This is the case:

My site is getting a lot of trafic from an image (a company logo image) because this image is ranked 1.st in google search results for a company's title. (I have no idea how that happened)

This image is must for my website, but it is not relevant with site content so irrelevant people search for the image and finds out about my site, so that I get interesting statistics:

http://postimage.org/image/3oyvrjoz9/

Pros: Total Visits & Avg. New Visits
Cons: Avg. Page/Visit, Avg. Visit Duration, Bounce Rate

In summary I am confused if this image is helpful to my website ? Because I don't know the balance between those 5 statistics

P.S: My website is 2 months old, and we are working on seo at the moment

Another P.S: Kindly ask you to not provide assumtions, because I also have assumptions, I need real knowledge.

Edit: Search Keyword is: arcelik logo Search Site: google.com.tr Search URL: https://www.google.com.tr/search?hl=en&q=arcelik+logo&bav=on.2,or.r_gc.r_pw.r_qf.&bvm=bv.41524429,d.Yms&biw=1366&bih=667&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi&ei=oZIDUfutAseVswa9zYHwCw