Why can you jump further on the moon than on the earth?

Because the gravitational field strength on the moon (1.6N/kg)is smaller than the gravitational field strength on the earth (9.8N/kg). Weight= mass×gravitational field strength. Your mass is the same but as g is smaller, your weight decreases. weight is the gravitational force, the downwards force towards the centre of the planet, and as it will be smaller on the moon, the force of attraction between the moon and you is smalller so when you jumb you will reach a higher point above the ground than when you jumb on the earth. Basically the moon 'pulls' you less than the earth.

You do jump further because you weigh far less on the moon than earth

Independent variable is something that is changed in a experiment.