Fixed Base vs Chain Base
Index Numbers — Chapter 4, GSEB Class 12 Statistics
Head-to-Head Comparison
| Aspect | Fixed Base Method | Chain Base Method |
|---|---|---|
| Definition | Each year compared to the same fixed base year | Each year compared to the immediately preceding year |
| Denominator | Always P₀ (base year price) | Pn-1 (previous year price) |
| Formula | Index = (Pn / P₀) × 100 | Link Relative = (Pn / Pn-1) × 100 |
| Direct Comparison | ✓ Yes — compare any two years directly | ✗ No — must multiply link relatives |
| Simplicity | ✓ Easy to understand and compute | ✗ Requires chain multiplication |
| Recent Trends | ✗ May miss recent changes | ✓ Captures recent price movements |
| Base Year Relevance | ✗ Can become outdated over time | ✓ Always uses recent base |
| Error Accumulation | ✓ No error accumulation | ✗ Small errors multiply through chain |
| Direct Conversion | No conversion needed — already on fixed base | Multiply link relatives to convert to fixed base |
Merits and Limitations
Merits
- ✓Easy to understand — denominator never changes
- ✓Direct comparison between any two years is possible
- ✓No error accumulation across years
- ✓Government agencies (WPI, CPI) use this method
Limitations
- ✗Base year becomes outdated over long periods
- ✗May not reflect recent price trends accurately
- ✗Requires periodic revision of base year
Key difference: Fixed base gives one index per year against the same base; chain base gives year-over-year changes. Choose based on what you need to compare.
When to Use Which?
Use Fixed Base When:
- →You need to compare prices across many years directly
- →Simplicity is important (exam questions)
- →Long-term trend analysis is needed
- →Government reports (WPI, CPI use fixed base)
Use Chain Base When:
- →You want to capture year-to-year changes
- →Base year is very old and prices have changed drastically
- →Short-term trend analysis is needed
- →Financial market analysis (stock indices)
Key Takeaways
Key Takeaways
- Fixed base = stability (same denominator always); Chain base = sensitivity (denominator shifts each year).
- Fixed base allows direct comparison between any two years; chain base requires multiplying link relatives.
- Chain base captures recent trends better but errors can accumulate through multiplication.
- Fixed base is easier for exam problems; chain base is preferred when recent trends matter.
- Link relatives from chain base can be converted to fixed base by multiplying them together.