Reading Economic Data
Weighted Averages
Why some averages give more importance to some items than others, and how weighting shapes numbers like inflation and index returns.
A simple average treats every item equally. But often some items matter more than others. A weighted average gives each item a weight reflecting its importance.
A simple example
A student scores 80 in a test worth 20 percent of the grade and 60 in an exam worth 80 percent. The simple average of the two scores is 70. But the weighted average is 0.2 times 80 plus 0.8 times 60, which equals 16 plus 48, or 64. The exam counts more, so the weighted average is closer to 60.
Weights in inflation
Consumer price indices are weighted averages. Each item’s price change is weighted by its share in household spending. In India’s Consumer Price Index, food has had a large weight, close to half in the series based on 2012, because food takes a large share of household budgets. So a rise in food prices affects the headline inflation rate strongly.
When spending patterns change, statistical agencies update weights. India has been revising its CPI with a newer base year, which reduces the weight of food as households spend relatively more on other things.
Weights in stock indices
Stock market indices like the Nifty 50 and Sensex are weighted by the market value of companies’ freely traded shares. Larger companies have more influence, so a big move in one large company can move the whole index.
Weights and your own experience
Your personal inflation rate may differ from official figures if your spending pattern differs from the average household’s. A family that spends heavily on rent, school fees or medicines may experience higher or lower inflation than the official number.
Suppose food, with a weight of 45 percent, rises 10 percent in price, while everything else, with a weight of 55 percent, rises 2 percent. Headline inflation is 0.45 times 10 plus 0.55 times 2, which equals 4.5 plus 1.1, or 5.6 percent. Without knowing the weights, you could not predict the headline figure.
Many important economic figures, including inflation rates and stock indices, are weighted averages. Understanding the weights explains why some changes move the headline number much more than others.
- A weighted average gives each item a weight reflecting its importance.
- Consumer price indices weight items by their share of household spending.
- Stock indices weight companies by market value, so large companies move them most.
- Your own inflation may differ from official figures if your spending pattern differs.
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