To effectively collect data during an experiment focused on the transfer of kinetic energy in a sample of water and ice, the most relevant tool from the options provided is a thermometer.
A thermometer will allow the student to measure the temperature changes in the water and ice, which is critical for understanding how kinetic energy is transferred as the substances change state (e.g., from ice to water) and how energy is absorbed or released during this process.
While the other tools (meter stick, balance, graduated cylinder) have their uses, they are not as directly applicable to measuring kinetic energy transfer as the thermometer.