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Business Mathematics and Basic Statistics · Ch 8 — Index Numbers

Comparing the Three Methods

5

Comparing the Three Methods

The three methods can give noticeably different index numbers for the very same set of commodities, because each one distributes "importance" among the commodities differently:

MethodFormulaWhat decides each commodity's importanceTypical use
Simple AggregateP01=Σp1Σp0×100P_{01}=\dfrac{\Sigma p_1}{\Sigma p_0}\times100Nothing — every commodity's raw price counts equally, regardless of how much is boughtA quick, rough gauge only; distorted by high-priced but rarely-bought items and by the units prices are quoted in
Weighted AggregateP01=Σp1wΣp0w×100P_{01}=\dfrac{\Sigma p_1 w}{\Sigma p_0 w}\times100The quantity (or other weight) actually consumed of each commodity, usually base-year quantity q0q_0A realistic general price index that reflects genuine buying patterns
Cost of Living IndexCLI=ΣIWΣWCLI=\dfrac{\Sigma IW}{\Sigma W}Each commodity's own share of the household's total budget, WWMeasuring how much MORE a household must spend to keep the same standard of living