Inspired by "real-life examples of common distributions", I wonder what pedagogical examples people use to demonstrate negative skewness? There are many "canonical" examples of symmetric or normal distributions used in teaching – even if ones like height and weight don't survive closer biological scrutiny! Blood pressure might be nearer normality. I like astronomical measurement errors – of historic interest, they are intuitively no more likely to lie in one direction than another, with small errors more likely than large.
Common pedagogical examples for positive skewness include people's incomes; mileage on used cars for sale; reaction times in a psychology experiment; house prices; number of accident claims by an insurance customer; number of children in a family. Their physical reasonableness often stems from being bounded below (usually by zero), with low values being plausible, even common, yet very large (sometimes orders of magnitude higher) values are well-known to occur.
For negative skew, I find it harder to give unambiguous and vivid examples that a younger audience (high schoolers) can intuitively grasp, perhaps because fewer real-life distributions have a clear upper bound. A bad-taste example I was taught at school was "number of fingers". Most folk have ten, but some lose one or more in accidents. The upshot was "99% of people have a higher-than-average number of fingers"! Polydactyly complicates the issue, as ten is not a strict upper bound; since both missing and extra fingers are rare events, it may be unclear to students which effect predominates.
I usually use a binomial distribution with high $p$. But students often find "number of satisfactory components in a batch is negatively skewed" less intuitive than the complementary fact that "number of faulty components in a batch is positively skewed". (The textbook is industrially themed; I prefer cracked and intact eggs in a box of twelve.) Maybe students feel that "success" should be rare.
Another option is to point out that if $X$ is positively skewed then $-X$ is negatively skewed, but to place this in a practical context ("negative house prices are negatively skewed") seems doomed to pedagogical failure. While there are benefits to teaching the effects of data transformations, it seems wise to give a concrete example first. I would prefer one that does not seem artificial, where the negative skew is quite unambiguous, and for which students' life-experience should give them an awareness of the shape of the distribution.
Best Answer
In the UK, price of a book. There is a "Recommended retail price" which will generally be the modal price, and virtually nowhere would you have to pay more. But some shops will discount, and a few will discount heavily.
Also, age at retirement. Most people retire at 65-68 which is when the state pension kicks in, very few people work longer, but some people retire in their 50s and quite a lot in their early 60s.
Then too, the number of GCSEs people get. Most kids are entered for 8-10 and so get 8-10. A small number do more. Some of the kids don't pass all their exams though, so there is a steady increase from 0 to 7.