Finite group in which half or more of the elements are involutions

Definition
A finite group in which half or more of the elements are involutions is a finite group in which the number of defining ingredient::involutions (i.e., elements of order equal to $$2$$) is half or more of the order of the group.

This property is determined completely by looking at the order statistics of the group.

Groups of other orders
For all other orders, the only examples are the generalized dihedral groups.

Stronger properties

 * Finite generalized dihedral group