I was interested in the following sentence which appeared in an article by Andrew C. Rewkin titled “Misperceived Paths to Energy Savings" in The New York Times, The Opinion Pages, (August 17, 2010).
It is difficult to identify the actual energy someone saves by turning off the light each time they leave the room, for a few reasons: the types of lights people use varies, it’s difficult to measure how many times the lights are turned on and off per day, and if the behavior has been maintained over the long-term.
Can someone clarify if the fragment "the types of lights people use varies" is ungrammatical, as I think it is?
I would reword "varies" with "vary", but I'm not sure on this correction because I'm not able to identify the subject of the verb.
(Apologize in advanced if the question is not good for this site. If so, please delete. Thank you.)