An octave is 8 notes in any given scale. Do,re,mi, fa, so.la, ti, and then do. That's one octave. You can start anywhere, on any pitch. It's just 8 notes. So there can be theoretically limitless number of octaves on a musical scale, but humans are only capable of producing (and hearing) certain pitches.
Not every singer has the same voice, and some will have better vocal ranges (the number of octave they can sing) than others. However, it is very important to remember that an extremely wide vocal range is only as useful as the singer's ability to actually use it. If they can hit extremely low and high pitches in isolation--that's just great for showing off. If they can't sing a simple song like "Happy Birthday" and stay in tune--then they are pretty useless as singers. Always emphasize the quality of the voice over the quantity.
And a B2 to an F5 is about 2 1/2 octaves...which isn't bad for an untrained voice. Providing that you can actually sing those notes easily and not have to grunt, squeak, scream, or belch them out. To give you a frame of reference--"The Star Spangled Banner" spans about an octave and a half. To be able to sing it without any problems, a singer really needs to have at least a half pitch on either side of the high or low notes (in any given key) so they don't have to strain. If they have less than an octave and a half of vocal range---and many amateur singers do--then they can't sing that song in ANY key. Raise the pitch, lower the pitch--it won't matter. It will be too high or too low at one point or another. Someone with a 2 and a half octave range might actually be able to sing that song in more than one key, which allows for greater flexibility. Many show tunes and classical songs would also be available to a singer with this range. However, once again, depends on how much
actual control you have over your voice.
If you sing off key--you sing off key. If you want to learn to use your voice properly, ger a voice teacher. That way you can learn without risking damage to your voice.
Many amateur singers just concentrate on the "quantity" part---they want to get a big a range as humanely (and inhumanely) possible. They can barely sing in tune, but they risk permanent damage to their voices wanting to sing higher or lower than they comfortably can. Vocal training can actually expand your range---but only as far as teaching you how to access notes that are already within your capability--but you don't know how to get out.
Vocal ranges tend to be wildly exaggerated. Often by people who have no clue what an octave actually is. Or a singer's PR department. I think Mariah Carey is on 12 octaves now. Yeah, she has a phenomenal vocal range, but no where near the numbers we read about. And even she sticks to a certain range of notes she personally feels sound the "best" of her particular voice.