Without a press release from Apple (AAPL) crowing about their Christmas sales, we’re forced to rely on data from a mobile analytics firm and tweets from a Google (GOOG) senior vice president to make some rough guesses.

Here’s what we know:

• According to Flurry Analytics — which claims it can detect “roughly 100%” of all new smartphone and tablet activations by monitoring its clients’ 140,000 apps — a total of 6.8 million iOS and Android devices got activated around the world on Christmas Day, a 353% increase from Christmas 2010.
• According to Google’s Andy Rubin, who likes to release data material to his company on Twitter, a total of 3.7 million Android devices were activated on Christmas Eve and Christmas Day. (Via TechCrunch.)
• A week earlier, Rubin had tweeted that daily activations of Android devices now exceed 700,000. UPDATE: In the past, Christmas Eve activations have been about 50% higher than normal.
• If we assume (based on our update) that at least 1.1 million Android devices were activated on Christmas Eve, the number activated on Christmas Day could not exceed 2.6 million.
• If we can trust Flurry’s and Rubin’s numbers, that suggests at least 4.2 million iOS devices were activated on Dec. 25.
• Given that Android phones outsold iPhones by 2:1 worldwide in the second quarter of 2011 and more than 3:1 in the third quarter, it’s likely that if Apple did beat Android in the Christmas bake-off by more than a million and a half units, sales of the iPad and iPod touch probably accounted for the difference.

But this is just guesswork, and it doesn’t take into account sales of Amazon’s (AMZN) Kindle Fire, which wouldn’t show up in Google’s accounting of Android activations. We’ll get hard numbers in January when Apple reports its earnings for its first fiscal quarter of 2012, which ends Saturday.