So, I want to make a (semi serious) quiz that asks users to guess what most other people think on a range of controversial topics. At the end of the quiz, users will be informed of where they were most wrong about the views of others.
(I think there used to be a quiz show on telly that did this sort of thing - Family Fortunes perhaps).
I already have survey data in which most questions are answered on a five point scale:
agree strongly somewhat agree neither agree nor disagree somewhat disagree disagree strongly
as well as
'depends' (which I may choose to discard) 'refused to answer' (which I will discard)
Now the problem is that for some questions, the distribution of answers will have a wide spread (e.g. from agree strongly to neutral), or even be twin-peaked (for example some topics may polarize people into strong agreement/disagreement, or a lot may answer 'depends'). I don't want to score down a user for picking the 'wrong' popular response when several responses are near enough equally popular. But I think drawing a histogram is too much to ask of the statistical skills/level of engagement of the average user.
So how best to ask the user for their opinion on the distribution of answers to each question? Bearing in mind my aim is to determine the questions for which they most/least "understand other people" (in this limited sense!).
Jayfang's answer is quite good. However, I'm starting to think a simplified histogram is appropriate, after a lot of combining categories and eliminating minority responses first. The issue then is how to present a histogram concept in simple terms (which will be renormalized to sum to 100%). I'm thinking a series of buttons from 'less popular' to 'more popular' by each response, with a footnote that if you click the same for all of them (e.g. all less, or all more) that is just saying they are all the same.