On Wednesday morning, CNN published a new poll evaluating the state of the Democratic presidential primary fight. Former vice president Joe Biden had surged back into a healthy lead, enjoying a double-digit margin over Sens. Elizabeth Warren (D-Mass.) and Bernie Sanders (I-Vt.), who are jockeying for second. That was important news for Biden’s campaign, which had seemed to stall in the polls as Warren surged.

But then Thursday morning dawned. In Quinnipiac University’s new poll, Biden wasn’t doing quite as well. CNN and polling partner SSRS had Biden scooping up 34 percent of the vote among possible primary voters; Quinnipiac had him at 21 percent. What’s more, Quinnipiac showed Warren with the lead — beating Biden by seven points while CNN had her down 15.

Obviously, both of those things can’t be true. So which one is?

Before we try to answer that question, we’ll note that the difference between Biden and Warren in the two polls was represented across a range of demographic groups. Quinnpiac had Biden up three points with men and down 11 with women; CNN had Biden up 19 with men and 13 with women. He does better with men in both polls but much better with both groups in CNN’s.

There are big differences, though. Quinnipiac’s “very liberal” respondents gave Warren a massive edge. She also led by nearly 20 among “somewhat” liberal respondents. CNN’s “liberal” group, however, had Biden and Warren about tied.

One factor in the difference between the two polls is the margin of sampling error. We dug into this a bit on Wednesday, looking at the shifts in views of impeachment. In the Quinnipiac poll, the margin of error was 4.6 points. In CNN’s, it was 5.8 points. Meaning that the top-line numbers (the 34 percent that CNN had for Biden, for example) really sit in the middle of a range of possibilities (something like 28 to 40 percent in the Biden example).

The top five results in each poll can be depicted like this, with the points representing the reported poll result and the bars representing the range of the margin of error.

You’ll notice that the Warren result in each poll — 28 percent in Quinnipiac and 19 in CNN’s — is less significant than it might seem. The bottom of the Quinnipiac bar is lower than the top of the CNN bar, meaning that perhaps Warren’s real support, so to speak, was around 24 percent and, therefore, within each poll’s margin of error.

But we can’t say the same of the Biden results. The difference between the two polls is outside the margin of error. So what gives?

It’s hard to say. The polls were taken at slightly different times (Oct. 17 to Oct. 20 for CNN and Oct. 17 to Oct. 21 for Quinnipiac) and asked slightly different questions. Each pollster weighted its responses differently, which can make a big difference. Margin of error captures one part of what might explain the variation in a poll, but it doesn’t capture everything.

Update: The Times also points out that the CNN poll asked for views of candidates prior to asking the so-called “horse race” question, which might have some effect in a race where views are fluid.

That’s why most pollsters consider poll averages more reliable. Poll averages help smooth out some of the jumps and aberrations that can be seen in single polls, and tend to give a more accurate presentation of what’s happening. In 2016, for example, the RealClearPolitics average of polls going into Election Day had Hillary Clinton leading Donald Trump by 3.2 points. She won the popular vote by 2.1 points.

The Post’s average of polls has Biden with a three-point edge at the moment, leading Warren 28 to 25. Our average (which includes both the Quinnipiac and CNN polls) has Warren performing about as well as Quinnipiac’s poll but Biden somewhere in the middle of the two new results. (Sanders is about even in all three cases.)

It’s certainly possible that Quinnipiac’s result is something of an outlier to Warren’s benefit and CNN’s an outlier to Biden’s.

If we compare the polls to the RealClearPolitics average over time, we see that the results match the theory above. CNN’s poll shows Biden doing better than the average, while Quinnipiac’s shows a downward turn that matches the average. Quinnipiac also shows a downturn for Warren, matching RCP, but CNN’s support for Warren is closer to the average value.

There’s an enormous amount of political significance in these differences, if not electoral. Both campaigns can point to recent polls showing them with the lead — or trailing. Both results might convince some set of voters that their preferred candidate is the more electable one.

The reality, as usual, is more complex than that. We can say with confidence that Warren recently matched Biden’s support in the RCP average, but he has regained his advantage. Even with two new polls in hand, however, it’s complicated to say much more than that.