Math majors, rejoice. Businesses are going to need tens of thousands of you in the coming years as companies grapple with a growing mountain of data.

Data is a vital raw material of the information economy, much as coal and iron ore were in the Industrial Revolution. But the business world is just beginning to learn how to process it all.

The current data surge is coming from sophisticated computer tracking of shipments, sales, suppliers and customers, as well as e-mail, Web traffic and social network comments. The quantity of business data doubles every 1.2 years, by one estimate.

Mining and analyzing these big new data sets can open the door to a new wave of innovation, accelerating productivity and economic growth. Some economists, academics and business executives see an opportunity to move beyond the payoff of the first stage of the Internet, which combined computing and low-cost communications to automate all kinds of commercial transactions.

The next stage, they say, will exploit Internet-scale data sets to discover new businesses and predict consumer behavior and market shifts.

Others are skeptical of the “big data” thesis. They see limited potential beyond a few marquee examples, like Google in Internet search and online advertising.

The McKinsey Global Institute, the research arm of the consulting firm, is coming down on the side of the optimists in a lengthy study to be published on Friday. The report, based on nine months of work is “Big Data: The Next Frontier for Innovation, Competition and Productivity.” It makes estimates of the potential benefits from deploying data-harvesting technologies and skills.

The McKinsey research unit, for example, says the value to the health care system in the United States could be $300 billion a year, and that American retailers could increase their operating profit margins by 60 percent.

But the study also identifies challenges. One hurdle is a talent and skills gap. The United States alone, McKinsey projects, will need 140,000 to 190,000 more people with “deep analytical” skills, typically experts in statistical methods and data-analysis technologies.

McKinsey says the nation will also need 1.5 million more data-literate managers, whether retrained or hired. The report points to the need for a sweeping change in business to adapt a new way of managing and making decisions that relies more on data analysis. Managers, according to the McKinsey researchers, must grasp the principles of data analytics and be able to ask the right questions.

“Every manager will really have to understand something about statistics and experimental design going forward,” said Michael Chui, a senior fellow at the McKinsey Global Institute.

The study estimates that the use of personal location data could save consumers worldwide more than $600 billion annually by 2020. Computers determine users’ whereabouts by tracking their mobile devices, like cellphones. The study cites smartphone location services including Foursquare and Loopt, for locating friends, and ones for finding nearby stores and restaurants.

But the biggest single consumer benefit, the study says, is going to come from time and fuel savings from location-based services — tapping into real-time traffic and weather data — that help drivers avoid congestion and suggest alternative routes. The location tracking, McKinsey says, will work either from drivers’ mobile phones or GPS systems in cars.

Personal location data raises privacy concerns. Both Google and Apple, for example, have faced protests recently for collecting location data without most users’ knowledge. The McKinsey report says such services should require that users have a choice and opt-in to use them, but the report does not deal with privacy issues in detail.

The sizable projected payoff for consumers, some experts say, is not surprising. “Much of the benefit of innovation always flows to consumers,” said Martin Baily, an economist at the Brookings Institution, who was an adviser on the study. “So the large consumer surplus makes sense.”

In health care, the biggest slice of the $300 billion gain is expected to come from more effectively using data to inform treatment decisions. The tools include clinical decision support to assist doctors, and comparative effectiveness research to make more informed decisions on drug therapy.

For example, the Department of Veterans Affairs and Kaiser Permanente save millions of dollars a year in treating many patients with high cholesterol with generic statins instead of branded statins, like Lipitor. But such tailored treatments require electronic health records for tracking results, and most of the nation’s hospitals and physicians still use paper records.

Skeptics say the economic payoff from harnessing big data sets is mostly wishful thinking so far. The nation’s technology-assisted increase in productivity began in 1995 and continued through 2004, having trailed off since, despite investments in data analytics.

“The big dividend mostly hasn’t arrived yet,” said Tyler Cowen, an economist at George Mason University.

The McKinsey authors say that the big-data trend is just getting under way. It will take years, they say, before the gains show up in the economic statistics, just as it did for computers to prove they were engines of productivity.

“But it’s clear that data is an important factor of production now,” said James Manyika, a director of the McKinsey Global Institute.