Perhaps ironically, the Federal government's bureaucratic approach to equitable pay is why public-sector jobs are not competitive in the United States. Why would a talented person work for a fraction of the pay that the private sector offers?
Of course the federal government might legitimately need higher average skill levels than the rest of the economy does. I wonder how that ratio, $76,810 / $51,960, compares to the ratio in other countries, particularly those with a reputation for being well-governed.
That's a useless comparison, you can't just take the mean over all workers like that. The Federal government employs a larger percentage of skilled workers, and a smaller percentage of burger-flippers, than the workforce as a whole.