Very well, since you insist.
From lejebolig.dk, when searching for "hus/villa" (house/villa) in the Copenhagen metropolitan area:
-2 rooms, 75 sq. m.: 7,000 DKK/month (~$1150)
-3 rooms, 67 sq. m.: 7,500 DKK/month (~$1200)
-5 rooms, 160 sq. m.: 8,000 DKK/month (~$1300)
-4 rooms, 100 sq. m.: 8,000 DKK/month (~$1300)
-4 rooms, 115 sq. m.: 10,200 DKK/month (~$1650)
-4 rooms, 90 sq. m.: 10,800 DKK/month (~$1750)
-3 rooms, 99 sq. m.: 10,800 DKK/month (~$1750)
And so on and so forth. The most expensive house on that site costs 24,800 DKK/month, which is around $4,000. The second-most expensive costs 16,000 DKK/month, or around $2600.
There is no way you'll find that most houses in Denmark rents for between $4000 and $8000.
EDIT: Corrected my numbers; I was using 5 DKK per USD, whereas it's 6 DKK per USD.
From lejebolig.dk, when searching for "hus/villa" (house/villa) in the Copenhagen metropolitan area:
-2 rooms, 75 sq. m.: 7,000 DKK/month (~$1150)
-3 rooms, 67 sq. m.: 7,500 DKK/month (~$1200)
-5 rooms, 160 sq. m.: 8,000 DKK/month (~$1300)
-4 rooms, 100 sq. m.: 8,000 DKK/month (~$1300)
-4 rooms, 115 sq. m.: 10,200 DKK/month (~$1650)
-4 rooms, 90 sq. m.: 10,800 DKK/month (~$1750)
-3 rooms, 99 sq. m.: 10,800 DKK/month (~$1750)
And so on and so forth. The most expensive house on that site costs 24,800 DKK/month, which is around $4,000. The second-most expensive costs 16,000 DKK/month, or around $2600.
There is no way you'll find that most houses in Denmark rents for between $4000 and $8000.
EDIT: Corrected my numbers; I was using 5 DKK per USD, whereas it's 6 DKK per USD.