The use of words ending in "-ics" is governed by whether you are referring to a single body of knowledge or to objects/things.
But statistics has something more than this.
These statistics you presented are a pack of lies.
In the first sentence, "statistics" is used in the sense of "the field of statistics" or "the study of statistics". These are singular concepts. But in the second sentence, suddenly "statistics" is referring not to a single set of knowledge, but to multiple pieces of data. A plural verb should be used.
Until recently optics has only been three dimensional, and holography belongs to this form, too.
The optics in her telescope were superb.
Here again, "optics" is a field or concept. In the first sentence, the speaker is discussing optics in general, as a single whole. In the second, the speaker is talking about the particular lenses in the telescope.
For "mathematics", compare:
The field of mathematics is distinguished by its numerous contributors from across the world and through time.
The mathematics of quantum physics are hard for the average person to understand.
Generally speaking, if you are referring to a unified whole or a single thing, use the singular verb form. If you are talking about specific particular objects or subdivisions of a subject, use the plural form.
The word "police" is rather special: It has no singular noun form. Something like that police over there is securing the scene would be incorrect. One would always construct sentences in the plural form like so:
The police are out in force today.
Anything done by the police will reflect on them.
Other words that take no singular form would include pants, trousers, scissors, and clothes.
Confusion arises because "police" is also used as an adjective. Consider these sentences:
A police department is housed in that building.
The police chief was highly visible at the town meeting.
In these two sentences, we are not speaking of "a police". You could easily remove the word from both sentences and they would make sense semantically and grammatically. Instead, the word describes the department or chief. It gives us context.
"Police" also has a verb form. You may encounter it like this:
The Boy Scout troop must police the area before they leave to remove any trash.
The verb means "to investigate, to search, to clean up". This certainly does fit in with a subset of the duties of a police department.
Best Answer
Both are correct, depending on what you mean to say. "Everyone has their own story" means "Each person has his or her own story" while "Everyone has their own stories" means "Each person has many stories." An individual person can have many things, and a group can collectively have one thing, so the object doesn't have to match the subject: "Dan has many cats," "They own a boat," "Carl's children have red bicycles," etc.
But if you're looking for the common aphorism, it's "Everyone has their own story", referring to the entire story of each person's life.