Battery drain proportional to number of apps installed?

I have two identical iPhone 5's at home, both started off with around about 5 hours 20min usage time, but then i started installing apps on one and not the other. But I disabled push notifications on all of them, quit apps, did a restart so that running background apps were the same on both phones. To test i used both phones for a day each using only the call function, sms/imessage, and 30 minutes of facebook and 30 minutes of safari, exactly. Screen brightness set at 33% on both. WIFI and LTE both on and full bars in same location at home over the weekend.

Near the end of the day when the 10% battery warning popped-up, this was the situation;

  • iPhone 5 with just core apps: usage time 6hrs 13 minutes standby time 15hrs 27minutes
  • iPhone 5 with 30 extra apps installed (but not in use): usage time 3hrs 41 minutes standby time 14hrs 11minutes

My usage is the same, the only difference is the number of apps installed. So my question is; Do installed apps even if theyre not running, have THAT much effect on the battery life of the device?

UPDATE: Complete list of installed apps aside from stock.

Instagram -- dropbox -- google search -- gmail -- drive -- chrome -- whatsapp

facebook -- soundhound (paid) -- Open Table -- Youtube

Bank of America -- Nokia Here Maps -- Bump -- ESPN

Facebook Messenger -- Amazon -- Ebay -- Groupon -- Tv Guide

Skype -- Kindle -- Google+ -- Speedtest -- Flashlight -- Pocket

Flipboard -- The VERGE -- Google Currents -- Pulse -- Camera+

Photosynth -- Pixlr Express -- Skitch -- Evernote -- Google Voice

Pitfall -- Flick Soccer -- Letterpress -- Infinity Blade 2 -- Metal Storm

Carnivore Hunter Pro -- NBA Jam -- Street Fighter vs Tekken

Falldown! -- Temple Run -- Stick Tennis -- EPOCH -- Totem Runner

Wikipedia -- Jasmine -- Fandango -- IM+ -- Twitter