Shawn Better, a tall, slim 16-year-old high school junior who kept pretty much to himself, went to his homeroom, first- and second-period classes at Ballou High School on Tuesday. He left school at 11 a.m., missing his next four classes.

About 7:30 p.m. on Tuesday, Better was found in a parking lot in the 4500 block of South Capitol Street SW. He had been shot once in the head. He died yesterday afternoon at Greater Southeast Community Hospital after lingering in a coma since the shooting.

D.C. police said they have discovered no motive or suspects.

"I would like to know why," said his mother, Yvonne Better, as she sat on a light brown, soft-cushioned chair in her Southeast Washington apartment."Why my son? . . . I'm not bitter. I'm just hurt. I can't be bitter.

"I don't know of anything a youngster that young could do that would cause someone to kill him . . . . He didn't have any money."

"He is a very,very well-liked young man," the school principal, Dennis Johnson, said yesterday while Better was still in a coma.

"One of the things that upsets the kids [at school] is that something like this would happen to such a nice kid."

Yvonne Better, who works in the mayor's command center, said her son, the youngest of four children, was staying with her daughter Gwen, 25, in Northwest Washington. He had gotten up Tuesday, dressed for school, helped his nephew get dressed and left for school.

He generally got home from school about 4 p.m. When his sister arrived home shortly after 5 p.m., her brother was not there.

She called her mother. "He has never stayed away from home," said Mrs. Better, who began to worry.

Better said she thought about calling the police, but from her experiences at the command center she knew that her son had to be gone for a certain period of time before a missing person report could be filled.

So she anxiously sat by the phone, waiting for a call that he was all right.

About 8 p.m. Tuesday, two District police officers knocked at the door of her apartment. They told her would have to go to the hospital to see her son.

When she got there she found that her son had been shot in the head. The bullet went through the back of his head to the front, lodging in his forehead. The physicians at the hospital told Better that, if her son lived, he would have been unable to function in any way.

Better said she was told that the parking lot where her son was found was a popular hangout for youths shooting craps.

She said she has no idea why her son was in the neighborhood, except perhaps that he was on the way to visit a friend who lived nearby.

"He doesn't like to argue," she said. "Sometimes when I would be hollering at him about something, he would say, 'Mama, don't holler anymore. He wasn't being disrespectful or anything. sIt was just that he didn't like to argue. That's him."

Better said her son, who attended Shad Elementary, Charles Young Elementary and Evans Junior High schools before Ballou, "had big goals. He wanted to go in the Air Force and work in communications."

She said he was a fanatic about mopeds, and his father -- from whom she is divorced -- had told him he would get him one if he improved his grades. One of the leaders in the Department of Recreation's roving leader program planned to tutor him in English and mathematics Tuesday evenings, she said.

Her son, who had a fancy for $80 loafers and designer jeans, had been looking for a job. "He was upset because nobody wanted to hire him because he was 16 and had no experience." He had been waiting for a letter from the city's Labor Department that he hoped would tell him he could take the civil service test.

"He's mostly a loner," said his sister, her eyes swollen from tears.

His classmates agreed. "He's a nice guy," said 15-year-old Leona Russell, a sophomore. "He wasn't rowdy . . . I cried when I heard what happened."

Johnson, the school principal, made an announcement over the school's public address system yesterday about the shooting. He encouraged any students or teachers who might know what happened to talk to the D.C. police. s

The police said that persons with any information about the shooting should call the D.C. homicide squad at 727-4347.