"wide range of interests" is correct and acceptable in written English. You can use it when you want to convey that one has multiple interests. For example, "John has a wide range of interests including music, sports, art and travel.".
"We have a wide range of interests with the Russians.
We cover a wide range of interests - Politics Weekly, Science Weekly, Football Weekly or Close Encounters.
The deal enabled Weidenfeld more time to pursue his wide range of interests.
He was a man of great talent with a wide range of interests.
He's a very learned person, with a wide range of interests".
Known for his intellectual curiosity and energy he poured himself into a wide range of interests.
She had a wide range of interests in the arts beyond her Hispanic literary studies.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.