If that's from random sampling then you're right. Positivity is normally derived from dividing the total number of infections by the total number of tests rather than random statistical sampling.
If it really was the case that 20% of school children in NI tested positive last week, that is a phenomenally high percentage and eclipses the highest point in the most effected areas at the height of Omicron. Also, at that rate, a considerable degree of herd immunity would be kicking in very shortly.
It is from random sampling, see this report:
www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/18february2022
As for herd immunity, given that BA.2 is growing quickly here, you might like to read the findings on reinfections from Denmark, seemingly occurring more frequently in the unvaccinated (yes children again):
twitter.com/kakape/status/1496082108867125255