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Class 12 Statistics Notes · GSEB

Definition and Meaning

Index Numbers — learn the meaning, definition, price relative formula, and simple average method with real-life examples. GSEB Class 12 Statistics notes with key exam points.

Last updated: 21 Sep 2026

Notes

Definition and Meaning

Index Numbers — Chapter 1 of Index Numbers, GSEB Class 12 Statistics

What is an Index Number?

Index Number
An index number is a statistical measure of change in a variable or group of variables over time. It is a ratio expressed as a percentage that shows how a quantity has changed relative to a base period.

Index Number as a Price Tag Comparison

Base Year (P₀)

₹40

Current Year (P₁)

₹52

Index =

130

30% increase

An index number is always relative — never an absolute value. It tells you how much something changed, not what the value is.

Price Relative

A price relative compares the price of a single item in the current year to its price in the base year. It is the simplest form of an index number.

Price Relative Formula

R=P1P0×100R = \frac{P_1}{P_0} \times 100

Try it yourself — select an item:

Base Price (P₀)

₹40

Current Price (P₁)

₹52

Price Relative (R)

130.0

R = (52 / 40) × 100 = 130.0 → Price increased by 30.0%

If R > 100 → price has risen. If R < 100 → price has fallen. If R = 100 → no change.

General Index Number

While a price relative tracks one item, a general index number combines multiple price relatives into a single number to show the overall price movement of a group of items.

Simple Average of Price Relatives

General Index=∑RN=∑(P1P0×100)N\text{General Index} = \frac{\sum R}{N} = \frac{\sum \left(\frac{P_1}{P_0} \times 100\right)}{N}

Example: Computing General Index

ItemP₀ (₹)P₁ (₹)R = (P₁/P₀) × 100
Rice (1 kg)4052130.0
Milk (1 L)5664114.3
Diesel (1 L)90105116.7
Onion (1 kg)3045150.0
Sum (ΣR)511.0

General Index = 511.0 / 4 = 127.7

Overall prices increased by 27.7% compared to the base year

Base Year and Current Year

Base Year (P₀)

  • The reference point for comparison
  • Its index value is always 100
  • Also called the “year of reference”
  • Example: 2015 as base → all 2015 prices = 100

Current Year (P₁)

  • The year you want to compare to the base
  • Its index shows change relative to base = 100
  • Also called the “given year”
  • Example: 2024 prices relative to 2015 base
The base year is not fixed forever. Governments periodically change the base year to keep the index relevant. India's CPI uses 2012 as base; WPI uses 2011-12.

Key Takeaways

Key Takeaways

  • An index number is a statistical measure of change in a variable over time, expressed as a ratio percentage.
  • Price Relative R = (P₁ / P₀) × 100 — compares one item's price to the base year.
  • If R > 100, price has risen; if R < 100, price has fallen; if R = 100, no change.
  • General Index combines multiple price relatives: ΣR / N (simple average of price relatives).
  • Base year (P₀) = reference point with index always 100; Current year (P₁) = the year being compared.
  • Index numbers are always relative — they show percentage change, not absolute values.