What's a Bathroom?

Recently a sellers of ours pointed out a mistake on the description of his property and it was with the # of bathrooms the home had.  The listing real estate agent correctly entered the information into our mls system, 2.5 baths but when the data was distributed to other web sites it was posted as 3 bathrooms totaling up the 2 full baths and the 1 half bath.  But is 2 and a half bathrooms a proper description of what the property offers?

 I guess I wasn't to busy that day so  I started to think, what the heck is a half bath?  It is a room that you can take half a bath in? No not unless you can bathe in sink or worse.  So why do we call a room with a sink & toilet a bathroom? OK I know,  focus, time to get back to work.