Index numbers flashcards

Topic 8: Index numbers

What is the base year of an index?

The year used for comparison. Every price relative for the base year is 100.

What is a price relative?

The price of one item in the given year, as a number where the base-year price is 100.

What is a weight in an index number?

A number showing how much importance an item has in the index.

What is a weighted aggregate index number?

One figure that summarises the price change of several items, using weights.

What does a price relative above 100 show?

Prices have risen. A relative of 108 means 8% higher than in the base year.

A fabric cost Rs 480 per metre in the base year and costs Rs 408 now. Find the price relative

408 ÷ 480 × 100 = 85. The price has fallen by 15% since the base year.

A school bag has price relative 125 and now costs Rs 750. Find its base-year price

Base-year price = (given-year price ÷ price relative) × 100 = 750 ÷ 125 × 100 = Rs 600.

How do you calculate a weighted aggregate index, and where do the weights come from?

Index = Σ(weight × price relative) ÷ Σ(weights). If weights are not given, use base-year expenditure: base-year price × base-year quantity.

Base prices 20, 45, 10; base quantities 30, 12, 60; current prices 23, 54, 11. Find the weighted index

Relatives 115, 120, 110. Weights 600, 540, 600 (sum 1740). (69 000 + 64 800 + 66 000) ÷ 1740 = 199 800 ÷ 1740 = 114.8.

An index rises from 125 to 140. What is the percentage increase?

(140 − 125) ÷ 125 × 100 = 12%. Divide by the earlier index; the 15-point difference is not the percentage.

What are the limitations of a fixed-weight index?

Weights go out of date as buying changes; buyers substitute cheaper items, so the index can overstate rises; new or omitted items are missing; and an average hides different spending patterns. Link each point to an item in the question.