Why use functors over functions?

Compare

double average = CalculateAverage(values.begin(), values.end());

with

double average = std::for_each(values.begin(), values.end(), CalculateAverage());

What are the benefits of using a functor over a function? Isn't the first a lot easier to read (even before the implementation is added)?

Assume the functor is defined like this:

class CalculateAverage
{
private:
   std::size_t num;
   double sum;
public:

   CalculateAverage() : num (0) , sum (0)
   {
   }

   void operator () (double elem) 
   {
      num++; 
      sum += elem;
   }

   operator double() const
   {
       return sum / num;
   }
};