I always learn things from listening to the radio. On 'The Infinite Monkey Cage', I heard Brian Cox rattle off a 'rule of thumb', which goes something like:
A number plus or minus the square root of the sample size is consistent with random sampling error.
https://www.bbc.co.uk/programmes/b04yfsst (listen from 20 minutes in)
I hadn't heard that one, but deploying those key research tools, the back of an envelope and a pencil, I could see where it comes from.