A group of 250 Fairfax Hospital physicians guessed wrong six out of 10 times in a recent quiz on such common medical costs as blood tests, semi-private rooms and X-rays.

The doctors' poor showing was made public yesterday at the opening of a campaign by the Fairfax Hospital Association and the county medical society to sharpen public awareness -- including doctors' -- of high health care costs.

The quiz results, in which doctors and residents were asked to estimate 20 common hospital fees "simply tell us we [doctors] have a lot of room for improvement in becoming cost-conscious," said Dr. Leon I. Block, president of the medical society.

The doctors scored poorly despite a 25 percent plus-or-minue allowance for error. Among the costs many doctors guess wrong on:

Blood count -- $9.00

Semiprivate room for day -- $110.

First half hour of operating room -- $140.

Chest X-ray -- $26.

Skull X-ray (one-to-three views) -- $28.10.

To follow up the quiz, the hospital association and medical society are giving the county's 600 doctors a brochure listing common costs.

A second brochure is being sent to 100,000 households in the county. The brochure encourages patients to get a second medical opinion on treatment or surgery and urges them to check fees and prices with their doctor in advance.

As for doctors and their attitudes in the past, Block said, "We really didn't know what things cost. The attitude was to do the right thing -- and hang the cost."

With pressure mounting from all quarters to hold down the costs of health care, Block said that attitude no longer has a place.

"The cost of an illness is part of the illness," he said, "and it has to be considered . . . We're not going to sit there with a calculator, but we have to be conscious of costs."

Dr. Roger A. Snyder, chairman of the medical society's cost containment committee, said doctors "are not going to be offended if a patient brings up the question of money. I think doctors wish people knew more about what they were getting into. It would save recriminations later.

"While almost every test has some potential benefit," Snyder said, "we have to learn to measure in a better fashion than we have in the past whether the benefit is greater than the cost."

He said a national survey found that 90 percent of all skull X-rays taken in one year were not justified by symptoms. The needless X-rays, he said, cost $100 million.

The cost-control efforts at Fairfax, Commonwealth, Doctors and Mount Vernon hospitals -- the three institutions operated by the Fairfax association -- are voluntary, Block and Snyder stressed. They are the Fairfax health-care establishments' answer to the Carter administration's proposal to put a mandatory cap on hospital costs.

"A voluntary program is the only way you can contain costs and maintain quality care," Block said. "A cap of spending will result in a rationing of health care services. I don't want to do the rationing."