Some Boeing 737s have this exit indicator in the cabin, attached in a seemingly odd position, next to the overhead bins, instead of in the middle.
Why is it placed here?
You dont have this tagged with a jurisdiction and the answer may vary a bit by country regulations but here in the US under the FAA the requirements do not explicitly state the sign must be in the middle of the aircraft:
(b)Emergency exit signs -
(1) For airplanes that have a passenger seating configuration, excluding pilot seats, of >10 seats or more must meet the following requirements:
(i) Each passenger emergency exit locator sign required by § 25.811(d)(1) and each passenger emergency exit marking sign required by § 25.811(d)(2) must have red letters at least 1 1/2 inches high on an illuminated white background, and must have an area of at least 21 square inches excluding the letters. The lighted background-to-letter contrast must be at least 10:1. The letter height to stroke-width ratio may not be more than 7:1 nor less than 6:1. These signs must be internally electrically illuminated with a background brightness of at least 25 foot-lamberts and a high-to-low background contrast no greater than 3:1.
(ii) Each passenger emergency exit sign required by § 25.811(d)(3) must have red letters at least 1 1/2 inches high on a white background having an area of at least 21 square inches excluding the letters. These signs must be internally electrically illuminated or self-illuminated by other than electrical means and must have an initial brightness of at least 400 microlamberts. The colors may be reversed in the case of a sign that is self-illuminated by other than electrical means.
So if its easier due to electronic cabling, head room, brackets, or any other factor manufacturers are free to mount the sign off center.