Which one is most correct way of describing the number? Should it say:
reported that 414 (which is 78%) of (the) 530 people.
or is it:
reported that 414 (which is 78%) OUT of (the) 530 people.
Either is correct, and you will see both.
The problem comes from the fact that it is quite idiomatic to say "414 out of 530" but not at all idiomatic to say "78% out of 530." With the sentence constructed as you currently have it, some will find awkward whatever you say.
I might advise rewriting along the lines of "414 out of 530 (78%) ..." or just "78% of 530 ..."
EDIT: When talking about inferences from samples, it is important to know the size of the sample to estimate the reliability of any inferences being made. But what we are usually interested in are the proportions shown by the sample because we want to extrapolate to the overall population that the sample is presumed to represent. Thus, upon reflection, saying "78% of a sample of 530" is probably best if the 530 are a sample. That is, your English should make clear whether you are dealing with descriptive statistics or inferential statistics.