Index numbers (base 100)

The price of chocolate went from 2.35 to 2.73 euros, the price of coffee from 4.12 to 5.44 euros. Which one increased more? Hard to see... Economists invented an elegant tool for this: the index with base 100. You pick a reference date, declare that the value there is worth 100, and express every other value proportionally.

The formula is direct: index = 100 × (value at the studied date) ÷ (value at the reference date). It is a proportional table in disguise! If a price goes from 250 to 290 euros, its index becomes 100 × 290/250 = 116. The huge advantage: reading is immediate. An index of 116 means a 16% increase since the reference; an index of 87 means a 13% decrease. The index is just the multiplier times 100.

Beware of the vocabulary trap: when an index goes from 110 to 121, it gains 11 index POINTS, but the change is not 11%! The rate is always computed with a quotient: 121/110 = 1.1, a 10% increase. Index points are subtracted, percentages come from division. Journalists often mix them up, but not you.

Indexes are used everywhere: consumer price index, stock market indexes, production indexes. Their superpower is comparison: by bringing chocolate and coffee to a common base 100, you immediately see which one increased more, even though their prices in euros are completely different. Setting the base to 100 is like putting two fractions over the same denominator!