Averaging relatives and the CPI

Another method uses price relatives. The price relative of an item is P1 ÷ P0 × 100: its current price as a percentage of its base price. If sugar went from ₹40 to ₹46 a kg, its price relative is 46 ÷ 40 × 100 = 115.

• The simple average of relatives adds the relatives and divides by their number. Again, every item gets equal importance.
• The weighted average of relatives gives each relative a weight (W), usually the item's share of spending: Σ(W × R) ÷ ΣW.

For example, a family spends 50% of its budget on food, 30% on housing and 20% on clothing, and their price relatives are 120, 110 and 105. The index = (50 × 120 + 30 × 110 + 20 × 105) ÷ 100 = (6000 + 3300 + 2100) ÷ 100 = 114. The family's cost of living has risen by 14%.

This is how a Consumer Price Index (CPI), also called the cost of living index, is built. It measures the average change in the retail prices of a typical basket of goods and services that a group of consumers buys. A CPI above 100 means the cost of living has risen since the base period; below 100, it has fallen.

In India's CPI (base 2012 = 100), the weights show what households spend most on: food and beverages 45.86, miscellaneous 28.32, housing 10.07, fuel 6.84, clothing 6.53, and pan, tobacco and intoxicants 2.38.