Assuming you are using Microsoft SQL Server, which does not have a built-in Median function, you can do something like shown below. Since you haven't provided any sample data, or even which table you are trying to update, this is just a guess on my part. If that is not what you are expecting, post more details - sample data, table schema etc.
;WITH MedianCTE AS
MedianVaccinations = PERCENTILE_CONT(.5) WITHIN GROUP(ORDER BY daily_vaccinations) OVER (PARTITION BY country)
SET daily_vaccinations = MedianVaccinations
INNER JOIN MedianCTE AS c ON
c.country = t.country
t.daily_vaccinations IS NULL;