The Tokyo metropolitan area is investigating the number of people who got influenza in 419 hospitals. In the week beginning the 11th of November the average number of people who got influenza and went to hospital was 1.86 in one hospital. When the average exceeds 1 person an epidemic is considered to have started.

As a scientist, I see mathematics being butchered all the time in the media. I'm wondering if this is another example, or whether my Japanese is wrong.

What is the average taken over? I would assume it is the average over the 419 hospitals, but then 平均は、１つの病院で１．８６人でした makes no sense to me. Why are they talking about one specific hospital? Perhaps １つの means 'each' in this case? I'm not aware of this as a valid translation though.

If I interpret this correctly then an average of 1.86 people per hospital per week doesn't sound worth reporting to me. Maybe I also misunderstood 流行.

In summary, I'd be happy if １つの病院で wasn't there, but the numbers still sound too small to be interesting, which makes me think I've misunderstood.

This means "per one hospital", as you suspected, not "in one hospital". I think this is a bit of bad writing; this would be clearer if it were written, "1つの病院あたり（で）". I think the source is this news from NHK news easy version, and the corresponding version says, 'インフルエンザの患者は１つの医療機関当たり１．８６人'. (Note that, although a bit confusing, as a native speaker I had no problem interpreting the sentence. Although it is dependent on the context)

1. Isn't 1.86 too low?

Again, you are making a correct observation. 1.86 does seem to be too low, but "流行が始まる" means something other than you (and I, initially,) first imagine.

This graph shows the past statistics of the influenza epidemic. Each year, the peak lies at 30-40 /定点, so that's the amount we'll be dealing with in real epidemic. What values > 1 signifies, on the other hand, is the start of the annual epidemic; "Hey guys, this season has come. We are beginning to be infected by influenza, and soon it'll be more widespread" (Influenza is a disease that is fairly rare in seasons other than winter). I haven't been able to find any academic source that supports the threshold, but I think now we have the idea.

Putting aside whether it's an unambiguous writing style for journalism or not, I must say that I didn't even notice slight weirdness when I read this paragraph. If we consult a dictionary:

(indicates a limit in time, space, and amount; or a standard)

As you see in the second example, 五つで二〇〇円 means "¥200 per five pieces" or "five for ¥200" (not only this five but generally), and this phrase likewise, as "1.86 per hospital" or "1.86 a hospital". I think it's a normal interpretation when で follows a number.

If they really wanted to say "in a certain hospital", I suppose they'd use ある病院 instead of １つの.

For the low number of infected people, just see @Yosh's answer.

• +1 for adding the ある病院 bit. That really makes a distinction of "a hospital (counter)" and "a hospital (specific place)" – psosuna Dec 4 '17 at 18:46

Thanks to nkjt in the comment metro.tokyo.jp/tosei/hodohappyo/press/2017/11/30/11.html.

If it goes exponentially, the number avg.1.86 per hospitals/through each hospital might be the sign of epidemic. 一つの here should imply for each in this case.

As from the article (Total report number / 419 fixed points for observation) = 1.86, the number is the average value for each hospital. Therefore, "1.86" should be a representative value for the data.