incorrect because they approximate changes, not exact real incomes. Option D is incorrect; currency differences must be accounted for separately.

​Source: Business Statistics (SP Gupta, MP Gupta.)

Index numbers are important because they simplify complex data (like hundreds of prices or quantities) into a single figure, making trends easy to understand. Option A is wrong because they show relative, not absolute values. Option C is wrong; data collection is still needed. Option D is wrong; they are useful for both historical and current trend analysis.
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Source: Investopedia, Business Statistics (Md. Abdul Aziz) 
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Index numbers are sensitive to the choice of base year and the method of weighting different components. Poor selection can distort results. Option A is wrong because a base year is essential. Option C is incorrect because index numbers are approximate measures. Option D is incorrect; they have extensive practical use.
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Source: Business Statistics (SP Gupta,  MP Gupta)

​The Fisher Ideal Index is less biased than Paasche or Laspeyres because it combines both quantity bases. Paasche can underestimate price changes if quantities increase. Option A is wrong; Fisher requires more data (both current and base year quantities). Options C and D are incorrect; prices and quantities are needed.
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Source: Business Statistics (Md. Abdul Aziz)

Fisher index geometrically averages Laspeyres and Paasche, balancing the overestimation of Laspeyres and underestimation of Paasche. Paasche index specifically uses current year quantities as weights. Option B is wrong because Fisher uses geometric, not arithmetic mean. Option D is incorrect; both require prices and quantities.

Fisher’s Ideal Index is termed “ideal” because it satisfies both time reversal and factor reversal tests, which are desirable criteria of consistency for index numbers. Dorbish-Bowley fails the factor reversal test; Marshall-Edgeworth fails time reversal test. Options A and C are incorrect since Fisher requires extensive data (both period quantities). Option D is false; Fisher generally lies between Laspeyres and Paasche.
​Source: “Index Numbers in Theory and Practice” – R.G.D. Allen

Laspeyres index uses base-year quantities, ignoring substitution toward cheaper goods — so it overstates inflation. Paasche uses current-year quantities, incorporating substitution, which tends to understate inflation. Fisher, being geometric mean of the two, typically lies in between. Hence option B is correct.
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Source: Live mcq class

Index numbers measure relative changes, but they cannot predict exact future values. They are useful for tracking inflation, economic trends, and production changes. Options A, B, and D are all valid uses.

​​Source: Fundamentals of Applied Statistics (S.C. Gupta & V.K. Kapoor)

The Fisher Ideal Index is considered “ideal” because it combines both the Laspeyres index (based on base year quantities) and the Paasche index (based on current year quantities) using the geometric mean. This reduces bias present in using only one quantity base.

The Paasche Price Index uses current year quantities as weights, which can be hard to obtain or unreliable. Option A describes Laspeyres’ bias. Option C is characteristic of Fisher. Option D is not a general limitation; Paasche can be used internationally if data is available.
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Source: Business Statistics (SP Gupta, MP Gupta) 

Because the Paasche Index uses current year quantities, it often understates inflation if consumers shift to cheaper goods (substitution effect) ( অর্থাৎ প্যাশে ম্যাথড ইনফ্লেশনকে ছোট করে দেখে বা ধরতে পারে না ইনফ্লেশনকে)।  Laspeyres uses fixed base year quantities and often overstates inflation অর্থাৎ ল্যাসপেয়ার্স ম্যাথোড ইনফ্লেশনকে বড় করে দেখে বা বেশি গুরুত্ব দেয়।  Fisher, as the geometric mean, balances both. Option C is wrong; Fisher usually lies between Laspeyres and Paasche. Option D is wrong; quantities are explicitly used.

​Source: Business Statistics (SP Gupta, MP Gupta)

The Laspeyres Index uses base year quantities as weights. Since consumers usually shift to cheaper substitutes when prices rise (substitution effect), using fixed base-year quantities fails to reflect this shift, often overstating the increase in price. That’s why it tends to overestimate inflation. 
​(এটা ইনফ্লেশনকে বড় করে দেখে, ক্রেতারা যে কমদামি পণ্য কেনে, এটাকে কনসিডার করে না। এটাকে upward bias ও বলে। অন্যদিকে প্যাশে ম্যাথড উল্টা, সেটা ইনফ্লেশনকে ছোট করে দেখে, তাই downward bias)

The Dorbish & Bowley (Durbin) Method is an arithmetic mean of the Laspeyres and Paasche indices.It is meant to reduce the upward bias of Laspeyres and downward bias of Paasche by averaging them. It does not use the geometric mean (that is Fisher), nor does it avoid price relatives.

