ST. PAUL — Enrollment for health coverage through Minnesota’s insurance exchange more than doubled from its first month to its second, according to figures released Wednesday.

With the Jan. 1 start of coverage under the federal health law now less than a month away, officials at MNsure said 24,586 individual Minnesotans have completed the enrollment process. That translates to insurance coverage for an estimated 71,579 people, since many individual signups are for family plans.

The rate of sign-ups spiked from October, when 10,940 people signed up, to November, when 13,646 people signed up.

Of the nearly 25,000 signed up so far, more than three-quarters are on public insurance plans: MinnesotaCare or Medical Assistance, the state’s Medicaid program. The remaining signups — 4,478 — have been for private insurance.

So far, of those who signed up for private insurance, 55 percent are women and the median age is 50. Health care officials have said the federal overhaul needs large numbers of younger enrollees in order to succeed, but MNsure Executive Director April Todd-Malmlov said the agency sees younger enrollees as more likely to procrastinate and expect more to sign up in the days before the Dec. 23 deadline to get coverage immediately on Jan. 1.