The six-month old effort to reduce Uncle Sam's midmanagement bulge-by eliminating 40,000 jobs paying $26,000 to $67,000 a year-may be based on incomplete or imaccurate date, the General Accounting Office reports.

GAO made its study for Rep. William Ford (D-Mich.). Ford, a staunch friend of federal workers, chairs the House Post Office-Civil Service Committee. He hopes the data will persuade the administration to slow its job-cutting program, or inspire Congress to overrule it.

The four-year program was launched last October, when federal agencies began cutting the number of Grade 11 through 15 jobs by not filling some of the positions when they became vacant. The Office of Management and Budget has cut personnel funds for most agencies, and the Office of Personnel Management is monitoring the cutback, which is supposed to reduce the number of mid-level jobs by 2 percent each year through 1988.

The exercise means that fewer middle- and upper-grade jobs will be available to employes seeking to move up the career ladder.

An estimated 540,000 federal workers, 39 percent of the total white-collar work force, are in grades 11 through 15, compared with 21 percent in 1959, according to the Office of Personnel Management. OPM says that some of the difference can be explained by technical changes in government -- there are more computer specialists now and fewer keypunch operators, for instance.

But OPM says that the government still has a higher ratio of supervisors to employes when compared with industry.

Studies by OPM and the President's Private Sector Survey on Cost Control (the Grace Commission) have concluded that the government has many more employes who are overgraded and overpaid for the work they do than does the private sector.

An OPM study last year said 30 percent of all federal workers in the Washington area were overpaid, and that its spot check in the field indicated that 14 percent of all jobs were overgraded.

The Grace Commission said that a study of five major firms (which it did not name) showed that they ran a much leaner operation with fewer high-paid employes.

GAO, which monitors the executive branch for Congress, said it supports grade control and efforts at managing salaries and jobs but is "not convinced that the studies cited provide a sound basis" for concluding that the government should get rid of 40,000 of its mid-level jobs.

GAO, in very diplomatic language, said the Grace Commission report on position management in industry contains data that "may not be representative of the private sector as a whole." For instance, GAO said the Grace Commission report did not say how big the firms it studied were, did not say what industry they were drawn from or define the kind of nationwide firm that could fairly be compared with the government.

The congressional agency also said that OPM had never stated how many GS 11 through 15 employes it thought the government should have, but simply contended that there were too many.

Several major federal operations -- Defense, Justice and the Federal Aviation Administration -- have been exempted in whole or in part from the job-cutting exercise. Others are asking for partial exemption, and the GAO report may help them.