Eddard Stark (Ned) who has a pathetic life is one of the protagonist in the novel A Game of Thrones--book one of A Song of Ice and Fire written by George R.R. Martin. It is a splendid fantistorical tale. Ned was the Lord of Winterfell, however, because of the intimate relationship with the King, he became Hand of the King. He found the incredible secret of Queen and her children. Unfortunately, after the death of the King, he was framed up as a traitor and be executed by the new King.
Some people think his stupid put him to death. Here's a link of other people's analysis of Eddard Stark with interesting pictures.
On the contrary, I will use the Big Five model of personality to analyze Eddard Stark in the first Chapter to show you a true Ned. In the first Chapter, Ned stay with his sons who watch their father sentence an escaped Night Watch. After cutting the escaped Night Watch's head off, Ned comforts his second youngest son, Bran, who is only 7 years old. And he tells Bran:" Our way is the older way. The blood of the First Men still flows in the veins of the Starks, and we hold to the belief that the man who passes the sentence should swing the sword. If you would take a man's life, you owe it to him to look into his eyes and hear his final words. And if you cannot bear to do that, then perhaps the man does not deserve to die. One day, Bran, you will be Robb's bannerman, holding a keep of your own for your brother and your king and justice will fall to you. When that day comes, you must take no pleasure in the task, but neither must you look away. A ruler who hides behind paid executioners soon forgets what death is." (A Game of Thrones P16)
From this conversation, we can infer that Eddard Stark is low in Openness to Experience ("Our way is the older way." He respects and complys with the old rules--a very conventional person.) In additionally, he is very high in Conscientiousness. Although he knows that the sentence will make him uncomfortable (" you must take no pleasure in the task"), Ned still teaches Bran to respect the criminal ("you owe it to him to look into his eyes and hear his final words") and introspect himself to keep impartial ( "if you cannot bear to do that, then perhaps the man does not deserve to die"). He is responsible to not only the rules, the criminal, the life and death, but also to his heart. He is kind of Agreeable person--after sentencing the escaped Night Watch, he did not forget to care about his little son and teach him the rules. We can see his deep love and hope to his son from this talk.
So, in the conclusion, Eddard Stark should be a person who is low in Openness to Experience, but high in Conscientiousness, and with some Agreeableness. He is not good at Extraversion (we can see it from the whole story) and not related to Neuroticism at all.