Question

to determine if a drug has an effect on patient illness, a researcher gives the drug to 100 patients and gives a placebo to another group of 100 patients.
what type of study is this?
complete
✓ experiment
a principal conducts a study to find the average age of all math teachers in a given high school by recording all their ages.
what type of study is this?
done

Explanation:

This study involves collecting and recording existing data (ages of all math teachers in the high school) without manipulating variables, which fits the definition of a census (a type of observational study that collects data from every member of a defined population).

Answer:

census (or observational study - census is the more specific term here)