Is there a single word for someone who likes or loves to examine statistics?
A statistician is one who collects and/or works with statistics. You are unlikely to find a single word in wide use for someone who enjoys consuming statistics as an amateur pastime, although people often coin such words as needed by appending -[o]phile or -[o]holic to the root word, or to a derivative of it: statophile, statoholic.
The closest I can think of is a number-cruncher:
a person or thing that performs a great many numerical calculations, as a financial analyst, statistician, computer, or computer program.
More generic words for people who like math are nerd and geek or coined words like mathophile.
Quantophrenia n. Excessive reliance on or use of facts and figures that can be derived using statistical or mathematical procedures
This is a bit more work-related than what you’re asking, but in a business context, someone who focuses on analysing things numerically is a quant.
In UK slang: Statto!
Angus Loughran... rose to fame as "Statto", the resident statistician on the BBC Two television show Fantasy Football League. Clad in a dressing gown and pyjamas, he would stand in the corner of the set and provide facts and figures on each of the guests' fantasy football teams, while being made fun of by hosts Frank Skinner and David Baddiel.