interesting read, this KNMI stuff (official dutch weather agency).
interesting because it states that the wind direction is explicitly not a weighted average, but an average where each windvector is first scaled back to a unitvector, before being averaged. It is based on a mechanical construction, so at zero windspeed, the last recorded value is being used.
Also interesting, because all wind measurements are based on a 3 second sliding period consisting of 4 samples per second.
Most of the article is about how measurements are reported in abbreviated codes targeted for specific use, e.g. aerospace. They all have different ways of defining average windspeed and gust, which makes it hard to compare.