Does hyperconjugation stabilize a carbocation more than a free radical? Which of the following statements is correct about methyl group?  
  
  
  It stabilizes both carbocation and free radical equally.
  It stabilizes a free radical more than a carbocation.
  It stabilizes a carbocation more than a free radical.
  None of these.
  


I thought the answer would be (1). Keeping in mind these structures: The methyl group can stabilize the carbocation and the free radical group attached to it equally through hyperconjugation. However, the answer given is (3). How is this possible? Why is the carbocation more stable than the free radical? Are the structures I drew wrong?
A carbonation is deficient in 2 electrons whereas a free radical is only 1 electron deficient. Thus any type of stabilisation working on a carbonation will be much more effective as it is more electron deficient. Hence, hyperconjugation or inductive electron donation stabilises a carbocation more than it does a free radical.