Answer:
This depends on the type of the thermometer, but when working with glass thermometers, (Hg especially) you should not put them near the edge of the table.
This is because it will easier to accidentally touch it and throw it into the ground, breaking the thermometer.
This is bad not only for the material loss of the lab instrument, but also because the mercury inside the thermometer is dangerous, so you really want to keep the thermometers in a safe place.
Then this would be false, do not leave the thermometers near the edge of the table (or in any place where it can fall and break)