The Dorbish & Bowley index requires quantities for both the base and current year, since it combines Laspeyres (base year quantities) and Paasche (current year quantities). This makes it more data-intensive and burdensome in practice. Option C is incorrect because it reduces but does not eliminate bias. Option D is not true; it is suitable for any number of commodities given data availability.
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​Source: Index Numbers in Theory and Practice. (R.G.D. Allen) 

In weighted index numbers, each commodity is given a weight denoting its relative importance (generally quantity or value). In unweighted index numbers, all items are given equal importance, regardless of how much is consumed or produced.
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Source: Statistics-HSC. (Md. Abdul Aziz) 

The Simple Aggregative Price Index is calculated by summing current prices and dividing by the sum of base prices — it doesn’t use any weights for individual commodities, hence it is unweighted. All the others (Laspeyres, Paasche, Fisher) are weighted index numbers, as they use quantities as weights.
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​Source: Business Statistics (SP Gupta, MP Gupta.)

Index numbers assume that the quality and characteristics of goods remain constant over time. In reality, products often improve or deteriorate in quality, which affects price — this leads to a quality bias, making index numbers less reliable. Therefore, change in quality of goods is a major limitation.
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​Source: Index Numbers in Theory and Practice. (R. G. D. Allen) 

Unweighted index numbers assign equal importance to all commodities — meaning that a cheap item and an expensive item influence the index equally. This often distorts the true change because, in reality, consumers spend more on some items than others.
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​Source: Investopedia

Explanation:
Dorbish–Bowley index is defined as the arithmetic mean of Laspeyres and Paasche:
(140+120)/2=130.

Fisher’s Ideal Index is the geometric mean:
√(140×120)=√16800≈129.6.
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Hence, Option C correctly states the comparison between them.

The CPI tracks changes in the average price level of a fixed basket of goods and services purchased by consumers, thus indicating how the purchasing power of money changes over time due to inflation. It is not directly related to production cost (A), producer profits (C), or wholesale prices (D — that’s WPI).
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Source: Fundamentals of Applied Statistics (Gupta & Kapoor)  

In the CPI, each item in the consumption basket is assigned a weight proportional to the share of consumer expenditure on that item (e.g., rent has a higher weight than soap). This reflects the relative importance of goods in actual consumer spending. Option A describes unweighted indices. Option C is false because quantities (through expenditure weights) matter. Option D is incorrect because CPI weights are updated periodically to reflect changes in consumer habits.

​Source: Economics (Samuelson & Nordhaus)   

Explanation: CPI is generally based on a fixed basket of goods & services consumed by urban households. As a result, it does not capture rural consumption patterns, leading to sampling bias. Prices faced by rural consumers may differ, so CPI may not represent the true living cost of the entire population.
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​Source: Elements of Statistics (John A. Bowley & A. L. Bowley)   

In a weighted index number, weights reflect the relative importance (value share or quantity share) of each commodity in the basket (e.g., Laspeyres, Paasche, Fisher use weights). Unweighted index numbers treat all items as equally important, regardless of their contribution to total expenditure.
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​Source: Statistics-HSC (Md Abdul Aziz) 

Weighted index numbers are more appropriate when commodities differ significantly in their importance to consumers or the economy.
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Source: Index Numbers in Theory and Practice (R.G.D. Allen) 

Explanation: The defining characteristic of weighted index numbers is the use of weights that represent the relative importance of each commodity, typically derived from quantity or expenditure shares. Unweighted indices do not use such weights.

Paasche’s Price Index is a weighted index that uses current year quantities as weights. While this makes it more reflective of current consumption patterns, it creates a serious practical problem: accurate current year quantity data is often unavailable or expensive to collect in real time, making the Paasche index difficult to compute regularly.
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​Source: Business Statistics (SP Gupta, MP Gupta)

Explanation: A good index number needs to accurately reflect changes in the data it represents. This requires sensitivity to fluctuations, unlike the other options which suggest rigidity or artificial constraints.

​Source:  www.vedantu.com

The Laspeyres index uses base-year quantities, leading to a higher value when prices rise. The Paasche index uses current-year quantities, resulting in a lower value during inflation. Therefore, the difference indicates an overestimation by Laspeyres during an increase in price.

​Source: Business Statistics (Md. Abdul Aziz) 

Option b directly defines the core function of each type of index. Hence, this the correct one.
​option a তে price index quantity of goods এর change করে বলা হয়েছে, যা ভুল।
​option b তে- সঠিক উত্তর। 
​option c তে- price index, base year ও current year দুটাই ব্যবহার করতে পারে, তাই ভুল।
​option d- option c এর মতোই ভুল

A population pyramid is used to show the age-sex structure of the population. The shape of the population pyramid reflects the characteristics of the population. The left side shows the percentage of males while the right side shows the percentage of women in each age group.

