Index numbers flashcards

Topic 10: 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.

How do you calculate a price relative?

(price in given year ÷ price in base year) × 100. Example: Rs 160 in the base year and Rs 184 now → 184 ÷ 160 × 100 = 115.

What does a price relative below 100 show?

Prices have fallen. A relative of 85 means 15% lower than in the base year.

How do you calculate a weighted aggregate index number?

Σ(weight × price relative) ÷ Σ(weights). It is a weighted mean, with the weights playing the part of frequencies.

Where do the weights come from when they are not given?

Base-year expenditure: base-year price × base-year quantity for each item.

Weights 40, 35 and 25 have price relatives 112, 105 and 130. Find the weighted index

(4480 + 3675 + 3250) ÷ 100 = 11 405 ÷ 100 = 114.05, so 114.1 to 1 d.p.

An index was 108 last year and is 118.8 this year. What is the percentage increase?

(118.8 − 108) ÷ 108 × 100 = 10%. The 10.8-point difference is not the percentage change.

What does an index of 118.2 mean?

Prices are 18.2% higher on average than in the base year, not 118.2% higher. It is an average change: not every item rose by that amount.

Give limitations of a weighted index number

Weights go out of date as spending patterns change; buyers switch to cheaper items, so a fixed basket can overstate rises; items outside the basket are missing; and the average hides differences between households.