Stat change discrepancies - advice needed

Items and Crafting
Hello Denizens of the Underworld!

Playing D3 I've come across something in the stats items that has led to me being a little confused! (yes, yes.. noob! l2p etc) Please, let me give you an example;

Arrow Abyss (A rare crossbow)
1.15 attacks per sec

+2 - 4 Fire Damage
Increased attacked speed by 5%
+7 life after each kill (not important here)
Socket = +4 - 8 damage

Recurve Bow of Flame (Blue standard magic bow)
8-39 damage (which is what it states but very rarely do i see evidence to prove it)
1.4 attacks per sec

+1 - 2 Fire damage

Ok, there's the stats of the two weapons in question, though just example items. Why is it then that D3 says equipping the Recurve Bow will increase my damage by 8.9 in the 'stat changes if equipped'?

They both have equal damage per second which makes me think that the other attributes arent taken into account?

Can anyone care to explain?

Thanks guys

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