Explanation: Demography is the statistical study of human populations, focusing on size, structure (age, sex, etc.), distribution, and changes over time (birth, death, migration).

Explanation: In the simple Average of price relatives, all items are given equal importance (no weights). Laspeyres, Paasche, and Fisher are weighted index numbers.

​Source: Statistics-HSC (Md. Abdul Aziz) 

Explanation: Unweighted Index ignore the relative importance (weights) of items. This is their main drawback. But any of the options given here is drawback, hence D is correct.

Simple Aggregate Index = (ΣP₁ / ΣP₀) × 100 = (15+25+45) / (10+20+30) × 100 = 85/60 × 100 = 141.67
Simple Average of Price Relatives = [(15/10×100 + 25/20×100 + 45/30×100)] / 3 = (150 + 125 + 150)/3 = 141.67

Consumer Price Index CPI in Bangladesh increased to 136.83 points in July from 133.85 points in June of 2025. Consumer Price Index CPI in Bangladesh averaged 86.20 points from 2011 until 2025, reaching an all time high of 136.83 points in July of 2025 and a record low of 52.53 points in May of 2011. 
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Source: Bangladesh Bureau of Statistics. Trading Economics. 

Explanation:
Index numbers often rely on selected items and weights, so they may not capture the full picture of all commodities or regions, leading to sampling bias.

Explanation:
CPI measures the average change in the retail prices of goods and services consumed by households, hence it is a price index. Bangladesh Bureau of Statistics states-"The consumer price index (CPI) reflects the average change over time in the retail prices of a specified set of final commodities and services representing the market basket of a given group of consumers."

CPI is often constructed with a fixed “market basket” of goods and services. Over time, consumer habits change (substitution effect, new goods, quality improvements), but CPI may fail to fully capture these, creating substitution bias.

CPI is based on a fixed basket of goods. If prices of some items rise, consumers may substitute cheaper alternatives. Also, CPI often fails to adjust fully for quality improvements (e.g., a better smartphone at the same price gives more value). As a result, CPI can overstate the rise in cost of living.

​Source: Lumen learning. 

Laspeyres (base quantities) tends to overstate inflation.
Paasche (current quantities) tends to understate inflation.
Fisher, being geometric mean, is ideal and conceptually most accurate.
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Source: Business Statistics (MP Gupta, SP Gupta)

The Best Price Index is also called the Fisher Ideal Price Index.

It is calculated as:

F=√(L⋅P)
Where:
L = Laspeyres Price Index (base year quantities)
P = Paasche Price Index (current year quantities)
It is considered the most accurate index because it balances the overstatement of Laspeyres and understatement of Paasche.

The general price level has increased by 40% since 2010.

Explanation:
CPI compares the cost of a fixed basket of goods and services relative to the base year.
A value of 140 means the basket now costs 40% more than in 2010, reflecting the rise in general prices.
​A correct statement for the questions is- " The general price level has increased by 40% since 2010"

CPI compares the cost of a fixed basket of goods and services in the current year with the base year.

A CPI of 125 means prices have risen 25% relative to the base year.

Fisher Index = √(Laspeyres × Paasche).
It balances the overstatement of Laspeyres and understatement of Paasche.
A value of 105 suggests an approximate 5% price increase, accounting for both base and current quantities.

Paasche Index uses current year quantities as weights.

An index less than 100 indicates a decline in the cost of purchasing the current year basket compared to the base year.

Factor reversal test satisfies if Pon​⋅Qon=Von
​Time reversal test satisfies if Pon.Pno= 1 
​Here, Pon= price index for current year (n) with respect to base year (0)
​Pno= price index for current year (o) with respect to base year (n)
​Qon=  Quantity index for current year (n) with respect to base year (0)
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Source: Business Statistics (Md. Abdul Aziz)

Factor reversal test satisfies if Pon​⋅Qon=Von ​Time reversal test satisfies if Pon.Pno= 1  ​Here, Pon= price index for current year (n) with respect to base year (0) ​Pno= price index for current year (o) with respect to base year (n) ​Qon=  Quantity index for current year (n) with respect to base year (0) ​

​Source: Business Statistics (Md. Abdul Aziz) 

Fisher's index is called ideal index number. It is geometric mean of L and P index. 

Laspeyres Index uses base year quantities as weights.

An index of 120 means that the cost of purchasing the same basket of goods has risen by 20% compared to the base year.