What is the optimum average score for a quiz? 100%? Not in my view. It is 62.5%, or a number close to that.

When using a quiz as a summative assessment, your goal is *maximum discrimination*. That is, you want to be able to see as clearly as possible which students have ‘got it’ and which have not.

Consider a multiple choice question with 4 options – the most common format.

- A student who knows the answers to none of the questions will, on average, still score 25% by randomly clicking.
- A student who knows the answers to all the questions will score 100%.

Your ideal is that your students scores will be spread out between these two extremes. Armed with this information you will know, at least in theory, what each student needs to move them on.

A quick way to see that you have pitched the quiz at the right level is to look at the average score. If it is half way between 25% and 100%, then you’ve got it just right. And half way from 255 to 100% is of course 62.5%. QED.

This is not the whole story, as other question types have different middle points.

- A yes/no question returns an average of 50% from random clicking; hence its centre-point is 75%.
- A cloze question does not have the random-click problem, so it’s 50%.
- The centre-point calculation for a checkbox question is quite complicated, and depends strongly on the number of options.

All the above is true for any multiple choice assessment. At Yacapaca, how closely students score to the optimum is a major factor in our question quality metric. This in turn determines how likely the question is to be returned by a search and included in a quiz. Thus, questions that are too hard or too easy are simply evolved out of the system over time.