Oreki Houtarou is the main protagonist in Hyouka. At first, he is very lazy, then after he meets Chitanda, he starts solving mysteries and becomes a little active. He takes a course in humanities in second year. But I am curious what is his real purpose in life?
That's a great question--for a great anime--however Oreki doesn't really seem to want to do anything specifically with his life. On top of this the anime doesn't mention this either.
It's assumed he doesn't want to do anything specific due to his personality: energy conserving. More like he wishes to breeze through life doing everything as averagly as possible in order to conserve energy. If you go to the Oreki Houtarou wiki page and down to Oreki's quotes you can get a good idea of what kind of person he is.
Oreki's Motto: "I don't do anything I don't have to. What I have to do, I do quickly."
Episode 22, 22:50-23:00: "About the business side you gave up on... How about I take care of that for you?"
However if we look at 22:50 to 23:00 we can see Oreki sort of "fantasizing" about helping Chitanda with her duties of running the Chitanda family in the future. However Oreki gives up and doesn't actually tell Chitanda he'll help her. In this sense Oreki ends up actually wanting to help Chitanda and ends up moving a bit away from his motto. However he decides not to help Chitanda after realizing how Satoshi felt when he turned down Ibara, e.g. undeserving.