Simple (Unweighted) Index Numbers 🧮

In Simple Index Numbers, all items are treated as equally important. There are no weights assigned.

There are two main methods:

1. Simple Aggregative Method
2. Simple Average of Price Relatives Method

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1. Simple Aggregative Method ➕

This is the easiest method. We simply sum up the prices of current year and divide by the sum of prices of base year.

Formula

P_01 = (∑ p1 / ∑ p0) * 100

• ∑ p1 = Sum of current year prices
• ∑ p0 = Sum of base year prices

[!WARNING] Limitation: This method is influenced by the units of the items.

• If Milk is in Litres (Price ₹60) and Gold is in grams (Price ₹6000), Gold will dominate the index just because its unit price is high.

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2. Simple Average of Price Relatives ➗

To solve the unit problem, we first calculate the percentage change for each item (Price Relative) and then take their average.

Steps:

1. Calculate Price Relative (P) for each item:

   P = (p1 / p0) * 100
   

2. Take the average of these Ps.

Formula (Using Arithmetic Mean):

P_01 = ∑ P / N

(Where N is number of items)

Formula (Using Geometric Mean - Better):

P_01 = Antilog( ∑ log P / N )

(Geometric Mean is strictly preferred for Index Numbers, but AM is easier)

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Example Calculation 📝

Data:

Item	Price 2020 (Base) p0	Price 2024 (Current) p1
A	20	30
B	40	60
C	10	12

Method 1: Simple Aggregative

• ∑ p0 = 20 + 40 + 10 = 70
• ∑ p1 = 30 + 60 + 12 = 102
• P_01 = (102 / 70) * 100 = 145.71

Method 2: Average of Price Relatives (AM)

1. Calculate P for each:
   • A: (30/20) * 100 = 150
   • B: (60/40) * 100 = 150
   • C: (12/10) * 100 = 120
2. Sum of P (∑ P) = 150 + 150 + 120 = 420
3. Average: 420 / 3 = 140

Note: The results (145.71 vs 140) differ.

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Summary

Method	Formula	Pros	Cons
Simple Aggregative	(∑ p1 / ∑ p0) * 100	Very Easiest	Affected by units/high prices.
Avg of Relatives	∑ P / N	Not affected by units	Calculation is longer.

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