How do we decide if 中 is ちゅう or じゅう?

Question

How do we decide if 中 is ちゅう or じゅう ?

For example, in this sentence １０人中３人はビデオを持っている which pronunciation should we use?

What about this: そのピアニストの演奏中、彼らは一心に耳を傾けた。

Answer 1

• じゅう (or, rarely: ぢゅう) is used for expressions covering a length of time (resp. area) from start to finish, in its entirety. I.e. "through", "all of":

一年中【いちねんじゅう】all year

一日中【いちにちじゅう】all day

世界中【せかいじゅう】all over the world

• ちゅう is for pointing a particular time (resp. specific location) out of an interval (resp. general area). I.e. "out of", "during":

午前中【ごぜんちゅう】[at some point] during morning

会議中【かいぎちゅう】in a meeting [e.g. "he is in a meeting at the moment"]

Note that in some cases, both can be used and the only way to tell would be from context (e.g. an expression followed by に is more likely to be ちゅう) or in speech:

来月中【らいげつじゅう】all of next month

来月中【らいげつちゅう】[some time] next month

Answer 2

"out of" is 「ちゅう」, "through" is 「じゅう」.

中 ちゅう
(suf,abbr,n-suf) medium; average; middle; moderation; middle school; China; in; out of (e.g. three out of ten people); during (a certain time when one did or is doing something); (P)
中 じゅう
(suf) through; throughout; in the course of; all over or throughout (e.g. a place)

EDIT:

That second example is "during", so 「ちゅう」.