When the bad news came to the town of Angola, N.Y., on Lake Erie, no one would believe it. The U.S. Census Bureau, compiling the first tentative results of this spring's nationwide head count, said the town's population had dropped 15 percent in a decade -- to 2,268 residents.

Local officials were outraged and sent the police door to door to count housing units. They came up with 846 units -- five fewer than the Census Bureau had logged. "It was a surprise," said Erie County planner Diane McFarland. "The census did a professional job."

In rochester, N.Y., where census-takers found a 23.1 percent population loss, 30 city officials and volunteers knocked on doors in the 16th Ward a few weeks ago and claimed afterward that a quarter of the area's black and Hispanic residents had been missed.

"Of the 30 houses I went to, 15 people weren't counted," said Councilman Joan Hensler. "Some of the people weren't home. Others appeared afraid to answer the door. Some never heard that a census was going on."

More than half of the nation's 39,000 counties, cities and towns have been given preliminary population figures by the Census Bureau in the last few weeks and the numbers reveal dramatic shifts in population.

Big cities, especially in the Northeast and Midwest -- after more than a century of rapid growth -- grew only 3.7 percent while the population at large went up by 9 percent. Rural communities grew 11.4 percent, and suburbs, 14.3 percent, according to census estimates.

But many of the communities that have lost population or have not grown as rapidly as they thought are protesting the figures. Court suits have been filed, recounts demanded. The concern is understandable; under laws passed in the last decade, more than $50 billion in federal and state funds are allocated according to census data. For each person not counted, a city might lose up to $150 in funds for school lunches, job development or road repairs.

Baltimore, for instance, lost 18.6 percent of its population in 10 years, leaving it with 737,557 residents, according to the preliminary census count, Mayor William Donald Schaefer, who believes the city has a population of 818,000 says the census figures would mean a loss of more than $16 million in federal funds.

Pittsburgh lost 21 percent of its population, according to census figures, dropping from 520,000 to 410,000. As a result, it will lose its status as a class II city -- above a half-million people -- and, consequently, the right to levy certain taxes governed by state law.

Although census workers are still in the streets rounding up uncounted stragglers, the bureau is allowing elected officials to peek at the rough figures under a new "local review" program. That way, they can point out mistakes before district census offices close, hopefully preventing lawsuits later.

Hoping to jack up their counts,, hundreds of cities have delved into their files of building permits, water hookups and tax records. Some have even taken aerial photos to check against census maps.

Detroit filed suit before the results were even delivered, demanding that the federal government adjust its figures to compensate for an anticipated undercount of low-income blacks. In 1970, the Census Bureau has found, 7.7 percent of the nation's blacks were not counted.

In Chicago, the Mexican-American Legal Defense and Education Fund has gone to court to try to force the Census Bureau to recanvass Hispanic neighborhoods where residents claim thousands of people were missed.

New York, Baltimore and Chicago also are preparing to sue to force the Census Bureau to keep its offices open longer and make more of an effort to count people who have not returned mail-back census forms. New York Mayor Edward Koch has warned that the city would lose a "hundreds of millions of dollars" in federal funds, as well as political power in the form of congressional and state legislative, seats.

"There are all sorts of problems with the census," said Joan Bannon, assistant director of the U.S. Conference of Mayors, which is joining in Detroit's suit."Most cities feel there is an undercount of both housing units and people. I think the whole thing is sort of a mess."

Bannon cited problems in cities as diverse as Newark, where she said census maps were illegible, and San Jose, where city officials can't believe the census count of an average 2.8 persons per household, given the majority Hispanic population -- a group with traditionally large families.

Vincent Barabba, a former Xerox Corp. executive who heads the Census Bureau, is confident that most complaints will evaporate after local officials and census-takers compare figures and a final count is made. "You have to have empathy with what these mayors are going through," he said.

Lord knows, when you try to count everybody in this country there are going to be problems. But we say to them, 'you show us where the people are and we'll go out and count them.'"

Barabba said the bureau is trying to correct wrong address lists and faulty maps that have plagued census-takers in many cities. Delayed paychecks, sloppy clerical work and widespread errors in filling out forms also have slowed the billion-dollar head count.

Officials in Ithaca, N.Y., have a sense of humor about the problem, Upon learning that the neighborhood of West Hill had been left out of the census, they issued a tongue-in-cheek press release: "Several thousand lost people were discovered late yesterday on West Hill . . . These people . . . may have been wandering for days without shelter or food."

Other cities are bewildered. "We have 4,000 or 5,000 people that either disappeared or something," said Wally Jahraus, the assessor in Aberdeen, S.D. The census counted 25,007 residents there 5.5 percent less than 10 years ago.Jahraus had estimated the population at 30,500.

While Sun Belt cities such as Orlando, Miami, Phoenix and San Diego are booming, many eastern and midwestern cities, including New York, Detroit, Cleveland, St. Louis, Philadelphia and Chicago, are expected to show dramatic population losses.

A major factor in the slowing of urban growth is the dramatic nation-wide shrinking of household size from an average of 3.33 persons in 1960 to 3.14 persons in 1970 andan estimated 2.78 persons in 1980. Looking at it another way: While the nation's population has grown about 9 percent overall, the number of housing units has almost tripled.

The smaller household size reflects a significant drop in the birth rate, the trend toward postponement of marriage and the increase in the number of elderly living alone.

Thus, Billings, Mont., where censustakers counted a 31.3 percent increase in housing units, had only 3.6 percent more people than it did 10 years ago. In hastings, Neb., City Administrator Harold Youngmeyer said a census figure showing a drop in population "strikes one as being a bit peculiar because they say we have had a 13.4 percent increase in the number of housing units."

Generally, families with children moved out of the cities and even out of close-in suburbs and settled on the outskirts of metropolitan areas. Rural communities grew 11.4 percent in population in the decade, while suburban areas grew 14.3 percent and cities grew 3.7 percent, according to the Census Bureau.