n June, the federal government spent $1,047 in stimulus money to buy a rider mower from the Toro Company to cut the grass at the Fayetteville National Cemetery in Arkansas. Now, a report on the government’s stimulus Web site improbably claims that that single lawn mower sale helped save or create 50 jobs.

Earlier that same month, when Chrysler got a $52.9 million stimulus order for new cars for the government, the struggling automaker claimed that the money did not save a single job.

Those two extremes illustrate the difficulties in trying to figure out just how many jobs can be attributed to the $787 billion stimulus program. Last week the Obama administration released reports from more than 130,000 recipients of stimulus money in which they claimed to have saved or created more than 640,000 jobs, but a review of those reports shows that some are simply wrong, while others contain apparently subjective estimates.

A spokesman for Toro said the 50-job figure was not accurate, making it one of a number of reports with apparent errors. In many other cases, though, claims of jobs created are simply judgment calls, often by recipients trying to follow complex federal guidelines.

More than half of all the jobs claimed — 325,000 — were those of educators that states said they were able to keep on the job thanks to stimulus aid. But some school districts said that they might not have actually laid off teachers without the stimulus money. Many Head Start programs reported saving the jobs of employees who in fact had simply been given raises with stimulus money — putting their claims of 8,000 jobs under review. Many states and private companies seem to have used different criteria when estimating whether stimulus aid had saved jobs or not, and when calculating full-time positions.

The reports, for all their shortcomings, do provide the first check of how the stimulus bill is working so far. They suggest that more than half the jobs claimed so far are in the public sector — despite the fact that President Obama has said that he expects only 10 percent of stimulus jobs to be in the public sector.

A computer analysis by The New York Times of government reports showed that at least 30,000 of the jobs were being claimed in highway, street and bridge construction, and at least 14,000 were with transit agencies. The analysis found that the $5 billion push to weatherize homes, which was delayed in many states because of uncertainty over how much money the workers should be paid, had yielded only a little over 5,000 jobs so far, nearly half of which were in Ohio.

The reports, which have been posted on the government’s Web site, www.recovery.gov, provide unusual transparency for government spending, showing how much money each contractor has received and where the work has been done, right down to the ZIP code. But they seem to raise as many questions as they answer.

The reports make no distinction between a newly created job and a saved job. They do not specify whether a job is in the public or private sector. And descriptions of the work vary in detail, making it difficult to categorize some work and to compare how various programs are doing.

Elizabeth A. Oxhorn, a White House spokeswoman on the stimulus, said that some of the data, which officials had always warned would contain errors, was rough because it was posted online quickly after it was received, in an effort at transparency. The jobs numbers would likely be adjusted both upward and downward, she said.

“As with all economic indicators — even statistics that have been around for decades — the brand-new measures posted last week are subject to subsequent revision, as further analysis clarifies and improves the data,” she said.

Although President Obama initially said that 90 percent of the jobs created by the stimulus program would be in the private sector, the data suggests that well over half of the jobs claimed so far have been in the public sector. They include the 325,000 jobs in education, including teachers, administrators and support staff, as well as many of the 73,000 other jobs paid for with education grants, many of which were in public safety.

Republicans, who overwhelmingly opposed the stimulus program, said the figures showed that the program was failing in its stated mission of creating a large number of private sector jobs. Administration officials said that they believed the stimulus program was still on track to save or create 3.5 million jobs by the end of next year, and that in the end 90 percent of the jobs would be in the private sector.

The job data can be loose. Philip Mattera, the research director for Good Jobs First, a labor-oriented research organization in Washington, examined the reports and found 2,464 projects that claimed no jobs at all, even though more than half of the work had been done, at a cost of more than $1 billion. That suggests that many projects have undercounted job creation.

But the dogs that do not bark are not receiving as much attention as those that do. Onvia, a Seattle company that tracks government spending at the federal, state and local levels, noted that the data is only as good as the recipients that have reported it, and pointed out a number of questionable reports.

In one, a Kentucky shoe store reported that it had created nine jobs with an $890 order for work boots. In another, a $7,960 contract for a “Basketball System Replacement” in Ohio claimed three jobs.

It was not clear what positions they played.