(CNN) Former South Bend, Indiana Mayor Pete Buttigieg, former Vice President Joe Biden, Vermont Sen. Bernie Sanders and Massachusetts Sen. Elizabeth Warren lead the field in the New Hampshire Democratic primary race, all within the top tier, according to a new poll from Monmouth University out Thursday.

Buttigieg receives 20% of support among likely New Hampshire voters, Biden with 19%, Sanders 18%, and Warren 15%, the poll's margin of error of roughly 5 points.

Polling in New Hampshire this cycle has been quite volatile. Although all recent high-quality polls in New Hampshire show the same four candidates near the top and in double digits, there has been significant variation in the order in which those candidates finish. A CBS News/YouGov poll released Sunday found Sanders and Biden ahead of Warren and Buttigieg, while a MassINC/WBUR poll last month put Buttigieg, Biden and Sanders at the top, with Warren a bit behind.

In the Monmouth poll, under the 10% mark, Minnesota Sen. Amy Klobuchar garners 6% support, Hawaii Rep. Tulsi Gabbard and businessman Tom Steyer both land at 4% and businessman Andrew Yang receives 3%. No other candidate is above 2% in the poll.

The qualification deadline for next week's CNN/Des Moines Register debate is Friday. Buttigieg, Biden, Sanders, Warren and Klobuchar have already qualified for the debate. Monmouth provided no other candidate with a qualifying poll.

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