What is an Index Number? Definition, Types & Formula Explained
Index numbers are vital statistical tools used to measure changes in variables like price or quantity over time. They are especially important for students preparing for board exams, competitive exams such as CA Foundation, or pursuing a career in commerce. Understanding index numbers equips learners with skills to interpret economic trends and business data.
| Type of Index Number | Description | Main Use |
|---|---|---|
| Price Index Number | Measures changes in the prices of goods or services over time. | Tracking inflation (e.g., Consumer Price Index, Wholesale Price Index) |
| Quantity Index Number | Measures changes in the quantity or volume of goods produced, consumed, or sold. | Comparing production levels |
| Value Index Number | Measures overall change in value (price × quantity) of items. | Analyzing total sales or output |
What is Index Number?
An index number is a calculated value representing the relative change in a variable (like price, quantity, or value) between two periods. The period used as a comparison is called the base year, usually set at 100. Changes in the index show increases or decreases compared to the base year.
Formulas and Key Methods in Index Numbers
There are several ways to construct index numbers. Each method uses different formulas and weights. Below is a table of major formulas usually asked in school and competitive exams.
| Method | Formula | Features |
|---|---|---|
| Laspeyres Price Index | (Σ P1Q0 / Σ P0Q0) × 100 | Base year quantities as weights |
| Paasche Price Index | (Σ P1Q1 / Σ P0Q1) × 100 | Current year quantities as weights |
| Fisher’s Ideal Index | √(Laspeyres Index × Paasche Index) | Geometric mean; satisfies most tests |
| Simple Aggregative Index | (Σ P1 / Σ P0) × 100 | No weights used |
| Consumer Price Index (CPI) | (Σ W × I / Σ W) | Used for cost of living adjustments |
MCQs on Index Numbers
-
Which type of average is best to construct an index number?
A) Arithmetic mean
B) Harmonic mean
C) Geometric mean
D) All of the above
Answer: Geometric mean -
Index number for the base year is always ________?
A) 100
B) 0
C) 1
D) 50
Answer: 100 -
The index number used to measure the change in the number of goods is called ________?
A) Price index number
B) Quantity index number
C) Value index number
D) None of the above
Answer: Quantity index number -
Fisher’s Ideal Index is called “ideal” because it ________?
A) Uses arithmetic mean
B) Satisfies both time reversal and factor reversal tests
C) Is simple to calculate
D) None of the above
Answer: Satisfies both time reversal and factor reversal tests -
Which index number formula uses current year quantities as weights?
A) Laspeyres
B) Paasche
C) Fisher’s
D) Simple Average
Answer: Paasche -
In index numbers, the base year is usually set as:
A) 1
B) 100
C) 0
D) 10
Answer: 100 -
Price index numbers are used to:
A) Study price level changes
B) Measure quantity changes
C) Analyze value changes
D) None of the above
Answer: Study price level changes -
Cost of Living Index is another name for:
A) Wholesale Price Index
B) Quantity Index
C) Consumer Price Index
D) Value Index
Answer: Consumer Price Index -
The period for which the index number is being calculated is called:
A) Current period
B) Base period
C) Normal period
D) None of the above
Answer: Current period -
In Laspeyres Price Index, what is used as weights?
A) Price current year
B) Quantity base year
C) Price base year
D) Quantity current year
Answer: Quantity base year
Common Uses and Importance of Index Numbers
Index numbers are used by governments and businesses to track inflation, measure production trends, adjust salaries (dearness allowance), and guide economic policies. Students often see questions on index numbers in commerce syllabi for classes 11 and 12, as well as in competitive exams such as CA Foundation and SSC.
Calculation Example for Fisher’s Ideal Index
Suppose Laspeyres Index is 110 and Paasche Index is 108. Fisher’s Ideal Index is:
- Fisher’s Index = √(110 × 108) ≈ 109
This example helps understand calculation methods, as commonly tested in exams.
Applications, Limitations, and Real-World Context
- Tracking inflation (e.g., using the Consumer Price Index)
- Adjusting wages against price rises (Dearness Allowance)
- Comparing production in industries across years
- Limitation: Index numbers may become outdated if base year is too old or if goods/services change frequently
Related Topics for Further Study
- Read about the Difference between Wholesale Price Index and Consumer Price Index to understand index types better.
- For deeper insights, explore Important Index Numbers or Statistics in Economics.
- See real applications in Methods of Measuring National Income.
- Practice more MCQs with textbook-based solutions.
Page Summary
Index numbers help track changes in prices, quantities, or values over time using methods like Laspeyres, Paasche, and Fisher’s Index. Mastering index numbers is essential for commerce exams and real-world business analysis. At Vedantu, we support students in understanding and applying these concepts for academic success.
FAQs on Index Numbers MCQs: Key Concepts, Formulas, and Practice Questions
1. What is an index number?
An index number is a statistical measure that shows how a variable, like price or quantity, changes over time or between locations. It helps compare values between different periods using a base year and a current year. Index numbers are crucial tools in economics and statistics.
2. What are the main types of index numbers?
The primary types of index numbers are price index numbers (measuring price changes), quantity index numbers (measuring quantity changes), and value index numbers (measuring the combined effect of price and quantity changes). Understanding these types of index numbers is key to interpreting economic data.
3. Which index number is considered 'ideal', and why?
Fisher's Ideal Index Number is considered the 'ideal' index because it satisfies both the time reversal test and the factor reversal test. These tests ensure consistency and reliability in index number calculations. This is a crucial concept in index number methodology.
4. How is the base year chosen for index numbers?
The base year in index numbers should be a period that is considered 'normal,' free from significant economic fluctuations or unusual events. It's also essential that complete data is available for the base year to ensure accurate calculations and comparisons. The selection of the base year significantly impacts the results of index number calculations.
5. How are index numbers calculated?
Index number calculations involve several methods, including Laspeyres, Paasche, and Fisher's Ideal Index. These methods use different weighting schemes to aggregate data. Understanding these index number methods is crucial for accurate computations.
6. What are the major uses of index numbers in economics?
Index numbers have various applications, including measuring inflation, tracking changes in real income, assessing the cost of living, and analyzing broader economic trends. They provide insights into economic performance and patterns.
7. How do you decide whether to use the Laspeyres or Paasche index?
The choice between Laspeyres and Paasche indices depends on the available data and the specific analytical objective. Laspeyres uses base period weights, while Paasche uses current period weights. The selection influences the interpretation of results.
8. What are the limitations of index numbers?
Index numbers have limitations, including the potential for an outdated base year, inappropriate weights, changes in the items included in the index, and subjective choices in methodology. Understanding these limitations of index numbers is essential for accurate interpretation.
9. How do index numbers relate to purchasing power?
Index numbers and purchasing power are inversely related. When the price index rises, purchasing power decreases, and vice versa. This relationship is critical for understanding the impact of inflation on consumers.
10. What is the importance of weights in weighted index numbers?
Weights in weighted index numbers ensure that items of greater importance have a larger impact on the overall index value than less important items. This reflects their relative significance in the market or economy. Proper weighting is essential for an accurate index.
11. What is the base year in an index number?
The base year is the reference period against which changes in a variable are measured when calculating an index number. It's usually assigned a value of 100, and subsequent years' values are expressed as percentages of the base year.
12. How are index numbers expressed?
Index numbers are typically expressed as percentages relative to a base year, which is usually set to 100. For example, an index of 110 indicates a 10% increase compared to the base year.
