On a recent CNBC show, Maria Bartiromo asked how I could possibly not agree that typical CEO pay was excessive, since the average CEO earns 431 times the salary of an average production worker.

In my typically diplomatic style, I said that was untrue, a bad case of comparing apples to oranges.

In past columns, I explained what is terribly wrong with these so-called production-worker wage figures in “Unreal Wages” and what is wrong with CEO pay estimates in “CEO Pay Parade.” But this alleged ratio of CEO pay to average wages is much worse than its separate parts. Dividing one bogus statistic by another bogus statistic compounds the errors.

Couldn’t some journalist take the trouble to at least ask where these numbers come from? The statistic about CEOs’ earning 431 times as much as production workers seemed to come from the other guest on the CNBC show, a representative of the American Federation of State, County and Municipal Employees (AFSCME). It actually came from a Dec. 6 press release from the AFL-CIO, which wisely neglected to mention the actual source — a polemical pamphlet on “Executive Excess” from United for a Fair Economy and the Institute for Policy Studies.

That pamphlet claims executive compensation among 367 corporations rose to $11.8 million last year. Ironically, the AFSCME press release said, “Chief executive officers at big U.S. companies were awarded $5.74 million on average last year, 30.2 percent more than in 2003, according to the Corporate Library.”

But dividing $5.74 billion by 431 would leave average workers earning $13,318, which is too obviously ridiculous. The pamphlet instead claims “the average production worker made $27,460 in 2004.” Also ridiculous and also ironic: Not one of the well-paid members of the AFSCME union is included in that so-called average. What is included is the weekly wages of part-time workers, which were then foolishly multiplied by 52 weeks.

There are 15 million “production workers” in retailing, who worked an average of 30.7 hours a week in 2004, and 12.5 million in leisure and hospitality, who worked an average of 25.7 hours. If CEOs worked 26 to 31 hours a week, then it might seem fairer to compare their weekly salaries with these. But it would still be ridiculous.

Any pay figures for top executives at just a few hundred top firms are strikingly exceptional — not average — and largely an artifact of including stock options in the year during which they are exercised.

AFSCME claims CEO pay is excessive at just five companies, simply because those five CEOs earned more than the average among the S&P 500 last year. But somebody is always above any average, and top-paid CEOs are rarely the same people from one year to the next.

All but one of these supposedly overpaid CEOs work at financial firms — Merrill Lynch, Bank of America, US Bancorp and Countrywide Financial. Most people in such firms are paid much more than average, not just the executives. The average employee of Merrill Lynch does not earn $27,460, which is just part of what I meant about comparing apples with oranges.

Any survey of 375 or 500 companies is the cream of the crop, not an average of executive pay. The Washington Post reported in November that “an AFL-CIO affiliate … launched an online database of more than 60,000 companies, listing information about their executive compensation.” Average CEO pay among even the top 10,000 would surely be in the low six figures, and not more than 20 times what experienced employees earn in those same companies.

There are nine or 10 outfits, mostly magazines and newspapers, claiming to know how to estimate CEO compensation among only the biggest public corporations. No two of these surveys sample the same companies, use the same estimating techniques or come up with the same numbers — even for the same executives. Stocks options are never compensation for a single year, for example, yet that is how all surveys record them. USA Today double-counts such options for dramatic effect, including an estimate of the potential value of options in the year they are granted and also the actual value of those same options if and when they are exercised.

Numerous gullible journalists made it far too easy for this government employees’ union to grab self-aggrandizing attention by telling contradictory fables about CEO pay. “Shareholders, too, are increasingly restless,” wrote Wall Street Journal writer Joann Lubli. “Last week, a pension fund for the American Federation of State, County and Municipal Employees, the large public-employee union, said it has submitted shareholder resolutions for annual meetings at 26 companies next spring that call for nonbinding votes by shareholders on executive compensation.”

Actually, AFSCME submitted seven shareholder resolutions, ranging from frivolous to dangerous. Only two of those seven proposals, affecting only seven of the 26 firms, relate to holding down executive compensation. The union’s bungled rhetoric about CEO pay was obvious grandstanding to get free publicity.

Pension fund managers pretend they represent shareholders in general, or at least those pensioners who have no choice but to place their fate in the hands of notoriously politicized monopolies like the California Employees’ Retirement System. In reality, union leaders and pension managers represent themselves — their own personal and political interests.

Government workers who have their retirement funds at stake must want the businesses they invest in to do well. They cannot possibly believe that people who run any part of their unions also know how to run many profitable businesses from a distance. Union members are not that naive, but business journalists are another matter.