Do you need a subject in a sentence if it is implied from the previous sentence?

These two sentences sound good to me in my head, but the second sentence isn't an independent clause. In my mind, the subject of the second sentence is implicitly taken from the previous sentence. Is this grammatically correct, or would I need a different mark of punctuation to pull this off?

Collective nouns can either be singular or plural. Plural when thinking of individuals in the group, singular otherwise.

Solution 1:

It would be better to link them together with a colon:

Collective nouns can either be singular or plural: plural when thinking of individuals in the group, singular otherwise.

You might want to rearrange the sentence so that the word plural does not immediately follow itself.

A colon is useful here because the first half of the sentence sets things up (acts as an introduction) for the second half (which really contains the payload of the sentence). The Oxford Manual of Style has this to say about the colon (although this is only one of its uses):

The colon points forward: from a premise to a conclusion, from a cause to an effect, from an introduction to a main point; from a general statement to an example. It fulfils the same function as words such as namely, that is, as, for example, for instance, because, as follows, and therefore:

• There is something I must say: you are standing on my toes.
• It is available in two colours: pink and blue.
• French cooking is the restaurant's speciality: the suprêmes de volaille Jeanette was superb.
• She has but one hobby: chocolate.

The Oxford Manual of Style, 2002