When the preliminary census count for the District was released recently, the low figure brought a howl from Mayor Barry, who threatened to ask for a recount. The mayor's reaction was similar to that of a number of officials nationwide, who see the specter of reduced federal funding lurking in the shadow of low census figures.

These doomsday laments are based on the misperception that federal grants-in-aid to state and local governments move in lockstep with the census figures.

Although roughly $50 billion is distributed annually based in part on census data, the new census figures won't lead to much redistribution of that $50 billion. A number of shock absorbers and other properties of the federal funding systems dampen the impact of the new census data.

First, in most programs the 1980 census counts won't be replacing 1970 census figures but, rather, 1978 population estimates. So switching to the new census data will involve only a two-year updating.

Second, many programs have congressionally mandated minimum and maximum allocations to individual states and U.S. territorities, which override any formula allocation.

Third, in many programs only a portion of the available funds are distributed by formula, with the balance being distributed at the discretion of the sponsoring federal agency. These discretionary set-asides are intended to meet needs that are not reflected by the formula.

Fourth, most federal programs allocate funds to states rather then directly to local governments. State agencies distribute the funds within the state. Even if funds allocations to states are based exclusively on the census figures, at the local level the link between population change and funding change depends on how state agencies choose to divvy up the funds.

The fifth reason involves the size of the annual appropriations. The census figures are used in slicing up the pie, but usually not in setting the pie's size. Year-to-year changes in the national level of program expenditures can dominate distributional modifications in determining the changes in federal funds received by state and local governments.

What about the undercount? Here it is important to remember that we are grading on the curve. If the District's census count is, say, 10 percent low, the District gets shortchanged only if the average response rate in the rest of the nation is higher than 90 percent. It is the relative rate that counts.

The communities most seriously affected by the census will be those that gain or lose eligibility for specific federal programs as a result of the new census figures. Some programs have eligibility thresholds defined directly in terms of population. But the threshold effect is more often indirect, occuring through a reclassification of an area from one statistical category to another. Still, relatively few communities will be reclassified when the final census results are in.

All in all, funding shifts stemming from the final census figures will probably be in the same direction as the nation's population shifts: from Frost Belt to Sun Belt and from city to suburb. If funding were based entirely on census counts, then the new figures would cause the District to lose about 15 percent of its federal funds, while Arizona's funds would increase by a third. But the shock absorbers and fudge factors in the 100-plus federal programs using population data to distribute funds will weaken the census's effect. Areas fearing a precipitous drop in funding will be relieved, and those expecting large immediate gains will be disappointed.