Sales of existing single-family homes soared in November following six consecutive monthly declines, while total residential and nonresidential construction activity went up 8 percent, according to two reports released yesterday.

The National Association of Realtors' said in its monthly report that the median price of a home increased to $72,500, up $500 from October levels. The 9.1 percent sales gain from October to November brought the seasonally adjusted annual rate to 2.89 million units.

Meanwhile, the F. W. Dodge Division of McGraw-Hill Information Systems reported that the increase in total construction activity was spurred by a surge in commercial contracting, which had been sluggish over the past two months.

The New York-based construction market data firm said the start of $16.9 billion worth of new activity raised its seasonally adjusted Dodge Index of total construction to 158 from October's 146 and September's 144.

Lower mortgage interest rates and milder-than-usual weather in most parts of the country are credited with increasing the demand for homes.

"The main reason for the increase in sales is because of lower interest rates," said Frank Katusak, vice president and director of economics and research for the Realtors association. "The weather has also stimulated people to get back into the housing market, which allows them to act on their housing needs prior to the springtime."

George A. Christie, an economist at F. W. Dodge, said the rekindling in building activity may be in part because of the business community's concern over the possible loss of accelerated depreciation rather than the "growth recession" that some economic reports have suggested.

"Proposals for tax reform in fiscal year 1986 may have the perverse effect of enticing the start of a lot of new capacity in 1985 in order to qualify for more advantageous capital recovery regulations," Christie said.

The increase in home resales follows a downturn that began last May and became progressively worse during the summer. "When interest rates began to fall, we began to see resale activity pick up," Katusak said.

But the healthy increase still was 6.5 percent below the 1984 peak sales rate of 3.09 million units recorded in April. It also was 30.4 percent below the 4.15 million annual sales rate of November 1978, the highest rate recorded by the Realtors association in the 16 years it has been keeping such detailed records. November resales were 7 percent above the sales rate of November 1983.

Three of the four regions of the country showed sales increases in November. The largest gain came in the South, where sales jumped 17.7 percent for the month to an annual selling rate of 1.13 million units.

The Northeast reported an 8.5 percent gain to an annual selling rate of 510,000 units. Sales were up 8 percent in the West to an annual rate of 540,000 units. The lone decline was recorded in the Midwest, where existing homes sold at an annual rate of 710,000 units, down 1.4 percent from October.

Home prices showed the sharpest increase in the Northeast last month, rising to $83,700 -- up $2,600 from October to November. Prices increased in the South to $70,600, an increase of $600.

The West, which has had the most expensive homes, saw prices fall $2,300 to a median price of $95,100. In the Midwest, prices fell $400 to $55,600.

"I think the pretty strong showing we've had in resale activity should translate into an improving economy in 1985," Katusak said.

Although the median price for an existing single-family home in November was $72,500, the association said that 53.3 percent of all homes sold were between $40,00 and $90,000. Just 2.4 percent of the homes sold were under $20,000, and 2.2 percent had price tags of $250,000 or above.

In the construction industry, November's gain for nonresidential building was $6.4 billion, up 5 percent from October, F. W. Dodge said. A 60 percent gain in industrial building and a 20 percent increase in office building claimed the spotlight last month, but an 8 percent drop in institutional buildings such as educational and health care facilities adversely affected November's strength in commercial and industrial contracts.

On a year-to-date basis, total construction through November 1984 amounted to $196.1 billion, up 9 percent over the comparable 1983 period.