Although the figures reflect an improved economy, they also capture some of the underlying weaknesses in the housing market, namely the persistently large number of foreclosures that continued to drag down prices in January and attract investors.

Foreclosures and other distressed properties made up 37 percent of homes sold last month, the group reported. The cheap homes lured investors, who accounted for 23 percent of buyers, up from 20 percent the previous month and 17 percent a year ago.

As more investors entered the market, all-cash purchases surged to their highest level since the group started tracking the numbers in October 2008. The increase suggests that stringent lending rules are shutting out traditional buyers and empowering people with hefty sums of cash to close deals, said Lawrence Yun, the group’s chief economist.

But the January sales numbers may be deceptively high, said Mark Vitner, senior economist at Wells Fargo Securities.

After reports of widespread paperwork errors surfaced in October, many major lenders temporarily halted foreclosures. Some have since lifted the freeze. “Sales that would have normally taken place in October, November and December got pushed into January,” Vitner said.

None of this bodes well for home prices, because foreclosures tend to drag down values. The median price nationwide fell 3.7 percent, to $158,000, in January, the Realtor group said.

Many economists said that if the economy takes a turn for the worse or oil prices rise significantly because of political turmoil in the Middle East, consumer confidence could wane and home sales could plunge.

Some economists also cast doubt on the Realtor group’s numbers, suggesting that they were inflated because of its methodology. Most recently, mortgage research firm CoreLogic said the sales results could have been overstated by 15 to 20 percent in 2010.

Yun said his group will review data from the past few years.

He acknowledged a possible “upward drift” in the numbers. The sales data are collected from local multiple listing services. A Realtor, for instance, may advertise a home in two neighboring cities. When the home sells, the transaction may be counted twice, he said.

A decline in homes sold by owner may also distort the numbers, Yun said. Multiple listing services include mainly properties advertised by Realtors. As more sellers have turned to Realtors in recent years, the increase may register as an increase in sales when it is only a rise in transactions by Realtors, he said.

Yun cautioned that no housing data is flawless. The CoreLogic data, for instance, came from court records. As the recent foreclosure paperwork debacle shows, not all court records are accurate.