WoW get damage range from DPS

I would like to understand how World of Warcraft calculates its damage range from Speed and Damage per Second. Here is an example of what the character sheet shows:
Without Weapon
Damage: 5  6
Speed: 2.00
DPS: 2.6
With Weapon
Damage: 9  12
Speed: 2.90
DPS: 3.5
Only weapon stats
Damage: 3  5
Speed: 2.90
DPS: 1.4
My attack power is 29 which translates into 2.1 DPS added additionally.
If I'm not mistaken there must be some kind of formula to get the damage range e.g. 9  12 from Speed(2.90) and DPS(3.5). If I multiply Speed by DPS I get 10.15 which fits into the damage range, but what I want to understand is how do they calculate the minimum damage of 9 and the maximum damage of 12?

Now that I understand your question correctly, the answer is you can't.
All weapons/melee attacks have a base damage range that are set by the item. You don't calculate the range from your other stats, the weapons have a set range and the DPS (Damage per second) is calculated from that average damage divided by the attack speed.
Take this sword for example: https://www.wowhead.com/wotlk/item=37401/redswordofcourage
The average damage of the range is 229.5. Considering the speed is 1.6 (time between attacks), the DPS is 229.5 / 1.6 = 143.44.
This weapon: https://www.wowhead.com/wotlk/item=37179/infantryassaultblade
Follows the same math. Damage per second of 338.5 / 2.6 = 130.19.
Since the calculations are based on average damage, we can't determine the range working in reverse since that is our calculation value. Using the 338.5 average damage from the second weapon, we can't tell if the range is 337340 or 1676.
Feel free to browse all the weapons on wowhead, they all have a base damage range that are set for the item.