Understanding this passage is a key matter in discipling another, especially for spiritual babes, to help foster an inquiring mind but discerning spirit.
I hope you do not lose interest in the interpretation of this verse, because it is important to determine which of three cases of a conditional phrase applies, a nuance no fully explored in KJV.
But here is a view on this verse from the old commentator Albert Barnes, in case you don;t have it:
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Acts 17:11
These were more noble than those in Thessalonica - Ησαν ευγενεϚεροι, Were of a better race, extraction, or birth, than those at Thessalonica; but the word refers more to their conduct, as a proof of their better disposition, than to their birth, or any peculiar lineal nobility. It was a maxim among the Jews, that “none was of a noble spirit who did not employ himself in the study of the law.” It appears that the Bereans were a better educated and more polished people than those at Thessalonica; in consequence far from persecuting:
1. They heard the doctrine of the Gospel attentively.
2. They received this doctrine with readiness of mind: when the evidence of its truth appeared to them sufficiently convincing, they had too much dignity of mind to refuse their assent, and too much ingenuousness to conceal their approbation.
3. They searched the Scriptures, i.e. of the Old Testament, to see whether these thing were so: to see whether the promises and types corresponded with the alleged fulfillment in the person, works, and sufferings of Jesus Christ.
4. They continued in this work; they searched the Scriptures daily, whether those things were so.
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Our concern, however, in interpreting this passage is to translate the phrase with greater precision than the ambiguosity of the AV or DRB.
That's why we should always consult the original language when looking for the true meaning and intent. If we look at the words used in Acts 17:11 more closely it becomes more clear.
The word meaning "more noble" is eugenesteroi (εὐγενέστεροι) which, as is common in Greek, is a combination of several words. In that form it is only used once in all of scripture.
The first part εὖ means "well" or "well done", "to do well" or "act rightly".
The second part of the word gínomai (γίνομαι) – properly, to emerge, become, transitioning from one point (realm, condition) to another.
Then context of usage needs to be taken into consideration. The context here would indicate a translation of "they properly acted more rightly".
Looking at the rest of that verse we see that they "properly acted more rightly" with (δέχομαι - dechomai) "ready reception of what is offered" and every day (ἀνακρίνω - inquire into, investigate, question) the scriptures (γραφὰς - graphé - passage of scripture, the scriptures).
(γραφὰς - graphé) in the New Testament generally referred to the Hebrew scriptures and we also find in used in 2 Pet 3:16 where Peter indicates the letters of Paul are considered scripture.