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For full context:
<https://www3.nhk.or.jp/news/html/20180127/k10011304581000.html>

The sentence in question: 日本で働く外国人労働者は去年１２７万人 **余りと** 、統計を取り始めた **平成２０年以降最** も
**多くなった** ことが厚生労働省の **まとめで** わかりました。

My attempt at translation: "Concerning the foreigner employees who work in
japan, through the conclusion of the ministry of health, labour and welfare we
know that last year it became more than 1270000 since 20 years heisei era
where they began taking the statistics."

So I basically ignored the と in 余りと because I didnt know how to interprete it.
The entry on jisho didnt seem to fit either <http://jisho.org/search/amarito>
.

Im also not sure if I resolved the nominal phrase 統計を取り始めた **平成２０年以降最**
correctly by making 統計を取り始めた a relative attribute.

I think that 余り and 多くなった are somehow related, since the foreigners "became
more than...". However, the more semantics already is in the word あまり, which
is why it seems like a doublette if 多くなった follows.

Ultimately, Im very skeptical about my interpretation of まとめで. I interpreted で
as a particle indicating a means because it fit my interpretation well, but
since my interpretation had a lot of guesses, I feel like this is probably not
right xD
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question
grammar
How to understand 余りと and 以降最も多くなった。
と is and. It connects the two things that can be known from the summary (まとめ)
of the statistics. 最{もっと}も多くなった means the number has reached the peak since
the statistics started. The translation is (see kandyman's answer for a better
translation):

Through the summary of the Ministry of Health, Labour and Welfare we know that
last year there were more than 1,270,000 foreign employees who worked in
Japan, which is the highest number since 2008 (20th year of the Heisei Era),
when they began taking statistics.
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First of all the と goes with 分かる. The patterns is 。。。と分かった to mean something
like "It became clear that...".

The 統計を取り始めた is modifying 平成２０年, ie "since statistics began to be recorded in
Heisei 20". The 以降 is the "since" part above.

最も多くなった go together to mean "(became the) largest amount of..."

余り in this case just means "more than" or "over".

And まとめ is simply a "summary", ie a summary report published by the Ministry.

I would translate as follows:

"According to figures published in a summary by the Ministry of Health, Labour
and Welfare, the number of foreign employees working in Japan last year grew
to more than 1,270,000. This is the largest number documented since records
began in 2008."
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answer
The と is a quotative particle. Here it continues to （最も）多くなった.

> 『日本で働く外国人労働者は去年１２７万人余り』 **と** 、（統計を取り始めた平成２０年以降）最も **多くなった**

It can be roughly understood as 「～というふうに・というように・のように、多くなった」.

Similar examples:

>   * 参加者は200名 **と多くなった** 。 The number of participants grew to 200.
>   * 数値は80％ **と** 、今までで最も **高かった** 。 The number was the highest ever, being
> 80%.
>   * 結果は５対０ **と** 、初出場ながら **健闘しました** 。 The team did well with a score of 5 to
> 0, even though it was their first appearance in the tournament.
>

* * *

As the other posters said...

余り means "a little more than [a phrase with a number]".

> あまり【余り】  
>  （造）《数を表す語に付いて》それより少し多い意を表す。[余]{よ}。  
>  「二百余りの申し込みがあった」「ひと月余りが経過した」  
>  (明鏡国語辞典)

and まとめ is "summary" (or "conclusion" or "report", depending on the context.)

As for the other part and a full translation, please refer to the other
posters' answers...
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answer