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> 東京都はインフルエンザになった人の数を４１９の病院で調べています。１１月２０日からの１週間にインフルエンザになって病院に来た人の
> **平均は、１つの病院で１．８６人でした** 。平均が１人以上になると、流行が始まったと考えます。  
>  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.
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reading-comprehension
Bad maths or my bad Japanese?
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.

流行 normally implies something gets popular in a group.e.g. Pokémon go,
hairstyle, songs, etc. The word is used when a widespread phenomenon is
observed. So, this time, influenza gets epidemic or pandemic in some area.
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1. About "1つの病院で"

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](http://www3.nhk.or.jp/news/easy/k10011241291000/k10011241291000.html)
from NHK news easy version, and the [corresponding
version](http://www3.nhk.or.jp/news/html/20171130/k10011241291000.html) 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)

  2. 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](http://www.metro.tokyo.jp/tosei/hodohappyo/press/2017/11/30/11.html)
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.
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> 平均は、１つの病院で１．８６人でした

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:

> [**で**](https://dictionary.goo.ne.jp/jn/148951/meaning/m0u/%E3%81%A7/)
>
> **４** 期限・限度・基準を表す。「一日で仕上げる」「五つで二〇〇円」  
>  _(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.
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