The growth rate of the euro area is a statement about the change in the union's aggregate output. An equally weighted average of national growth rates is a statement about the average member. They need not coincide because an economy representing a large share of production does not receive the same economic weight as a much smaller member.
Eurostat's quarterly national-accounts metadata explains the presentation of current-price and volume measures and warns that chain-linked member-country levels do not generally sum to the chain-linked aggregate. Its account of European aggregation sets out the role of country levels and compatible prices. Neither method amounts to averaging the growth headlines with one equal vote for each country.
Prices and membership must remain comparable
The example uses additive values deliberately. Summing separately published chain-linked country levels and treating the result as a new official real aggregate can introduce another error. A proper reconstruction needs the agency's aggregation inputs, common price basis and linking method. An initially plausible country-weighted approximation should be labeled as such when it does not reproduce the official construction.
Geographic coverage needs equal care. Comparing the output of a larger membership group this year with that of a smaller group last year mixes production growth with a change in the statistical boundary. A constant-composition series addresses a different question from a series reflecting membership as it changes. The series label and metadata should establish which one is being used before a growth rate is calculated.
The same discipline applies to vintage. If one national estimate has been revised and the regional aggregate still reflects an earlier release, a researcher may be combining observations that were never compiled together. A reconciliation should record the extraction date and available estimates rather than treat every temporary difference as a failure of aggregation.