CHAPTER 7- Index Numbers || STATISTICS FOR ECONOMICS || Class 11th || NCERT CBSE || NOTES IN ENGLISH || 2024-25

CHAPTER 7- Index Numbers

Introduction

Index numbers are statistical tools used to measure changes in the magnitude of a group of related variables.
They provide a summary measure of changes in things like prices, production, employment, and other economic variables over time.
For example, when prices of goods fluctuate or production output changes, an index number can provide a single figure to represent these changes.

An index number measures the average change in a set of related variables.
It compares the changes between two periods—often called the base period (the point of reference) and the current period (the time of comparison).
Index numbers are typically expressed as percentages, with the base period given a value of 100.
Price Index Numbers compare changes in prices, while Quantity Index Numbers compare changes in production or employment.

If the price index number for 2023 compared to 2010 is 250, this means that prices in 2023 are 2.5 times higher than in 2010.

There are different methods to calculate index numbers, with the most common being the aggregative method and the method of averaging relatives.

This method adds up the prices (or quantities) of all goods in the current period and the base period and calculates the change between them.
The formula for the simple aggregative price index is:
P01=ΣP1ΣP0×100P_{01} = \frac{\Sigma P_1}{\Sigma P_0} \times 100
P01=ΣP0ΣP1×100 Where:

Suppose the prices of goods in the base period (2010) were Rs 2, 5, 4, and 2. In the current period (2023), the prices are Rs 4, 6, 5, and 3. The simple price index would be:
P01=4+6+5+32+5+4+2×100=138.5P_{01} = \frac{4 + 6 + 5 + 3}{2 + 5 + 4 + 2} \times 100 = 138.5
P01=2+5+4+24+6+5+3×100=138.5 This means prices have risen by 38.5%.

In this method, we assign weights to items based on their relative importance in the total expenditure.
The formula for a weighted aggregative price index is:
P01=Σ(P1×q0)Σ(P0×q0)×100P_{01} = \frac{\Sigma (P_1 \times q_0)}{\Sigma (P_0 \times q_0)} \times 100
P01=Σ(P0×q0)Σ(P1×q0)×100 Where:

This method calculates the ratio of current prices to base prices for each commodity, and then averages these ratios.
The formula for the simple average of relatives is:
P01=1n×ΣP1P0×100P_{01} = \frac{1}{n} \times \Sigma \frac{P_1}{P_0} \times 100
P01=n1×ΣP0P1×100 Where:

The CPI measures the changes in the cost of living by tracking the prices of a selected "basket" of goods and services.
If the CPI for industrial workers was 100 in 2001 and 277 in 2014, it means the cost of buying the same basket of goods increased from Rs 100 in 2001 to Rs 277 in 2014.

The WPI measures the changes in prices at the wholesale level, tracking the prices of goods before they reach consumers.
For example, a WPI of 253 in 2014, with a base of 2004-05, means wholesale prices have increased by 153% compared to the base year.

The IIP measures the change in the production of industries like mining, manufacturing, and electricity.
The index uses the formula:
IIP=Σ(q1×W)Σ(q0×W)×100IIP = \frac{\Sigma (q_1 \times W)}{\Sigma (q_0 \times W)} \times 100
IIP=Σ(q0×W)Σ(q1×W)×100 Where:

q1q_1
q1 = quantity produced in the current year
q0q_0
q0 = quantity produced in the base year
WW
W = weight of the item based on its importance in the total industrial output

When constructing index numbers, several factors must be considered:

Purpose of the index: It's important to know whether you're measuring prices, quantities, or other variables.
Selection of items: The items included must be representative of the group you're measuring. For example, in a CPI, food and housing may be weighted more heavily because they make up a large part of the average household budget.
Choice of base year: The base year should be a normal year, without any extreme economic events. It should also not be too far in the past.

Index numbers are important tools for understanding changes in prices, production, and other economic variables.
They play a critical role in policy-making, helping governments track inflation, plan for economic growth, and adjust wages or interest rates.
Commonly used indices include the CPI, WPI, and IIP, each offering insights into different aspects of the economy.