RALEIGH — People over the age of 65 are struggling to live in North Carolina, according to a new analysis that concludes median incomes and Social Security do not cover seniors’ cost of living in the state.

The Elder Economic Security Standard Index was developed by a Washington, D.C.-based group called Wider Opportunities for Woman and the Gerontology Institute at University of Massachusetts Boston. A single person over the age of 65 who rents a home needs almost $21,000 annually to live independently, according to the index.

“We’ve become a state where people can’t afford to get old,” said Jim Moore, president of the nonprofit group, the North Carolina Alliance for Retired Americans.

One woman told him at a news conference Tuesday that she sold her home and moved in with her son and daughter-in-law. After paying a few basics, such as health care, she has about $220 a month for other expenses. “And there are so many others,” he said. “ ... It’s hard to believe so many are getting by on just a couple of hundred dollars a month.”

The index covers a basic budget: housing, food, health care, transportation and miscellaneous, which includes personal items. Orange County has the highest index for a senior with a mortgage (almost $30,000), while Surry County has the lowest (almost $23,000).

But that doesn’t mean it’s easier to live in one county over another, said Maggie Flowers, interim director of the elder economic security initiative at WOW. “Just because the cost of living is lower doesn’t mean incomes are higher,” she said Tuesday. “So people could still be struggling even if the cost of living is lower.”

Not surprisingly, housing and health care account for more than half the statewide average of living in North Carolina. For some people, health care accounts for almost a quarter of expenses, Flowers said.

Ninety-eight percent of those over 65 living in North Carolina receive Social Security, which is the sole source of income for almost one-third of that population, the index says. “Median incomes do not cover the cost of the index, and Social Security payments do not cover the index,” Flowers said.

The alliance will give the report to elected officials, whom Moore hopes read it and learn “what it’s really like to live in this state, to be a senior, be retired, be elderly.” He also hopes seniors will learn and take advantage of the federal and state benefits available to them.

WOW plans to release a state-by-state comparison of the cost of living for seniors later this week.