What key pieces of information are available to decide on the reactivity of the materials?

The relative number of bubbles being produced allows the observer to make a qualitative assessment of how fast the reaction is happening.

What information (not available in the diagram) could be used to give a numerical value to the reactivity?

Here the observer would need to gather data either on the number of bubbles produced per unit of time or better still collect the volume of gas produced.

How could the experimenter describe the observations made?

The data from the experiment is converted to a value per unit of time. Number of bubbles or volume of gas produced per unit of time. Not only can the experimenter place the materials in order of their relative reactivity but now there is a numerical value for that reactivity for the conditions under which the experiment was conduced. This is rate.