The District government yesterday was ordered to pay $289,000 to the family of a Southwest Washington man who was shot in the back and killed by police three years ago after a quarrel about his unregistered bicycle.

A D.C. Superior Court jury awarded the money to the widow and three children of George White as compensation for wages the 29-year-old man would have earned if he had not been fatally shot in September 1976.

In a three-week trial, the D.C. government contended that officer Gregory Gaston shot White in self-defense after White appeared to point a weapon at him.

But attorneys for White's widow, Deborah, argued that he was not armed at the time he was shot.

Jury foreman Roger Noble said yesterday that at least a third of the jurors had made up their minds in favor of Deborah White from the beginning of the jury's two days of deliberations.

"The most persuasive element in the trial was the photograph showing the bullet wound in the back," Noble said. "It was our feeling that even a fleeing suspect should not be shot in the back."

According to various witnesses' testimony, the incident occurred like this:

White left his apartment on his 10-speed bicycle in early evening, saying he was going to a hobby shop to buy supplies to complete an oil painting.

He stopped at the corner of Mississippi Avenue and 1st Street SE to talk with friends when two police officers drove past. White shouted something to the officers that could not be recalled exactly by witnesses. The officers drove around the block and returned.

The officers asked White for his identification and whether his bicycle was licensed. When White failed to produce the registration, the officer said they would have to impound the bike.

A shoving match broke out as the police tried to take the bike. The police officers begin beating White with their nightsticks. Both White and the officers fell down and then White jumped to his feet and ran off.

He dashed through a small clump of trrees nearby and the officers sent out a call describing him and saying he was wanted for assaulting a police officer. a

Gaston testified he saw White jog out of the wooded area near 150 Xenia St. SE and yelled for him to stop. White stopped and began to turn toward the officer with what appeared to be a weapon in his hand, Gaston testified. The detective said he fired in self-defense.

Witnesses for Deborah White testified that Gaston drove up, jumped from his car and assumed a shooting position as White started away.

The witnesses testified that they found a hunting knife eight feet away from White's body.But another witness testified he saw police take a small knife from White's pocket after he had been shot.

Several jurors said yesterday that they did not give much weight to additional testimony by police that small-caliber pistol was found in a sweater White tossed aside just before he was shot. Some jurors said they believed the weapon was placed in the sweater by police.

Deborah White said her husband, a building maintenance employe for the National Park Service, had several freinds who were police officers.

A beautician until her husband's death, White now supports her two daughters, Nicole, 7, and Shelita, 9, and a son Derrick, 4, with social security money and a veteran's pension.

"The children still ask a lot of questions about how their father died," she said. "I don't tell them he was shot in the back by the police. I don't want them to grow up prejudiced toward the police. I'd rather they forgive and try to forget."

At the time of her husband's death, she said they shared a dream of someday buying a small house and saving up to send their children to college.

"Now I can make that dream come true," she said.