Cryptic crossword clue
Annoyed over department providing a representative sample 5-7

The most common and most likely answer to this crossword clue is the 5 plus 7 letter word CROSS SECTION

I've seen this crossword clue in Financial Times
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Buddy explains!

The straight part
We know that "representative sample" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case representative sample = cross section.
The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.
This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.

What does CROSS SECTION mean?

CROSS SECTION noun
  1. A section formed by a plane cutting through an object, usually at right angles to an axis.
  2. A sample meant to be representative of a whole population.
  3. The probability that a particular nuclear reaction will take place.

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