The phrase "a variety of activities" is correct and usable in written English. You can use it when you want to refer to numerous different types of activities. For example: "We offer a variety of activities to keep our students engaged in the learning process.".
Linda and Al became Roosevelt Island pioneers in 1975 where they were actively involved in a variety of activities.
The reservoir supports a variety of activities including water-skiing, sailing, angling and bird watching.
The "prevention for positives" efforts cover a variety of activities.
From Unity Village a variety of activities are carried on.
The residents can also participate in a variety of activities, like clubs for music, baking, painting and gardening.
Global Handwashing Day in Eritrea 15 October 2015 - Global Handwashing Day was celebrated with a variety of activities across Eritrea.
A variety of activities were reported by the children as a means of earning a living.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com