Base Year Methods
Index Numbers — Chapter 3, GSEB Class 12 Statistics
Fixed Base Method
In the fixed base method, every year is compared to the samebase year. The base year never changes — it is “fixed.”
How it works — Ladder Diagram
110.0
2018
BASE
118.0
2019
125.0
2020
132.0
2021
140.0
2022
Every year compared to 2018 (base) — the bottom rung never moves
Worked Example
| Year | Price (Pn) | Base (P₀ = 2018) | Index = Pn/P₀ × 100 |
|---|---|---|---|
| 2018 | 110 | 100 | 110.0 |
| 2019 | 118 | 100 | 118.0 |
| 2020 | 125 | 100 | 125.0 |
| 2021 | 132 | 100 | 132.0 |
| 2022 | 140 | 100 | 140.0 |
Denominator is always P₀ (2018 prices).That's why it's called “fixed base” — the base never shifts.
Chain Base Method
In the chain base method, each year is compared to the immediately precedingyear. The base “chains” forward — shifting with every year.
How it works — Shifting Rungs
100.0
2018
107.3
2019
105.9
2020
105.6
2021
106.1
2022
Each year compared to the previous year — the base shifts forward each time
Worked Example
| Year | Price (Pn) | Previous (Pn-1) | Link Relative |
|---|---|---|---|
| 2018 | 100 | — | 100.0 |
| 2019 | 110 | 110 | 107.3 |
| 2020 | 118 | 118 | 105.9 |
| 2021 | 125 | 125 | 105.6 |
| 2022 | 132 | 132 | 106.1 |
Converting chain to fixed base: Multiply all link relatives together.
Example: Fixed base index for 2020 = (107.3 × 105.9) / 100 = 113.6 (vs direct 125.0 — slight difference due to rounding).
Example: Fixed base index for 2020 = (107.3 × 105.9) / 100 = 113.6 (vs direct 125.0 — slight difference due to rounding).
Key Takeaways
Key Takeaways
- Fixed Base: every year compared to the same base year — Pn/P₀ × 100. Simple and easy to understand.
- Chain Base: each year compared to the previous year — Pn/Pn-1 × 100. Captures recent trends better.
- Fixed base denominator (P₀) never changes; chain base denominator shifts with every year.
- Chain base link relatives can be converted to fixed base by multiplying them together.
- Fixed base is easier for direct comparison across years; chain base is better for detecting recent changes.