Is it ethical to award points for hilariously bad answers?

Is it ethical to award a few points for this answer?

No.

It does not demonstrate understanding. If I wrote a good-intentioned, but poor answer and got the same amount of points, I'd be peeved.

I tend to give at least 1 point out of 10 for almost anything that could be construed as being relevant to the question.

Compared to the responses I tend to give 1/10 for, this is better in several regards:

• It has a logic to it.
• The writer obviously knows it is wrong.
• The writer demonstrates knowledge of something (in this case normal distributions).
• The writer demonstrates some intellectual creativity.

It depends somewhat on my standards for partial credit on the problem, but I'll probably give a good coherent joke response 3/10. On occasion it might be 2/10 if I feel like I need to reserve 3/10 for slightly correct responses that are less good than some responses I'm giving 4/10 for.

Let's face it - awarding of partial credit isn't perfectly accurate, and any numerical score I give has an error bar of a few percent. (Almost always, the central limit theorem works and the errors mostly cancel out rather than stacking up, leaving still a few percent error.) I think it's fine to put a thumb on the noise here.

It depends on what form of ethics you are following.

Virtue ethics? Truth is a virtue; this answer is not true, so to reward it as though it was the truth is dishonest and unethical. Your job is to reward truthful answers, not funny ones, so you would be in dereliction of your duty.

Hedonic ethics? What matters is making people happy. Giving the student extra marks will make him happy, but if the students who gave more accurate answers find out, it will make them all unhappy. Allowing that to happen would be unethical. Therefore we must consider whether they are likely to find out...

Kantian deontological ethics? What if every examiner always gave points for funny answers? It would create a situation where the ability to tell jokes was more useful for achieving qualifications than studying. This would be bad for society. Therefore, this is unethical.