What is the effect of rounding counts of artefacts, like books or courses available?

Question

I have been researching to find the right way to display the total number of artefacts, in this case, books available for sale in a website. Another example is the number of courses available in a site. The number is somewhere between 1300 and 1350, and I am wondering,

• Do we round down or round up?
• To the nearest 5, 10, or 100?
• Is it wise to combine with words like: "Approximately..." "more than..." and "about..."
• Can we cheat a bit?

What is the side effect of these choices if I want the users to just go home with the feeling that there are enough books to subscribe for a monthly payment, without deception?

Answer 1

If you ask me, you can give a rough approximation of the actual quantity. Don't exaggerate too much. Suppose you have 1379 books. You don't say you have 2000 books. That's just too much. Also, you wouldn't want to reveal the correct number either. Just speak out these sentences to a friend and ask him which sounds the best, which I believe will be the one I suggest to be the best option:

1. I have approximately 1400 books.
2. I have about 1400 books.
3. I have over 1300 books.

I would suggest the third option:

I have over 1300 books.

I'll tell you why. It's all about the deception. Suppose you have 1379 books. You could still say you have over 1370 books. You could even say I have over 1378 books. Even though you only have one book more than what you claim, technically, it's still valid. But, the multiples of 10s and 100s have their own impact. So you can go with those options too. The word 'over' gives the listener an infinite upper-bound situation. So that's the best choice, if you ask me.

In short, if you had 1379 books, the best way to say that is:

I have over 1300 books.

Answer 2

How to round properly has been studied in detail by physical scientists (you need rules so people don't distort their measurements, intentionally or accidentally), and by linguists. With respect to correctness, you can take a page from the physical sciences and think about "significant digits": If you estimate a number to an accuracy of about one hundred, it makes no sense to report it as "2738"; the final digits have no validity, so you might as well round to the nearest 50. In short: Round to steps that are about half the size of your uncertainty, and round to the nearest round quantity.

With respect to impressions, think also about what your users want to know. If they just need an indication of how many pages of results follow, "around 2700" is fine, while "around 158,270" may strike users as slightly strange. You must have noticed that google search results have a header like "About 7.840 results (0,67 seconds)", which conveys that the true number of results may be different (and will most likely change as you page through them).

When we don't have a specific need for an exact figure, an estimate to within 10% of the correct figure is good for general purposes [citation missing]. That's two significant digits, so providing many more may strike the reader as strange. Krifka (see link above) mentions the oddness of Swiss street signs that warn "stop sign in 103 meters".

Now about rounding down. "More than X" is technically true for any quantity greater than X, but as @Ayyash alluded to in a comment, it's usually strange to underestimate by too much. Old example: Imagine McDonald's advertizing "more than 1000 hamburgers sold". The technical explanation is that it's semantically correct but pragmatically anomalous, because it gives less information (that is, useful information) than the author is capable of giving. However, a low-ball estimate is indeed appropriate in some contexts: Airlines often report "more than 6 seats available" even if the plane is empty: the exact number is irrelevant to most users, who just need to know if the flight or fare is almost sold out. (This also allows the airline to avoid giving out too much operational info.)

So in the end, what accuracy you provide depends on your circumstances.