mean and standard deviation

Hi everyone,

I'm trying to explain why the following conclusion is not valid:

A student notes that the Wednesday class had a larger mean homework score than the Tuesday class and then concludes that the standard deviation must be larger in the Wednesday class.

I know that this can't be true because the two are not dependent on each other, but I tried an example and it seems to be true. When the mean was 8 the standard deviation was 1.30 and when the mean was 240/21 the standard deviation was 12.021.

Can someone give me a hint on this, please?

Thank you