NEW YORK >> They’re the $10 million men and women.

Propelled by a soaring stock market, the median pay package for a CEO rose above eight figures for the first time last year. The head of a typical large public company earned a record $10.5 million, an increase of 8.8 percent from $9.6 million in 2012, according to an Associated Press/Equilar pay study.

Last year was the fourth straight that CEO compensation rose following a decline during the Great Recession. The median CEO pay package climbed more than 50 percent over that stretch. A chief executive now makes about 257 times the average worker’s salary, up sharply from 181 times in 2009.

The best paid CEO last year led an oilfield-services company. The highest paid female CEO was Carol Meyrowitz of discount retail giant TJX, owner of TJ Maxx and Marshall’s. And the head of Monster Beverage got a monster of a raise.

Over the last several years, companies’ boards of directors have tweaked executive compensation to answer critics’ calls for CEO pay to be more attuned to performance. They’ve cut back on stock options and cash bonuses, which were criticized for rewarding executives even when a company did poorly. Boards of directors have placed more emphasis on paying CEOs in stock instead of cash and stock options.

The change became a boon for CEOs last year because of a surge in stocks that drove the Standard & Poor’s 500 index up 30 percent. The stock component of pay packages rose 17 percent to $4.5 million.

“Companies have been happy with their CEOs’ performance and the stock market has provided a big boost,” says Gary Hewitt, director of research at GMI Ratings, a corporate governance research firm. “But we are still dealing with a situation where CEO compensation has spun out of control and CEOs are being paid extraordinary levels for their work.”

The highest paid CEO was Anthony Petrello of oilfield-services company Nabors Industries, who made $68.3 million in 2013. Petrello’s pay ballooned as a result of a $60 million lump sum that the company paid him to buy out his old contract.

Nabors Industries did not respond to calls from The Associated Press seeking comment.

Petrello was one of a handful of chief executives who received a one-time boost in pay because boards of directors decided to re-negotiate CEO contracts under pressure from shareholders. Freeport-McMoRan Copper & Gold CEO Richard Adkerson also received a one-time payment of $36.7 million to renegotiate his contract. His total pay, $55.3 million, made him the third-highest paid CEO last year.

The second-highest paid CEO among companies in the S&P 500 was Leslie Moonves of CBS. Moonves’ total compensation rose 9 percent to $65.6 million in 2013, a year when the company’s stock rose nearly 70 percent.

“CBS’s share appreciation was not only the highest among major media companies, it was near the top of the entire S&P 500,” CBS said in a statement. “Mr. Moonves’ compensation is reflective of his continued strong leadership.”

Media industry CEOs were, once again, paid handsomely. Viacom’s Philippe Dauman made $37.2 million while Walt Disney’s Robert Iger made $34.3 million. Time Warner CEO Jeffrey Bewkes earned $32.5 million.

The industry with the biggest pay bump was banking. The median pay of a Wall Street CEO rose by 22 percent last year, on top of a 22 percent increase the year before. BlackRock chief Larry Fink made the most, $22.9 million. Kenneth Chenault of American Express ranked second with earnings of $21.7 million.

Like stock compensation, performance cash bonuses jumped last year as a result of the surging stock market and higher corporate profits. Earnings per share of the S&P 500 rose 5.3 percent in 2013, according to FactSet. That resulted in an average cash bonus of $1.9 million, a jump of 12.9 percent from the prior year.

More than two-thirds of CEOs at S&P 500 companies received a raise last year, according to the AP/Equilar study, because of the bigger profits and higher stock prices.

CEO pay remains a divisive issue in the U.S. Large investors and boards of directors argue that they need to offer big pay packages to attract talented men and women who can run multibillion-dollar businesses.

“If you have a good CEO at a company, the wealth he might generate for shareholders could be in the billions,” says Dan Mitchell, a senior fellow at the Cato Institute, a libertarian think tank. “It might be worth paying these guys millions for doing this type of work.”

CEOs are still getting much bigger raises than the average U.S. worker.

The 8.8 percent increase in total pay that CEOs got last year dwarfed the average raise U.S. workers received. The Bureau of Labor Statistics said average weekly wages for U.S. workers rose 1.3 percent in 2013. At that rate an employee would have to work 257 years to make what a typical S&P 500 CEO makes in a year.

“There’s this unbalanced approach, where there’s all this energy put into how to reward executives, but little energy being put into ensuring the rest of the workforce is engaged, productive and paid appropriately,” says Richard Clayton, research director at Change to Win Investment Group, which works with labor union-affiliated pension funds.

Investors have become increasingly vocal about executive pay since the recession. This has led to an increasing number of public spats between boards of directors, who propose pay packages, and shareholders, who own the company. These fights become public during “say on pay” votes, when shareholders have an opportunity to show they approve or don’t approve of pay packages. Votes are non-binding, but companies sometimes act when there is clear disapproval from shareholders.

Petrello was the best-paid CEO largely because the board of directors of Nabors Industries’ wanted to end his previous contract. Under that contract, Petrello could have been owed huge cash bonuses, and the company could have paid out tens of millions of dollars if he were to die or become disabled. The board changed his contract following “say on pay” votes in 2012 and 2013 that showed shareholders were unhappy with how Nabors paid its executives.

There have been other signs of shareholder concern about CEO pay. This month, 75 percent of Chipotle Mexican Grill shareholders voted against a proposed pay package for co-CEOs Steve Ells and Montgomery Moran. Ells earned $25.1 million in 2013 while Moran earned $24.3 million, a 27 percent rise in compensation for each. Chipotle spent $49.5 million on CEO pay last year, the fourth highest in the S&P 500.

“Companies are now taking the time to think through their pay practices and are talking more with shareholders,” says Hewitt of GMI Ratings. “There’s still a long way to go but pay practices are getting better.”

To calculate a CEO’s pay package, the AP and Equilar looked at salary as well as perks, bonuses and stock and option awards, using the regulatory filings that companies file each year. Equilar looked at data from 337 companies that had filed their proxies by April 30. It includes CEOs who have been at the company for two years.

One prominent name not included in the data was Oracle CEO Larry Ellison, who is typically one of the best paid CEOs in the country.

Oracle files its salary paperwork later in the year, so Ellison was excluded in the 2013 survey data. He was awarded $76.9 million in stock options for Oracle’s fiscal year ending May 2013, according to proxy filings.

Among other findings:

— Female CEOs had a median pay package worth more than their male counterparts, $11.7 million versus $10.5 million for males. However, there were only 12 female CEOs in the AP/Equilar study compared with 325 male CEOs that were polled.

— The CEO who got the biggest bump in compensation from 2012 to 2013 was Rodney Sacks, the CEO of Monster Beverage. Sacks earned $6.22 million last year, an increase of 679 percent. Monster’s board of directors awarded Sacks $5.3 million in stock options to supplement his $550,000 salary and $300,000 cash bonus.