For years, we’ve been told that low incomes make most elderly vulnerable. The reality is that this describes only a minority of the very poor and very old, often single women.

It’s routinely said that the elderly’s median household income — the income of the household exactly in the middle — is lower than that of the non-elderly population. That’s true. In 2012, it was $33,848 compared with $57,353 for the under-65 population. We’re then supposed to imagine that the median income accurately reflects the lot of most elderly. That’s not true.

For starters, the median almost certainly understates the actual income of many older Americans. Writing recently in the Wall Street Journal, Andrew Biggs and Sylvester Schieber argued that withdrawals from individual retirement accounts (IRAs) and 401(k) plans are systematically under-counted by the government’s Current Population Survey (CPS), which estimates median incomes. In 2008, for example, the CPS captured only $5.6 billion in IRA income, when retirees paid taxes on $111 billion of IRA income as reported to the Internal Revenue Service.