style - Why end sentences with commas instead of periods when the sentence is in a quote?

I've seen styles where writers end sentences with commas if it is inside double quotes and styles where writers end sentences with periods.

For example:

"She's late again." mumbled Jason.

versus:

"She's late again," mumbled Jason.

Why is it considered common practice to end a sentence with a comma instead of a period?

Answer

Because you are attaching your speaker tag to the dialogue being spoken. If you were using an action tag, or separating the speaker tag from the dialogue, then the quoted material stands alone and uses a period. Other punctuation varies.

Examples:

"She's late again," mumbled Jason. [comma]

"She's late again." Jason looked down the street, hoping vainly to see her. [action tag; period. speaker is implied to be Jason]

"She's late again." Jason made an irritated noise, then said to Maria, "Can you look out the window and tell me if you spot her?" [speaker tag for a different sentence; period]

Jason sighed. "She's late again." Maria nodded. Jason asked, "Can you look out the window and tell me if you spot her?" [speaker tag for two different sentences; speaker is implied to be Jason for the first; periods throughout]

"Can you see her?" asked Jason. [Because this is a question, even though it's a complete sentence, it ends in a question mark before the quote, and not a comma.]

"I see her!" Maria shouted. [Same idea, with an exclamation point.]