The New York metropolitan area remains the nation's most expensive housing market while Des Moines is the cheapest, according to a survey of median prices for existing single-family homes, the National Association of Realtors said this week.

The New York area, which includes northern New Jersey and Long Island, was the price leader in the fourth quarter of 1987 with a $180,800 median price, meaning that half of the area's houses cost more and half cost less.

In the third quarter, New York homes had a median price of $183,000, the Realtors' group said.

Boston remained in second place in the last three months of 1987, although its median of $178,600 was down $3,000 from the third quarter.

The San Francisco Bay area ranked third with a median of $176,000, followed by Orange County, Calif., at $174,500. Hartford, Conn., was fifth at $163,800 and the Los Angeles area was sixth at $145,200.

Other cities in the 10 most expensive housing markets were seventh-ranked San Diego at $131,800; Providence, with a median of $127,400; the Washington area at $122,400 and, with a median of $103,200, the Florida community of West Palm Beach, Boca Raton and Delray Beach.

The national median existing home price was $84,300 in the fourth quarter, 5.1 percent higher than the $80,200 price listed for the fourth quarter of 1986.

Des Moines, with a median of $52,000, ranked as the least expensive housing area of the markets surveyed. Toledo was 49th at $52,900, Grand Rapids, Mich., was 48th at $53,100 and Louisville was 47th at $53,400 in the fourth quarter.

The areas topping the nation in home value increases were Providence, R.I., with an appreciation rate of 32.2 percent from the last quarter to 1986 to the final three months of 1987. Hartford was second with an appreciation rate of 21.7 percent while the Washington area had the third highest rate of 20 percent, the NAR said.

Houston experienced the largest decrease in value, down 7.2 percent from the previous year to a median of $62,700. Oklahoma City was next with a 5.6 percent depreciation rate to a median of $59,400.

John Tuccillo, NAR's chief economist, said he expects a general slowdown in housing activity in 1988.

"We expect price appreciation to be lower {and} existing-home sales activity is likely to be lower by 8 percent or 9 percent," he said.