Chapter 10: Index Numbers

10.1 Index Numbers

• An index number is a statistical measure of the change in a variable in a particular year compared to a base year. The base normally has the value 100. (p.272)
• Index number: I = (Q₁ / Q₀) × 100, where Q₀ is the price/quantity at the base time and Q₁ is at a specific time. (p.274)
• Index > 100 means an increase compared to the base year; index < 100 means a decrease. (p.274)
• Index number is a ratio expressed in percentage without writing the percentage symbol. (p.274)
• Changing base: I_2018/2015 = (I_2018/2010 / I_2015/2010) × 100. (p.275)
• For successive percentage changes, find the new quantity step by step using the index formula. (p.276)

10.2 Composite Index

• A composite index combines several indices to measure overall change, using weightages that show the importance of each item. (p.279)
• Composite index: Î = ΣI_iw_i / Σw_i, where I_i are index numbers and w_i are weightages. (p.279)
• Weightage can be given as numbers, ratios, percentages, or readings from bar charts or pie charts. (p.279)
• If no weightages are given, assume they are equal for every index number. (p.280)
• Steps: find each price index, build a table of I_i, w_i, I_iw_i, then compute the composite index and interpret it. (p.281)
• The composite index can be used to find an unknown cost: I = (Q₁ / Q₀) × 100. (p.282)