1 - The 873,00 jobs added is a BLS estimate. Not based on any hard employment data.
2 - To arrive at the 7.8% rate the administration went back and bumped the July employment up by 40,000 and bumped the August employment up by 46,000.
Jack Welch Refuses to Back Down on Unemployment Numbers in Fiery Exchange With Chris Matthews
“We had 600,000 government jobs added in the last two months. We had 873,00 jobs by a household survey — which is a total estimate — from 50,000 phone calls. Of those, 600,000 were temporary workers. Chris, these numbers are all a series of assumptions. Tons of assumptions. And it just seems somewhat coincidental that the month before the election, the numbers go one-tenth of a point below where the president started. Although, I don’t see anything in the economy that says these surges are true.”
U.S. unemployment rate falls to 7.8 percent
"In addition, job gains were revised upward by 40,000 for July (to 181,000) and by 46,000 for August (to 142,000), casting a slightly rosier light on what had been perceived as a summer slump."
By the way...did you happen to check where your “Jack Welch” link goes to? ;-)